Scientific method Essay Example for Free

Scientific method Essay Outline and illustrate three characteristics of sense-data. (15 marks) Anticipate the following characteristics: †¢ We are immediately/directly acquainted with sense-data, (from which we infer a mindindependent reality). †¢ Sense-data are (usually) mental or mind-dependent. †¢ Sense-data exist only as they are perceived. †¢ Reports regarding sense-data are incorrigible. †¢ Sense-data are nothing other than how they appear – they have no hidden depths. †¢ The sense-data I experience will vary according to the conditions in which I perceive an object. †¢ Sense-data, unlike physical objects, can have indeterminate process. †¢ Sense-data and physical objects/distinguishing sense-data. Illustrate examples are likely to differ depending on the points being made and can be drawn from various sources: Illusions and delusions (e. g. bent sticks, mirage, hallucinations), perceptual relativity (the real shape of the coin, the real properties of the table), phenomenology (apparent and real speckled hens) or time-lag arguments (seeing the ‘sun’) that distinguish between the way the world appears and the way it is. Consider the claim that the weaknesses of representative realism outweigh its strengths. (30 marks) Knowledge and Understanding Anticipate the following outline of representative realism: There is a material reality independent of our perception of it – an external world – from which experience originates. But our perception of material objects is mediated via ‘ a veil of perception’. Our immediate awareness is of an ‘internal’ non-material something – ‘ideas’ or sense-data – that we take as representative of mind independent external reality. The claim that there is an external world is a hypothesis. Interpretation, Analysis and Application Possible strengths †¢ Unlike common sense, representative realism can account for illusions/hallucinations by proposing we experience ideas/sense-data. †¢ Representative Realism gets the epistemological project right: I have to start from my own ‘experience’ and work outward to an external world. †¢ Representative Realism acknowledges the scientific claim that mind-independent reality is not as it appears to us (and the primary/secondary qualities distinction might be used here to articulate this point.) †¢ Representative realism acknowledges a distinction between appearance and reality but it is able to counter scepticism: it is reasonable to suppose that there is a mindindependent reality that impinges upon me in systematic ways, not subject to will, which my experience ‘represents’ in ways similar to your experience. Possible weaknesses †¢ Representative Realism is incompatible with Empiricism because it makes claims about mind-independent reality that transcend any possible experience: it makes empty assertions devoid of empirical consequences (e.g. ‘a something we know not what’); it illegitimately draws inferences from familiar experience (e. g. observations of casual relations) to support judgements regarding a reality that ‘must be strange’ (Russell). †¢ The apparatus employed by representative realism cannot avoid scepticism: a veil of perception intermediate between object and perceiver opens up an unbridgeable gap. †¢ Representative Realism (at least in its ‘pure’ empiricist form) does not have the resources to escape solipsism. †¢ The scientific appearance/reality distinction need not have any exceptional ‘philosophical significance regarding what there is; it just regulates what counts as relevant/irrelevant when scientists do science (c. f. demarcation issues like ‘Are we doing psychology or sociology? ’ ‘Is that a philosophical point of history? ’). †¢ A candidate might compare representative realism with other positions (e. g. idealism) just as long as the comparison highlights possible strengths and weaknesses of representative realism. †¢ Appeals to Occam’s Razor. Both direct realism and idealism are ontologically parsimonious contra representative realism. Assessment and Evaluation A candidate could argue for the following conclusions: †¢ The weaknesses outweigh the strengths †¢ The strengths outweigh the weaknesses †¢ The strengths and weaknesses balance out, more or less. †¢ Drawing out the implications of ‘something we know not what’ as Berkeley was to do. †¢ Support of direct realism e. g. exceptions can be allowed if they can be explained, correction by other senses. †¢ Presuppositions of recognising deceptions, †¢ Reid’s criticism of phenomenal variability – we can explain and predict. †¢ External world seen as hypothetical, but is this like a scientific hypothesis? Verification issues. †¢ How could we have the concept of a representation if we are only aware of representations. Analysis of how the concept works. †¢ If we cannot know physical objects, then neither can we know their causal powers. †¢ The external world could never be more than a probability. But how do we do the calculations needed for such a claim?

Concurrent Processes In Operating Systems

Concurrent Processes In Operating Systems The programming technique, to use interrupts to simulate the concurrent execution of several programs on Atlas computers was known as multiprogramming. It was pioneered by Tom Kilburn and David Howarth. Multiprogramming in early days was done using assembly level language. Slightest mistake in programs could make program unpredictable hence testing them was difficult also the assembly level language had no conceptual foundation. Operating systems designed using this multiprogramming techniques grew very huge and unpredictable their designers spoke about software crisis. This created an urgent research and development need for concurrent programming techniques. Computer scientists took the first step towards understanding the issues related to concurrent programming during mid 1960s, they discovered fundamental concepts, expressed them by programming notation, included them in programming languages and used these languages to write the model operating systems. These same concepts were then applied to any form of parallel computing. Introduction of Concurrent processes in operating systems Processes played a key role in shaping early operating systems. They were generally run in a strictly sequential order. Multiprogramming existed but the processes did not exactly run concurrently instead a time based mechanism was used in which a limited amount of time was given to each process. Even in those days the processors speed was fast enough to give and illusion that the multiple processes were running concurrently. They were called as timesharing or multiprogramming operating systems (November 1961, called CTSS Compatible Time-Sharing System also Multics the predecessors of UNIX developed by MIT) These type operating systems were very popular and were seen as a breakthrough during those times. The major drawback was complexity of the system design which made it difficult to make it more versatile and flexible so that a single all purpose OS could be built. Also the resource sharing done by these processes was primitive or inefficient and it only showed there was a lot of room for research and development. Work on these operating systems made way for concurrent processes. Most of the original concepts related to concurrency were developed during this period. These innovative ideas and concepts went on become the basic principles on which todays operating systems and concurrent applications are designed. (A major project undertaken by IBM in this direction was in 1964 the OS/360 for their new mainframes system 360) To build reliable concurrent processes understanding and developing basic concepts for concurrency was important let us talk about concurrency and some of its basic programming concepts. Concurrency In computer science, concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other. [Wikipedia] Let us consider a real life example a housing project such as the building of a house will require some work to go on in parallel with other works. In principle, a project like building a house does not require any concurrent activity, but a desirable feature of such a project is that the whole task can be completed in shorter time by allowing various sub tasks to be carried out concurrently. There is no reason any painter cannot paint the house from outside (weather permitting!), while the plasterer is busy in the upstairs rooms and the joiner is fitting the kitchen units downstairs. There are however some constraints on concurrency which is possible. The brick layer will normally have to wait until the foundation of the house had been layered before he could begin the task of building the walls. The various tasks involved in such a project can usually be regarded as independent of one another, but the scheduling of the tasks is constrained by notions of a task A must be completed b efore task B can begin A second example is that of a railway network. A number of trains making journeys within a railway network, and by contrast with the previous example, when they start and they end is generally independent of most of the other journeys. Where the journeys interact though is at places where routes cross or use common sections of track for parts of journeys. We can in this example regard the movement of trains as programs in execution, and the sections of track as the resources which these programs may or may not have to share with other programs. Hence the two trains run concurrently in case their routes interact sharing the same resources without interrupting each other similar to concurrent processes in operating systems. So as discussed earlier we understand that processes are important to implement concurrency so let us discuss the process as a concept which will introduce us to the most important concept for concurrency i.e. threads! Fundamental concepts Process A process is a running program; OS keeps track of running programs in form of processes and their data. A process is made of multiple threads. Threads The need to write concurrent applications introduced threads. In other words, threads are processes that share a single address space. Each thread has its own program counter and stack. Threads are often called lightweight processes as N threads have 1 page table, 1 address space and 1 PID while N processes have N page tables, N address spaces and N PIDs. Therefore, a sequence of executing instructions is called a thread that runs independently of other threads and yet can share data with other threads directly. A thread is contained inside a process. There can exist multiple threads within a process that share resources like memory, while different processes do not share these resources. A simple thread example There are two classes defined in this example namely SimpleThread which is a subclass of the Thread class and TwoThreads class. class SimpleThread extends Thread { public SimpleThread(String str) { super(str); } public void run() { for (int i = 0; i { System.out.println(i + + getName()); Try { sleep((int)(Math.random() * 1000)); } catch (InterruptedException e) {} } System.out.println(DONE! + getName()); } } The method SimpleThread() is a constructor which sets the Threads name used later in the program. The action takes place in the run() method which contains a for loop that iterates ten times that displays the iteration number and the name of the Thread, then sleeps for a random interval of up to a second. The TwoThreads class provides a main() method that creates two SimpleThread threads named London and NewYork. class TwoThreads { public static void main (String[] args) { new SimpleThread(London).start(); new SimpleThread(NewYork).start(); } } The main() method also starts each thread immediately following its construction by calling the start() method. Following concepts are mostly used at the thread level and also the issues discussed are encountered while implementing concurrency. Race condition A race condition occurs when multiple processes access and manipulate the same data concurrently, and the outcome of the execution depends on the particular order in which the access takes place.[http://www.topbits.com/race-condition.html] It is not so easy to detect race condition during program execution if it is observed that the value of shared variables is unpredictable, it may be caused because of race condition. In concurrent programming there are more than one legal possible thread executions hence order of thread execution cannot be predicted. Race condition may produce uncertain results. Outcome of race condition may occur after a long time. In order to prevent unpredictable results because of race condition, following methods are used- Mutual exclusion Mutual exclusion (often abbreviated to mutex) algorithms are used in concurrent programming to avoid the simultaneous use of a common resource, such as a global variable, by pieces of computer code called critical sections. (Wikipedia) -Critical Region (CR) A part of code that is always executed under mutual exclusion is called a critical region. Due to this, the compiler instead of the programmer is supposed to check that the resource is neither being used nor referred to outside its critical regions. While programming, critical section resides when semaphores are used. CRs are needed only if the data is writeable. It consists of two parts: Variables: These must be accessed under mutual exclusion. New language statement: It identifies a critical section that has access to variables. There are two processes namely A and B that contain critical regions i.e. the code where shared data is readable and writable. -Semaphores Semaphores are mechanisms which protect critical sections and can be used to implement condition synchronization. Semaphore encapsulates the shared variable and using semaphore, only allowed set of operations can be carried out. It can suspend or wake processes. The two operations performed using semaphores are wait and signal, also known as P and V respectively. When a process performs P operation it notifies semaphore that it wants to use the shared resource, if the semaphore is free the process gains access to the shared variable and semaphore is decremented by one else the process is delayed. If V operation is performed, then the process notifies the semaphore that it has finished using shared variable and semaphore value is incremented by one. By using semaphores, we attempt to avoid other multi-programming problem of Starvation. There are two kinds of Semaphores: Binary semaphores: Control access to a single resource, taking the value of 0 (resource is in use) or 1 (resource is available). Counting semaphores: Control access to multiple resources, thus assuming a range of nonnegative values. -Locks The most common way to implement mutex is using locks. A lock can be either locked or unlocked. The concept is analogues to locks we use in our doors; a person enters the room, locks the door and starts working and leaves the room after finishing the job, if another person wants to enter the room when one person is already inside, he has to wait until the door gets unlocked. Subtasks in a parallel program are often called threads. Smaller, lightweight versions of threads are known as fibres, which are used by some parallel computer architecture and bigger versions are called as processes. Many times threads need to change the value of shared variable, instruction interleaving between programs could be in any order For example, consider the following program: Thread A Thread B 1A -Read variable X 1B Read variable X 2A Increment value of X by 1 2B Increment value of X by 1 3A Write back to variable X 3B Write back to variable X As we can see in the example both the threads are carrying out same steps which are to read the shared variable, increment its value and write back its value to the same variable. It is clear how vital it is to execute these instructions in correct order, for instance if instruction 1A is executed between 1B and 3B it will generate an incorrect output. If locks are used by one thread, another thread cannot read, write the shared variable. Following example explains usage of locks: Thread A Thread B 1A Lock variable X 1B Lock variable X 2A Read variable X 2B Read variable X 3A Increment value of X by 1 3B Increment value of X by 1 4A Write back to variable X 4B Write back to variable X 5A Unlock variable X 5B Unlock variable X Whichever thread locks the variable first, uses that variable exclusively, any other thread will not be able to gain access to shared variable until it is unlocked again. Locks are useful for correct execution but on the other hand they slow down the program. -Monitors A monitor is a mutual exclusion enforcing synchronization construct. Monitors provide more structure than conditional critical regions and can be implemented as efficiently as semaphores. Monitors are supported by a programming language rather than by the operating system. They were introduced in Concurrent Pascal and are used as the synchronization mechanism in the Java language. A monitor consists of code and data. All of the data and some of the code can be private to the monitor, accessible only to the code that is part of the monitor. Monitor has a single lock that must be acquired by the task to execute monitor code i.e. mutual exclusion is provided by making sure that execution of procedures in the same monitor are not overlapped. Active task is the term used for the task which owns the monitor lock. There cannot be more than one active task in the monitor. The monitors lock can be acquired by a task through one of several monitor queues. It gives up the lock either by blocking a condition variable or by returning from a monitor method. A condition variable is a queue or event queue that is part of the monitor. Two monitor methods called as wait and notify can only be accessed by a condition variable queue. The behaviour of a monitor is known by the relative priorities and scheduling of various types of queues. The monitor locks are acquired by the processes in the monitor queues. The queues may be combined in some implementations. The tasks compete for the lock when the monitor lock becomes free. Condition Variable: In order to make sure that processes do not enter a busy waiting state, they should notify some events to each other; this facility is provided by Monitors with the help of condition variables. If a monitor function wants to proceed by making a condition true then it has to wait for the corresponding condition variable. When a process waits, it gives up the lock and is taken out from set of runnable processes. When a process makes condition true then it notifies a waiting process using condition variable. The methods mentioned above are used to prevent race condition but they might result into serious problems like deadlock and starvation let us have a look at these problems one at a time as we go further. Deadlock Deadlock refers to a specific condition where two or more processes are each waiting for each other to release a resource, or more than two processes are waiting for resources in a circular chain. Conditions for deadlock to occur 1] Mutual exclusion: Mutual exclusion means only one process can use a resource at a time. 2] Hold and wait: A process may hold a allocated resource while awaiting assignment of other resource. 3] No pre-emption: A resource can be released voluntarily by the process holding it. One process cannot use resource forcefully held by another process. A process that receives such resources cannot be interrupted until it is finished using the resource. 4] Circular wait: A closed chain of processes exists, such that each process holds a resource required by another process in the chain. Deadlock occurs only when circular wait condition is not resolvable and circular wait is not resolvable if first three conditions hold hence all four conditions taken together constitute necessary and sufficient condition for deadlock. In the diagram above we can see that process P1 holds resource R1 and requests for resource R2 held by process P2 , and process P2 is requesting for resource R1. Methods to handle Deadlock 1. Deadlock prevention Deadlock prevention is to ensure that one of the four necessary conditions for deadlock can never hold in following ways: I1. Mutual exclusion: allocate one resource to only one process at a time. 2. Hold and wait: It requires a process to request and be allocated its resources before it begins its execution, or allow process to request a resource only when process has none. This may lead to low resource utilization. It also may give rise to starvation problem, a process may be held for a long time waiting for all its required resources. The application need to be aware of all the resources it requires, if it needs additional resources it releases all the resources held and then requests for all those it needs. 3. No pre-emption: If a process is holding some resources and requests for another resource held by some other process that cannot be allocated to it, then it releases all the resources currently held. The state of pre-empted resource has to be saved and later restored. 4. Circular wait: To make this condition fail, we can impose a total ordering on all resources types. It is also required that each process requests resources in strict increasing order. Resources from the same resource type have to be requested together. 2. Deadlock avoidance In deadlock avoidance, the system checks if granting a request is safe or not . The system needs additional prior information regarding overall potential use of each resource for each process i.e. maximum requirement of each resource has to be stated in advance by each process. 3. Deadlock detection: It is important to know if there exists a deadlock situation in the system hence an algorithm is needed to periodically check existence deadlock. Recovery from deadlock To recover from deadlock, the process can be terminated or we can pre-empt the resource. In terminating processes method we can terminate all the processes at once or terminate one process and then again check for deadlock. Similarly there are mechanisms like fair scheduling that can be used to avoid starvation of resources. -Fair scheduling Fair scheduling is to allow multiple processes to fairly share the resources. The main idea is to ensure each thread gets equal CPU time and to minimize resource starvation. -First in first out (FIFO) FIFO or First Come, First Served (FCFS) is the simplest scheduling algorithm that queues processes in the order they arrive in the ready queue. Scheduling overhead is minimal because context switches occur only when process terminates and re-organization of the process queue is not required. In this scheme, completion of every process is possible, hence no starvation. -Shortest remaining time With this scheduling scheme, processes with least processing time are arranged as the next process in the queue. To achieve this, prior knowledge of completion time is required. Consider a scenario where a shorter process arrives when another process is running, in this case the current process is stopped and is divided into two parts. This results in additional context switching overhead. -Fixed priority pre-emptive scheduling The operating system gives a fixed priority rank to every process, and the processes are arranged in the ready queue based on their priority this results in higher priority processes interrupting lower priority processes. Waiting and response times are inversely proportional to priority of the process. If there are more high priority processes than low priority processes, it may result into starvation of the latter processes. -Round-robin scheduling In this scheduling algorithm, each process is allotted a fixed time unit. There could be extra overhead if time unit per process allotted is very small. Round robin has better average response time than rest of the scheduling algorithms. There cannot be starvation since processes are queued based on any priority. Also there are some desired Properties of Concurrent Programs; these properties will ensure a reliable concurrent program. There are some characteristics that a concurrent program must possess. They can be either a safety or a liveness property. Safety properties assert that nothing bad will ever happen during a program execution. Examples of safety property are: à ¢Ã¢â€š ¬Ã‚ ¢ Mutual exclusion à ¢Ã¢â€š ¬Ã‚ ¢ No deadlock à ¢Ã¢â€š ¬Ã‚ ¢ Partial correctness A safety property is a condition that is true at all points in the execution of a program. Liveness properties assert that something good will eventually happen during a program execution. Examples include: à ¢Ã¢â€š ¬Ã‚ ¢ Fairness (weak) à ¢Ã¢â€š ¬Ã‚ ¢ Reliable communication à ¢Ã¢â€š ¬Ã‚ ¢ Total correctness Communicating sequential process Communicating sequential process was introduced in a paper written by C. A. R. Hoare in 1978. In this paper he described how various sequential processes could run in parallel irrespective of the processor (i.e. it can be a single core or multi-core processor). CSP is an integration of two terms, Communication and Sequential process. A communication is an event that is described by a pair C, V, where C is the name of the channel on which communication takes place and V is the value of the message which passes through this channel by C .A. R. Hoare. In a Sequential Process new process cannot be started until the preceding process has completed. As CSP was more of a programming language so most of the syntax and notations were inherited from ALGOL 60 programming language. Most of the notations were single character instead of English words. For example,? and ! represents input and output respectively. CSP inherits the concept of Co routines over old programming structures such as subroutines. The structure of Co routines is comprised of COPY (copies character from output of one process to the input of second process), SQUASH is used to replace specified character with other characters, DISASSEMBLE, ASSEMBLE and REFORMAT. -OCCAM One of the renowned implementation of CSP is occam. It is named after William of Ockam. It is a strict procedural language. It was developed at INMOS. Occam2 programming language is used in most of the software developing companies across the world. It is an extension of occam1 which lacks multi-dimension arrays, functions and other data type support. Occam2 came into existence in 1987s. The latest version is occam2.1 which was developed in 1994. BYTESIN operator, fixed-length array returned from procedures, named data types etc. were some of the new features of occame2.1. the compiler designed for occam2.1 named KRoC (Kent Retargetable occam Compiler) is used to create machine code from different microprocessors. Occam-pi is the name of the new occam variant which is influenced by pi-calculus. It is implemented by newer versions of KRoC. JCSP Java programming language also implements the concept of CSP by JCSP. JCSP is a complete programming implementation of CSP i.e. it does not contain deep mathematical algebra. JCSP is used to avoid race condition, deadlock, live lock and starvation programmatically via java programs. The main advantage of JCSP is that most of the algebraic part is already developed and stored in libraries so the programmer does not require strong mathematical skills. To invoke a method he needs to import these inbuilt libraries. Concurrency Test Tools Design a concurrent application is very challenging task. Maintaining interaction between concurrently executing threads is very difficult task for programmer. It is very difficult to understand the nature of threads from one run of a program as they are nondeterministic. As result, it becomes very difficult for testing and debugging. So it is good idea to invest in techniques which can avoid this conditions aid in the process of development. We are exploring these ideas with tools for concurrency. CHESS This is one of the important tools, created by Microsoft Research, which is used to test multithreaded code systematically. CHESS facilitates both model checking and dynamic analysis. It has the potential to detect race conditions, livelocks, hangs, deadlocks and data corruption issues. Concurrency errors are detected by investigating thread schedules and interleaving and for this it chooses a specialized scheduler on which it repeatedly runs regular unit test. The specialized scheduler creates specific thread interleaving. CHESS controls state space explosion using iterative context bounding which puts a limitation on number of thread switching. This supports scientifically experimented concept that most of the concurrency bugs can be revealed with less number of thread switches. This concept is far better than traditional model checking. CHESS uses Goldilocks lockset algorithm to detect deadlock and race condition. For reporting a livelock, it is anticipated that programmes terminate and exhibit fairness for all threads. THE INTEL THREAD CHECKER Similar to CHESS, INTEL THREAD CHECKER is used for detecting problems in concurrency like data races and deadlock and it also finds out erroneous synchronization. The thread checker makes use of source code or the compiled binary for making memory references and to monitor WIN32 synchronization primitive. At the time of execution, information given by the compiled binary is used for constructing partial order of execution; this step is followed by happens before analysis of the partial order obtained. For improving efficiency and performance, it is better to remember latest access to shared variable than to remember all accesses. The disadvantage of this tool is it cannot find all bugs while analysing long-running applications. RACERX Unlike first two dynamic analysis tools we have discussed above, RACERX is a static analysis tool. It is not required to comment the entire source code rather user gives table which contains specification of APIs which are useful in gaining and releasing locks. Using such small sized tables proves to be advantageous because they lessen the overhead of annotating entire source code. The working of RACERX is carried out in several phases. In the first phase, RACERX builds a Control Flow Graph once it has iterated through each source code file. CFG consists of information about function calls, use of pointers, shared memory and other data. When building CFG is done, calls to these APIs are marked. This first phase is followed by analysis phase which involves checking race condition and deadlock. The last phase is post processing errors reported, the purpose is to prioritize errors by their significance and harmfulness. CHORD This tool is used for Java language, it is context sensitive static analysis tool. Its flow insensitive nature makes it more scalable than other static tools with the disadvantage of low accuracy. It also deals with the distinguishing synchronization primitives available in Java. ZING ZING, a pure model checker tool, verifies the design of multi threaded programs. It has the ability to model concurrent state machines using its own language that describes complex states and transition. It assures the design quality by verifying assumptions and confirming the presence or absence of some conditions. KISS Microsoft Research developed another model checker tool, named KISS (Keep It Simple and Sequential) for concurrent C programs. It converts a concurrent C program into a sequential program that features the operation of interleaving and controls non-determinism. Thereafter, the analysis is performed by a sequential model checker. While using this tool, the programmer is expected to justify the validation of concurrency assumptions. Introduction of multi-core processors increased the importance on concurrency by many folds. Concurrency and multicore processor Multi core processors The computer industry is undergoing a paradigm shift. Chip manufacturers are shifting development resources away from single-processor chips to a new generation of multi-processor chips known as multicores. Multiple processors are manufactured by placing them on the same die. Hence they share the same circuit. A die is a small block of semiconducting material, on which a given functional circuit is fabricated. A) Single Core B) Multi Core Why were they introduced? As we grow further in terms of processing power the hardware industry faces three main challenges Power Amount of power consumed by processors has been increasing as more and more powerful processors have been introduced to the market. The environment cost and the energy needs have compelled the manufacturer as well as organisations to reconsider their strategies to an extent where change in way the processors are manufactured or operate was inevitable. Processors can be overclocked or underclocked. Overclocking a processor increases the number of instructions it can execute but at the same time increases the power consumption; also overclocking a processor does not guarantee a performance improvement as there are many other factors to consider. Increasing the number of processors per core (quad or eight) will further improve the power to performance ratio. Memory clock Memory clock has not improved like the CPU clock hence adding a limitation on the processor performance. Often the instruction to be fetched must be retrieved from relatively slow memory, causing the CPU to stall while waiting for the instruction to be returned. So instead of building faster CPUs underclock it and have more number of cores with their own dedicated memories to have more instructions executed in the same given time. Also the clock speed in itself wont grow infinitely due to fundamental physics it has hit a wall. Chips melt above 5GHz of clock speed. Many possibilities are opened by placing two or more powerful computing cores on a single processor. True concurrent applications can be developed only on multicore processors. On single core processors concurrent applications can overload the processor degrading the performance of the application. On multi-core systems, since each core has its own cache, the operating system has sufficient resources to handle most compute intensive tasks in parallel. What are the effects of the hardware shift on concurrent programming? The free lunch of performance in terms of ever faster processors is over- Microsoft C++ guru Herb Sutter. For past five decades the ever increasing clock speed has carried the software industry through its progress but now the time has come for the software engineers to face the challenge staring directly at them which they have managed to ignore so far. Also as more and more cores are added to hardware the gap between the hardware potential and the s

Schools Equating Disability with Inability to Learn :: Education Disabilities Teaching Essays

Schools Equating Disability with Inability to Learn One need not consult a scholar of education to learn that each and every individual experiences the educational system in a different way. Most people would even be able to point to the factors that most influence our differences in the way we are taught--race, class, and gender. In focusing in on those three, however, some factors which are pretty influential are sometimes ignored. One of these is physical and other disabilities. In an interview with a disabled individual, â€Å"Phillip", I learned a number of things. To begin with, I was ignorant about the extent of discrimination that disabled individuals face in the formal educational setting. Secondly, the discrimination that disabled individuals face is similar to that which economically disadvantaged individuals experience. In Phillip's case, the similarities were seen in the his being tracked in the lower level and the presumption that deaf is synonymous with ineducable. So although Phillip and I are of the same race, and our families are relatively close in socioeconomic status, we experienced school in a drastically different way--simply because Phillip has a hearing disability. Phillip has a profound sensorineural loss, which essentially means that he can hear very little of conversational speech, even though he wears a hearing aid in one ear. Although Phillip communicates without sign language and other augmentative communication, he has experienced many trials throughout his life, especially in the educational setting. He understands language only by reading lips and using contextual cues according to his environment. Phillip doesn't remember much of his elementary school experience, but for the most part, his language was very poor, from a developmental perspective, and he was kept in classes where there were only deaf students present. He refers to his elementary school experience as "positive," but isn't really sure whether it was just the fun and excitement of his youth which overwhelmed the barriers that he would later experience in his life. Phillip's true experience with discrimination in the school setting began when he entered junior high, where he was mainstreamed, and took subjects among all of his peers, whether they were hearing or not. In high school Phillip was partially mainstreamed. He took English and other required courses with his deaf peers, but for his electives and physical education, he was put in classes where the majority of the population was hearing. In junior high, Phillip has vivid memories of not being able to understand teachers.

The Lottery Essay -- essays research papers

Shirley Jackson’s insights and observations about man and society are reflected in her famous short story "The Lottery". Many of her readers have found this story shocking and disturbing. Jackson reveals two general attitudes in this story: first, the shocking reality of human’s tendency to select a scapegoat and second, society as a victim of tradition and ritual. Throughout history we have witnessed and participated in many events, where, in time of turmoil and hardship, society has a tendency to seize upon a scapegoat as means of resolution. The people of the village had been taught to believe that in order for their crop to be abundant for the year, some individual had to be sacrificed. "Lottery in June, corn be heavy soon", said Old Man Warner. The irony here is that villagers are aware that this act is inhumane but none want to stand and voice their opinion, for fear of going against society’s standards and being outcast or being stoned. "It’s not the way it used to be," Old Man Warner said clearly. "People ain’t the way they used to be." Fear that if they go against society they might be chosen as the lottery winner or there might be a truth, after all, that it would disrupt their corn season. "Some places have already quit lotteries," Mrs. Adams said. "Nothing but trouble in that," Old Man Warner said stoutly. "Pack of young fools." In stoning Tessie, the villagers treat her as a scapegoat onto wh...

The Idealization of Science in Sinclair Lewis Arrowsmith Essay

The Idealization of Science in Sinclair Lewis' Arrowsmith Sinclair Lewis's 1924 novel Arrowsmith follows a pair of bacteriologists, Martin Arrowsmith and his mentor Max Gottlieb, as they travel through various professions in science and medicine in the early decades of the twentieth century. Through the brilliant researcher Gottlieb and his protà ©gà ©, Lewis explores the status and role of scientific work at universities, in industry, and at a private research foundation as well as in various medical positions. The picture he presents is one of tension and conflict between the goals and ideals of pure science and the environments in which his protagonists have to operate. Although Gottlieb and Arrowsmith are able to pursue their research in some places, their work is continually obstructed and undermined. The conclusion of the novel seems to suggest that it is essentially impossible to truly practice pure scientific research in early twentieth century America. It is only when Arrowsmith abandons his family and his job, cuts his ties with the world and retreats into a sort of scientific monastery with his compatriot Terry Wickett that he is able to "feel as if [he] were really starting to work."1 Many of the tensions that appear in Arrowsmith reflect actual debates and conflicts in the real world. The debate over whether universities should be dedicated primarily to teaching or to research (and whether that research should be practical or abstract) was important in the development of modern colleges and universities. There was a great deal of argument over the virtues of research laboratories in industry, and over how much control companies should exert over the scientists working in their labs and over the direction of their ... ...an University, 178. 12. Lewis, Arrowsmith, 136. 13. Ibid., 280. 14. Frank Jewett qtd. in Kevles, The Physicists, 100. 15. George Wise, "Ionists in Industry: Physical Chemistry at General Electric, 1900 - 1915," Isis 74 (1983), 7. 16. Kevles, The Physicists, 99 - 100. 17. Ibid., 100. 18. David Noble, America By Design: Science, Technology and the Rise of Corporate Capitalism (Oxford: Oxford University Press, 1977), 112. Brackets as in the original. 19. Bruce, The Launching of Modern American Science, 141. 20. Frank Jewett qtd. in Noble, America By Design , 115. Ellipses as in the original. 21. Kevles, The Physicists, 25. 22. A. G. Bell & Hubbard qtd. in Ibid., 47. 23. Noble, America By Design, 112. Italics as in the original. 24. Lewis, Arrowsmith, 138. 25. Ibid., 409. 26. Hermann van Holst qtd. in Veysey, The Emergence of the American University, 150. The Idealization of Science in Sinclair Lewis' Arrowsmith Essay The Idealization of Science in Sinclair Lewis' Arrowsmith Sinclair Lewis's 1924 novel Arrowsmith follows a pair of bacteriologists, Martin Arrowsmith and his mentor Max Gottlieb, as they travel through various professions in science and medicine in the early decades of the twentieth century. Through the brilliant researcher Gottlieb and his protà ©gà ©, Lewis explores the status and role of scientific work at universities, in industry, and at a private research foundation as well as in various medical positions. The picture he presents is one of tension and conflict between the goals and ideals of pure science and the environments in which his protagonists have to operate. Although Gottlieb and Arrowsmith are able to pursue their research in some places, their work is continually obstructed and undermined. The conclusion of the novel seems to suggest that it is essentially impossible to truly practice pure scientific research in early twentieth century America. It is only when Arrowsmith abandons his family and his job, cuts his ties with the world and retreats into a sort of scientific monastery with his compatriot Terry Wickett that he is able to "feel as if [he] were really starting to work."1 Many of the tensions that appear in Arrowsmith reflect actual debates and conflicts in the real world. The debate over whether universities should be dedicated primarily to teaching or to research (and whether that research should be practical or abstract) was important in the development of modern colleges and universities. There was a great deal of argument over the virtues of research laboratories in industry, and over how much control companies should exert over the scientists working in their labs and over the direction of their ... ...an University, 178. 12. Lewis, Arrowsmith, 136. 13. Ibid., 280. 14. Frank Jewett qtd. in Kevles, The Physicists, 100. 15. George Wise, "Ionists in Industry: Physical Chemistry at General Electric, 1900 - 1915," Isis 74 (1983), 7. 16. Kevles, The Physicists, 99 - 100. 17. Ibid., 100. 18. David Noble, America By Design: Science, Technology and the Rise of Corporate Capitalism (Oxford: Oxford University Press, 1977), 112. Brackets as in the original. 19. Bruce, The Launching of Modern American Science, 141. 20. Frank Jewett qtd. in Noble, America By Design , 115. Ellipses as in the original. 21. Kevles, The Physicists, 25. 22. A. G. Bell & Hubbard qtd. in Ibid., 47. 23. Noble, America By Design, 112. Italics as in the original. 24. Lewis, Arrowsmith, 138. 25. Ibid., 409. 26. Hermann van Holst qtd. in Veysey, The Emergence of the American University, 150.

Decision Making Tools

P A R T I V QUANTITATIVE MODULES Quantitative Module Decision-Making Tools A Module OutlineTHE DECISION PROCESS IN OPERATIONS FUNDAMENTALS OF DECISION MAKING DECISION TABLES TYPES OF DECISION-MAKING ENVIRONMENTS Decision Making Under Uncertainty Decision Making Under Risk Decision Making Under Certainty Expected Value of Perfect Information (EVPI) DECISION TREES A More Complex Decision Tree Using Decision Trees in Ethical Decision Making SUMMARY KEY TERMS USING SOFTWARE FOR DECISION MODELS SOLVED PROBLEMS INTERNET AND STUDENT CD-ROM EXERCISES DISCUSSION QUESTIONS PROBLEMS INTERNET HOMEWORK PROBLEMS CASE STUDIES: TOM TUCKER’S LIVER TRANSPLANT; SKI RIGHT CORP. ADDITIONAL CASE STUDIES BIBLIOGRAPHY L EARNING O BJECTIVESWhen you complete this module you should be able to IDENTIFY OR DEFINE: Decision trees and decision tables Highest monetary value Expected value of perfect information Sequential decisions DESCRIBE OR EXPLAIN: Decision making under risk Decision making under uncerta inty Decision making under certainty 674 MODULE A D E C I S I O N -M A K I N G T O O L S The wildcatter’s decision was a tough one. Which of his new Kentucky lease areas—Blair East or Blair West—should he drill for oil? A wrong decision in this type of wildcat oil drilling could mean the difference between success and bankruptcy for the company.Talk about decision making under uncertainty and pressure! But using a decision tree, Tomco Oil President Thomas E. Blair identified 74 different options, each with its own potential net profit. What had begun as an overwhelming number of geological, engineering, economic, and political factors now became much clearer. Says Blair, â€Å"Decision tree analysis provided us with a systematic way of planning these decisions and clearer insight into the numerous and varied financial outcomes that are possible. †1 â€Å"The business executive is by profession a decision maker. Uncertainty is his opponent. Overcoming it is his mission. † John McDonaldOperations managers are decision makers. To achieve the goals of their organizations, managers must understand how decisions are made and know which decision-making tools to use. To a great extent, the success or failure of both people and companies depends on the quality of their decisions. Bill Gates, who developed the DOS and Windows operating systems, became chairman of the most powerful software firm in the world (Microsoft) and a billionaire. In contrast, the Firestone manager who headed the team that designed the flawed tires that caused so many accidents with Ford Explorers in the late 1990s is not working there anymore.THE DECISION PROCESS IN OPERATIONS What makes the difference between a good decision and a bad decision? A â€Å"good† decision—one that uses analytic decision making—is based on logic and considers all available data and possible alternatives. It also follows these six steps: 1. 2. 3. 4. 5. 6. Clearly define the problem and the factors that influence it. Develop specific and measurable objectives. Develop a model—that is, a relationship between objectives and variables (which are measurable quantities). Evaluate each alternative solution based on its merits and drawbacks.Select the best alternative. Implement the decision and set a timetable for completion. Throughout this book, we have introduced a broad range of mathematical models and tools to help operations managers make better decisions. Effective operations depend on careful decision making. Fortunately, there are a whole variety of analytic tools to help make these decisions. This modHosseini, â€Å"Decision Analysis and Its Application in the Choice between Two Wildcat Ventures,† Interfaces, Vol. 16, no. 2. Reprinted by permission, INFORMS, 901 Elkridge Landing Road, Suite 400, Linthicum, Maryland 21090 USA. J. D E C I S I O N TA B L E S â€Å"Management means, in the last analysis, the substitution of th ought for brawn and muscle, of knowledge for folklore and tradition, and of cooperation for force. † Peter Drucker 675 ule introduces two of them—decision tables and decision trees. They are used in a wide number of OM situations, ranging from new-product analysis (Chapter 5), to capacity planning (Supplement 7), to location planning (Chapter 8), to scheduling (Chapter 15), and to maintenance planning (Chapter 17). FUNDAMENTALS OF DECISION MAKINGRegardless of the complexity of a decision or the sophistication of the technique used to analyze it, all decision makers are faced with alternatives and â€Å"states of nature. † The following notation will be used in this module: 1. Terms: a. Alternative—a course of action or strategy that may be chosen by a decision maker (for example, not carrying an umbrella tomorrow). b. State of nature—an occurrence or a situation over which the decision maker has little or no control (for example, tomorrow’s w eather). Symbols used in a decision tree: a. —decision node from which one of several alternatives may be selected. b. —a state-of-nature node out of which one state of nature will occur. 2. To present a manager’s decision alternatives, we can develop decision trees using the above symbols. When constructing a decision tree, we must be sure that all alternatives and states of nature are in their correct and logical places and that we include all possible alternatives and states of nature. Example A1 A simple decision tree Getz Products Company is investigating the possibility of producing and marketing backyard storage sheds.Undertaking this project would require the construction of either a large or a small manufacturing plant. The market for the product produced—storage sheds—could be either favorable or unfavorable. Getz, of course, has the option of not developing the new product line at all. A decision tree for this situation is presented in F igure A. 1. A decision node A state of nature node Favorable market 1 Unfavorable market Favorable market 2 Unfavorable market no thi ng uct t str on plan C e g lar Construct small plant Do FIGURE A. 1 I Getz Products Decision Tree DECISION TABLES Decision tableA tabular means of analyzing decision alternatives and states of nature. We may also develop a decision or payoff table to help Getz Products define its alternatives. For any alternative and a particular state of nature, there is a consequence or outcome, which is usually expressed as a monetary value. This is called a conditional value. Note that all of the alternatives in Example A2 are listed down the left side of the table, that states of nature (outcomes) are listed across the top, and that conditional values (payoffs) are in the body of the decision table. 676 MODULE A D E C I S I O N -M A K I N G T O O L SWe construct a decision table for Getz Products (Table A. 1), including conditional values based on the following i nformation. With a favorable market, a large facility will give Getz Products a net profit of $200,000. If the market is unfavorable, a $180,000 net loss will occur. A small plant will result in a net profit of $100,000 in a favorable market, but a net loss of $20,000 will be encountered if the market is unfavorable. Example A2 A decision table TABLE A. 1 I Decision Table with Conditional Values for Getz Products ALTERNATIVES The toughest part of decision tables is getting the data to analyze.Construct large plant Construct small plant Do nothing STATES OF NATURE FAVORABLE MARKET UNFAVORABLE MARKET $200,000 $100,000 $ 0 $180,000 $ 20,000 $ 0 In Examples A3 and A4, we see how to use decision tables. TYPES OF DECISION-MAKING ENVIRONMENTS The types of decisions people make depend on how much knowledge or information they have about the situation. There are three decision-making environments: †¢ †¢ †¢ Decision making under uncertainty Decision making under risk Decision m aking under certainty Decision Making Under UncertaintyWhen there is complete uncertainty as to which state of nature in a decision environment may occur (that is, when we cannot even assess probabilities for each possible outcome), we rely on three decision methods: Maximax A criterion that finds an alternative that maximizes the maximum outcome. Maximin A criterion that finds an alternative that maximizes the minimum outcome. Equally likely A criterion that assigns equal probability to each state of nature. Maximax—this method finds an alternative that maximizes the maximum outcome for every alternative.First, we find the maximum outcome within every alternative, and then we pick the alternative with the maximum number. Because this decision criterion locates the alternative with the highest possible gain, it has been called an â€Å"optimistic† decision criterion. 2. Maximin—this method finds the alternative that maximizes the minimum outcome for every altern ative. First, we find the minimum outcome within every alternative, and then we pick the alternative with the maximum number. Because this decision criterion locates the alternative that has the least possible loss, it has been called a â€Å"pessimistic† decision criterion. . Equally likely—this method finds the alternative with the highest average outcome. First, we calculate the average outcome for every alternative, which is the sum of all outcomes divided by the number of outcomes. We then pick the alternative with the maximum number. The equally likely approach assumes that each state of nature is equally likely to occur. Example A3 applies each of these approaches to the Getz Products Company. 1. Example A3 A decision table analysis under uncertainty Given Getz’s decision table of Example A2, determine the maximax, maximin, nd equally likely decision criteria (see Table A. 2). TABLE A. 2 I Decision Table for Decision Making under Uncertainty STATES OF NAT URE FAVORABLE UNFAVORABLE MARKET MARKET $200,000 $100,000 $ 0 $180,000 $20,000 $ 0 MAXIMUM IN ROW $200,000 $100,000 $ 0 Maximax MINIMUM IN ROW $180,000 $20,000 $ 0 Maximin ROW AVERAGE $10,000 $40,000 $ 0 Equally likely ALTERNATIVES There are optimistic decision makers (â€Å"maximax†) and pessimistic ones (â€Å"maximin†). Maximax and maximin present best case–worst case planning scenarios. Construct large plant Construct small plant Do nothingTYPES 1. 2. 3. OF D E C I S I O N -M A K I N G E N V I RO N M E N T S 677 The maximax choice is to construct a large plant. This is the maximum of the maximum number within each row, or alternative. The maximin choice is to do nothing. This is the maximum of the minimum number within each row, or alternative. The equally likely choice is to construct a small plant. This is the maximum of the average outcome of each alternative. This approach assumes that all outcomes for any alternative are equally likely. Decision Making Under Risk Expected monetary value (EMV)The expected payout or value of a variable that has different possible states of nature, each with an associated probability. Decision making under risk, a more common occurrence, relies on probabilities. Several possible states of nature may occur, each with an assumed probability. The states of nature must be mutually exclusive and collectively exhaustive and their probabilities must sum to 1. 2 Given a decision table with conditional values and probability assessments for all states of nature, we can determine the expected monetary value (EMV) for each alternative.This figure represents the expected value or mean return for each alternative if we could repeat the decision a large number of times. The EMV for an alternative is the sum of all possible payoffs from the alternative, each weighted by the probability of that payoff occurring. EMV (Alternative i ) = ( Payoff of 1st state of nature) ? (Probability of 1st state of nature) + (Payoff of 2nd state of nature) ? (Probability of 2nd state of nature) + L + (Payoff of last state of nature) ? (Probability of last state of nature) Example A4 illustrates how to compute the maximum EMV. Example A4Expected monetary value Excel OM Data File ModAEx4. xla Getz Products operations manager believes that the probability of a favorable market is exactly the same as that of an unfavorable market; that is, each state of nature has a . 50 chance of occurring. We can now determine the EMV for each alternative (see Table A. 3): 1. 2. 3. EMV(A1) = (. 5)($200,000) + (. 5)( $180,000) = $10,000 EMV(A2) = (. 5)($100,000) + (. 5)( $20,000) = $40,000 EMV(A3) = (. 5)($0) + (. 5)($0) = $0 The maximum EMV is seen in alternative A2. Thus, according to the EMV decision criterion, Getz would build the small facility. TABLE A. I Decision Table for Getz Products ALTERNATIVES Construct large plant (A1) Construct small plant (A2) Do nothing (A3) Probabilities STATES OF NATURE FAVORABLE MARKET UNFAVORA BLE MARKET $200,000 $100,000 $ 0 . 50 $180,000 $ 20,000 $ 0 . 50 Decision Making Under Certainty Now suppose that the Getz operations manager has been approached by a marketing research firm that proposes to help him make the decision about whether to build the plant to produce storage sheds. The marketing researchers claim that their technical analysis will tell Getz with certainty whether the market is favorable for the proposed product.In other words, it will change Getz’s environment from one of decision making under risk to one of decision making under certainty. This information could prevent Getz from making a very expensive mistake. The marketing research firm would charge Getz $65,000 for the information. What would you recommend? Should the operations manager hire the firm to make the study? Even if the information from the study is perfectly accurate, is it worth $65,000? What might it be worth? Although some of these questions are difficult to answer, 2To EVPI pla ces an upper limit on what you should pay for information. eview these and other statistical terms, refer to the CD-ROM Tutorial 1, â€Å"Statistical Review for Managers. † 678 MODULE A D E C I S I O N -M A K I N G T O O L S determining the value of such perfect information can be very useful. It places an upper bound on what you would be willing to spend on information, such as that being sold by a marketing consultant. This is the concept of the expected value of perfect information (EVPI), which we now introduce. Expected Value of Perfect Information (EVPI) Expected value of perfect information (EVPI) The difference between the payoff under certainty and the payoff under risk.If a manager were able to determine which state of nature would occur, then he or she would know which decision to make. Once a manager knows which decision to make, the payoff increases because the payoff is now a certainty, not a probability. Because the payoff will increase with knowledge of which state of nature will occur, this knowledge has value. Therefore, we now look at how to determine the value of this information. We call this difference between the payoff under certainty and the payoff under risk the expected value of perfect information (EVPI). EVPI = Expected value under certainty Maximum EMVExpected value under certainty The expected (average) return if perfect information is available. To find the EVPI, we must first compute the expected value under certainty, which is the expected (average) return if we have perfect information before a decision has to be made. To calculate this value, we choose the best alternative for each state of nature and multiply its payoff times the probability of occurrence of that state of nature. Expected value under certainty = (Best outcome or consequence for 1st state of nature) ? (Probability of 1st state of nature) + (Best outcome for 2nd state of nature) ? Probability of 2nd state of nature) + L + (Best outcome for last state o f nature) ? (Probability of last state of nature) In Example A5 we use the data and decision table from Example A4 to examine the expected value of perfect information. Example A5 Expected value of perfect information By referring back to Table A. 3, the Getz operations manager can calculate the maximum that he would pay for information—that is, the expected value of perfect information, or EVPI. He follows a two-stage process. First, the expected value under certainty is computed. Then, using this information, EVPI is calculated.The procedure is outlined as follows: 1. The best outcome for the state of nature â€Å"favorable market† is â€Å"build a large facility† with a payoff of $200,000. The best outcome for the state of nature â€Å"unfavorable market† is â€Å"do nothing† with a payoff of $0. Expected value under certainty = ($200,000)(0. 50) + ($0)(0. 50) = $100,000. Thus, if we had perfect information, we would expect (on the average) $100 ,000 if the decision could be repeated many times. The maximum EMV is $40,000, which is the expected outcome without perfect information. Thus: EVPI = Expected value under certainty ? Maximum EMV = $100, 000 ? 40, 000 = $60, 000 In other words, the most Getz should be willing to pay for perfect information is $60,000. This conclusion, of course, is again based on the assumption that the probability of each state of nature is 0. 50. 2. DECISION TREES Decisions that lend themselves to display in a decision table also lend themselves to display in a decision tree. We will therefore analyze some decisions using decision trees. Although the use of a decision table is convenient in problems having one set of decisions and one set of states of nature, many problems include sequential decisions and states of nature.When there are two or more sequential decisions, and later decisions are based on the outcome of prior ones, the decision tree approach becomes appropriate. A decision tree is a graphic display of the decision process that indicates decision alternatives, states of nature and their respective probabilities, and payoffs for each combination of decision alternative and state of nature. Expected monetary value (EMV) is the most commonly used criterion for decision tree analysis. One of the first steps in such analysis is to graph the decision tree and to specify the monetary consequences of all outcomes for a particular problem.Decision tree A graphical means of analyzing decision alternatives and states of nature. DECISION TREES Decision tree software is a relatively new advance that permits users to solve decisionanalysis problems with flexibility, power, and ease. Programs such as DPL, Tree Plan, and Supertree allow decision problems to be analyzed with less effort and in greater depth than ever before. Full-color presentations of the options open to managers always have impact. In this photo, wildcat drilling options are explored with DPL, a product of Syn copation Software. 679 Analyzing problems with decision trees involves five steps: 1. 2. . 4. 5. Define the problem. Structure or draw the decision tree. Assign probabilities to the states of nature. Estimate payoffs for each possible combination of decision alternatives and states of nature. Solve the problem by computing expected monetary values (EMV) for each state-of-nature node. This is done by working backward—that is, by starting at the right of the tree and working back to decision nodes on the left. Example A6 Solving a tree for EMV A completed and solved decision tree for Getz Products is presented in Figure A. 2. Note that the payoffs are placed at the right-hand side of each of the tree’s branches.The probabilities (first used by Getz in Example A4) are placed in parentheses next to each state of nature. The expected monetary values for each state-ofnature node are then calculated and placed by their respective nodes. The EMV of the first node is $10,000. T his represents the branch from the decision node to â€Å"construct a large plant. † The EMV for node 2, to â€Å"construct a small plant,† is $40,000. The option of â€Å"doing nothing† has, of course, a payoff of $0. The branch leaving the decision node leading to the state-of-nature node with the highest EMV will be chosen. In Getz’s case, a small plant should be built.EMV for node 1 = $10,000 = (. 5) ($200,000) + (. 5) (–$180,000) Payoffs Favorable market (. 5) $200,000 Co n ct stru e larg pla nt 1 Unfavorable market (. 5) Favorable market (. 5) 2 Unfavorable market (. 5) –$ 20,000 –$180,000 $100,000 Construct small plant Do no th in g EMV for node 2 = $40,000 = (. 5) ($100,000) + (. 5) (–$20,000) $0 FIGURE A. 2 I Completed and Solved Decision Tree for Getz Products 680 MODULE A D E C I S I O N -M A K I N G T O O L S A More Complex Decision Tree There is a widespread use of decision trees beyond OM. Managers often appreciat e a graphical display of a tough problem.When a sequence of decisions must be made, decision trees are much more powerful tools than are decision tables. Let’s say that Getz Products has two decisions to make, with the second decision dependent on the outcome of the first. Before deciding about building a new plant, Getz has the option of conducting its own marketing research survey, at a cost of $10,000. The information from this survey could help it decide whether to build a large plant, to build a small plant, or not to build at all. Getz recognizes that although such a survey will not provide it with perfect information, it may be extremely helpful.Getz’s new decision tree is represented in Figure A. 3 of Example A7. Take a careful look at this more complex tree. Note that all possible outcomes and alternatives are included in their logical sequence. This procedure is one of the strengths of using decision trees. The manager is forced to examine all possible outcom es, including unfavorable ones. He or she is also forced to make decisions in a logical, sequential manner. Examining the tree in Figure A. 3, we see that Getz’s first decision point is whether to conduct the $10,000 market survey.If it chooses not to do the study (the lower part of the tree), it can either build a large plant, a small plant, or no plant. This is Getz’s second decision point. If the decision is to build, the market will be either favorable (. 50 probability) or unfavorable (also . 50 probability). The payoffs for each of the possible consequences are listed along the right-hand side. As a matter of fact, this lower portion of Getz’s tree is identical to the simpler decision tree shown in Figure A. 2. Example A7 A decision tree with sequential decisions First Decision Point Second Decision Point $106,400 Favorable market (. 8) nt Payoffs $190,000 2 $49,200 1 Su re rve fav sult y (. 4 ora s 5) ble $106,400 la –$190,000 ep $63,600 Favorable market (. 78) arg L $ 90,000 Small 3 Unfavorable market(. 22) plant –$ 30,000 No pla nt –$ 10,000 Unfavorable market (. 22) vey –$87,400 Favorable market (. 27) pla nt $190,000 –$190,000 $ 90,000 –$ 30,000 –$ 10,000 y( rve Su ults e res ativ g ne t sur 4 Unfavorable market (. 73) (. 27) .55 arke $2,400 Con duct m L e arg $2,400 Favorable market 5 ) Small plant nt Unfavorable market (. 73) No pla $49,200 $40,000 FIGURE A. 3 I Getz Products Decision Tree with Probabilities and EMVs ShownThe short parallel lines mean â€Å"prune† that branch, as it is less favorable than another available option and may be dropped. Do t no co nd uc ts ur ve y $10,000 Favorable market pla nt (. 5) $200,000 –$180,000 $100,000 –$ 20,000 $0 6 Unfavorable market (. 5) (. 5) L e arg $40,000 Favorable market 7 Small plant nt Unfavorable market (. 5) No pla DECISION TREES You can reduce complexity by viewing and solving a number of smaller treesâ⠂¬â€ start at the end branches of a large one. Take one decision at a time. 681 The upper part of Figure A. 3 reflects the decision to conduct the market survey.State-of-nature node number 1 has 2 branches coming out of it. Let us say there is a 45% chance that the survey results will indicate a favorable market for the storage sheds. We also note that the probability is . 55 that the survey results will be negative. The rest of the probabilities shown in parentheses in Figure A. 3 are all conditional probabilities. For example, . 78 is the probability of a favorable market for the sheds given a favorable result from the market survey. Of course, you would expect to find a high probability of a favorable market given that the research indicated that the market was good.Don’t forget, though: There is a chance that Getz’s $10,000 market survey did not result in perfect or even reliable information. Any market research study is subject to error. In this case, there remai ns a 22% chance that the market for sheds will be unfavorable given positive survey results. Likewise, we note that there is a 27% chance that the market for sheds will be favorable given negative survey results. The probability is much higher, . 73, that the market will actually be unfavorable given a negative survey. Finally, when we look to the payoff column in Figure A. , we see that $10,000—the cost of the marketing study—has been subtracted from each of the top 10 tree branches. Thus, a large plant constructed in a favorable market would normally net a $200,000 profit. Yet because the market study was conducted, this figure is reduced by $10,000. In the unfavorable case, the loss of $180,000 would increase to $190,000. Similarly, conducting the survey and building no plant now results in a $10,000 payoff. With all probabilities and payoffs specified, we can start calculating the expected monetary value of each branch.We begin at the end or right-hand side of the decision tree and work back toward the origin. When we finish, the best decision will be known. 1. Given favorable survey results, EMV (node 2) = (. 78)($190, 000) + (. 22)( ? $190, 000) = $106, 400 EMV (node 3) = (. 78)($90, 000) + (. 22)( ? $30, 000) = $63,600 The EMV of no plant in this case is plant should be built. Given negative survey results, $10,000. Thus, if the survey results are favorable, a large 2. EMV (node 4) = (. 27)($190, 000) + (. 73)( ? $190, 000) = ? $87, 400 EMV (node 5) = (. 27)($90, 000) + (. 73)( ? $30, 000) = $2, 400 The EMV of no plant is again $10,000 for this branch.Thus, given a negative survey result, Getz should build a small plant with an expected value of $2,400. Continuing on the upper part of the tree and moving backward, we compute the expected value of conducting the market survey. EMV(node 1) = (. 45)($106,400) + (. 55)($2,400) = $49,200 4. If the market survey is not conducted. EMV (node 6) = (. 50)($200, 000) + (. 50)( ? $180, 000) = $10, 000 EMV (node 7) = (. 50)($100, 000) + (. 50)( ? $20, 000) = $40, 000 The EMV of no plant is $0. Thus, building a small plant is the best choice, given the marketing research is not performed.Because the expected monetary value of conducting the survey is $49,200—versus an EMV of $40,000 for not conducting the study—the best choice is to seek marketing information. If the survey results are favorable, Getz should build the large plant; if they are unfavorable, it should build the small plant. 3. 5. Using Decision Trees in Ethical Decision Making Decision trees can also be a useful tool to aid ethical corporate decision making. The decision tree illustrated in Example A8, developed by Harvard Professor Constance Bagley, provides guidance as to how managers can both maximize shareholder value and behave ethically.The tree can be applied to any action a company contemplates, whether it is expanding operations in a developing country or reducing a workforce at home. 682 MODUL E A D E C I S I O N -M A K I N G T O O L S Smithson Corp. is opening a plant in Malaysia, a country with much less stringent environmental laws than the U. S. , its home nation. Smithson can save $18 million in building the manufacturing facility—and boost its profits—if it does not install pollution-control equipment that is mandated in the U. S. but not in Malaysia.But Smithson also calculates that pollutants emitted from the plant, if unscrubbed, could damage the local fishing industry. This could cause a loss of millions of dollars in income as well as create health problems for local inhabitants. Example A8 Ethical decision making Action outcome Is it ethical? (Weigh the effect on employees, customers, suppliers, community versus shareholder benefit. ) Do it Ye s Ye No s Ye Is action legal? s Does action maximize company returns? Don't do it No No Is it ethical not to take action? (Weigh the harm to shareholders versus benefits to other stakeholders. Ye s Don't do it Do it, but notify appropriate parties Don't do it No FIGURE A. 4 I Smithson’s Decision Tree for Ethical Dilemma Source: Modified from Constance E. Bagley, â€Å"The Ethical Leader’s Decision Tree,† Harvard Business Review (January–February 2003): 18–19. Figure A. 4 outlines the choices management can consider. For example, if in management’s best judgment the harm to the Malaysian community by building the plant will be greater than the loss in company returns, the response to the question â€Å"Is it ethical? † will be no.Now, say Smithson proposes building a somewhat different plant, one with pollution controls, despite a negative impact on company returns. That decision takes us to the branch â€Å"Is it ethical not to take action? † If the answer (for whatever reason) is no, the decision tree suggests proceeding with the plant but notifying the Smithson Board, shareholders, and others about its impact. Ethical decisions can be quite complex: What happens, for example, if a company builds a polluting plant overseas, but this allows the company to sell a life-saving drug at a lower cost around the world?Does a decision tree deal with all possible ethical dilemmas? No—but it does provide managers with a framework for examining those choices. SUMMARY This module examines two of the most widely used decision techniques—decision tables and decision trees. These techniques are especially useful for making decisions under risk. Many decisions in research and development, plant and equipment, and even new buildings and structures can be analyzed with these decision models. Problems in inventory control, aggregate planning, maintenance, scheduling, and production control are just a few other decision table and decision tree applications.KEY TERMS Decision table (p. 675) Maximax (p. 676) Maximin (p. 676) Equally likely (p. 676) Expected monetary value (EMV) (p. 677) Expected value of perfect in formation (EVPI) (p. 678) Expected value under certainty (p. 678) Decision tree (p. 678) S O LV E D P RO B L E M S 683 USING SOFTWARE FOR DECISION MODELS Analyzing decision tables is straightforward with Excel, Excel OM, and POM for Windows. When decision trees are involved, commercial packages such as DPL, Tree Plan, and Supertree provide flexibility, power, and ease. POM for Windows will also analyze trees but does not have graphic capabilities.Using Excel OM Excel OM allows decision makers to evaluate decisions quickly and to perform sensitivity analysis on the results. Program A. 1 uses the Getz data to illustrate input, output, and selected formulas needed to compute the EMV and EVPI values. Compute the EMV for each alternative using = SUMPRODUCT(B$7:C$7, B8:C8). = MIN(B8:C8) = MAX(B8:C8) Find the best outcome for each measure using = MAX(G8:G10). To calculate the EVPI, find the best outcome for each scenario. = MAX(B8:B10) = SUMPRODUCT(B$7:C$7, B14:C14) = E14 – E11 PROG RAM A. I Using Excel OM to Compute EMV and Other Measures for Getz Using POM for Windows POM for Windows can be used to calculate all of the information described in the decision tables and decision trees in this module. For details on how to use this software, please refer to Appendix IV. SOLVED PROBLEMS Solved Problem A. 1 Stella Yan Hua is considering the possibility of opening a small dress shop on Fairbanks Avenue, a few blocks from the university. She has located a good mall that attracts students. Her options are to open a small shop, a medium-sized shop, or no shop at all.The market for a dress shop can be good, average, or bad. The probabilities for these three possibilities are . 2 for a good market, . 5 for an average market, and . 3 for a bad market. The net profit or loss for the medium-sized or small shops for the various market conditions are given in the following table. Building no shop at all yields no loss and no gain. What do you recommend? ALTERNATIVES Small sho p Medium-sized shop No shop Probabilities GOOD MARKET ($) 75,000 100,000 0 . 20 AVERAGE MARKET ($) 25,000 35,000 0 . 50 BAD MARKET ($) 40,000 60,000 0 . 30 684 MODULE A SolutionD E C I S I O N -M A K I N G T O O L S The problem can be solved by computing the expected monetary value (EMV) for each alternative. EMV (Small shop) = (. 2)($75,000) + (. 5)($25,000) + (. 3)( $40,000) = $15,500 EMV (Medium-sized shop) = (. 2)($100,000) + (. 5)($35,000) + (. 3)( $60,000) = $19,500 EMV (No shop) = (. 2)($0) + (. 5)($0) + (. 3)($0) = $0 As you can see, the best decision is to build the medium-sized shop. The EMV for this alternative is $19,500. Solved Problem A. 2 Daily demand for cases of Tidy Bowl cleaner at Ravinder Nath’s Supermarket has always been 5, 6, or 7 cases.Develop a decision tree that illustrates her decision alternatives as to whether to stock 5, 6, or 7 cases. Demand is 5 cases Demand is 6 cases Demand is 7 cases Solution The decision tree is shown in Figure A. 5. St oc k5 ca se s Demand is 5 cases Demand is 6 cases Demand is 7 cases oc k7 ca Stock 6 cases St se s Demand is 5 cases Demand is 6 cases Demand is 7 cases FIGURE A. 5 I Demand at Ravinder Nath’s Supermarket INTERNET AND STUDENT CD-ROM EXERCISES Visit our Companion Web site or use your student CD-ROM to help with this material in this module. On Our Companion Web site, www. prenhall. com/heizer Self-Study Quizzes †¢ Practice Problems †¢ Internet Homework Problems †¢ Internet Cases On Your Student CD-ROM †¢ PowerPoint Lecture †¢ Practice Problems †¢ Excel OM †¢ Excel OM Example Data File †¢ POM for Windows DISCUSSION QUESTIONS 1. Identify the six steps in the decision process. 2. Give an example of a good decision you made that resulted in a bad outcome. Also give an example of a bad decision you made that had a good outcome. Why was each decision good or bad? 3. What is the equally likely decision model? 4. Discuss the differences between dec ision making under certainty, under risk, and under uncertainty. . What is a decision tree? P RO B L E M S 6. Explain how decision trees might be used in several of the 10 OM decisions. 7. What is the expected value of perfect information? 8. What is the expected value under certainty? 9. Identify the five steps in analyzing a problem using a decision tree. 10. Why are the maximax and maximin strategies considered to be optimistic and pessimistic, respectively? 685 11. The expected value criterion is considered to be the rational criterion on which to base a decision. Is this true? Is it rational to consider risk? 12.When are decision trees most useful? PROBLEMS* P A. 1 a) b) c) Given the following conditional value table, determine the appropriate decision under uncertainty using: Maximax. Maximin. Equally likely. STATES OF NATURE ALTERNATIVES Build new plant Subcontract Overtime Do nothing VERY FAVORABLE MARKET $350,000 $180,000 $110,000 $ 0 AVERAGE MARKET $240,000 $ 90,000 $ 60,0 00 $ 0 UNFAVORABLE MARKET $300,000 $ 20,000 $ 10,000 $ 0 P A. 2 Even though independent gasoline stations have been having a difficult time, Susan Helms has been thinking about starting her own independent gasoline station.Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table: SIZE OF FIRST STATION Small Medium Large Very large GOOD MARKET ($) 50,000 80,000 100,000 300,000 FAIR MARKET ($) 20,000 30,000 30,000 25,000 POOR MARKET ($) 10,000 20,000 40,000 160,000 a) b) c) d) e) For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000.Develop a decision table for this decision. What is the maximax decision? What is the maximin decision? What is the equally likely decision? Develop a decision tree. Assume each ou tcome is equally likely, then find the highest EMV. Clay Whybark, a soft-drink vendor at Hard Rock Cafe’s annual Rockfest, created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd): STATES OF NATURE (DEMAND) ALTERNATIVES Large stock Average stock Small stock BIG $22,000 $14,000 $ 9,000 AVERAGE $12,000 $10,000 $ 8,000 SMALL $2,000 $6,000 $4,000P A. 3 If the probabilities associated with the states of nature are 0. 3 for a big demand, 0. 5 for an average demand, and 0. 2 for a small demand, determine the alternative that provides Clay Whybark the greatest expected monetary value (EMV). P A. 4 For Problem A. 3, compute the expected value of perfect information (EVPI). *Note: OM; and means the problem may be solved with POM for Windows; means the problem may be solved with Excel P means the problem may be solved with POM for Windows and/or Excel OM. 686 MODULE A D E C I S I O N -M A K I N G T O O L S H. Weiss, Inc. is considering building a sensitive new airport scanning device. His managers believe that there is a probability of 0. 4 that the ATR Co. will come out with a competitive product. If Weiss adds an assembly line for the product and ATR Co. does not follow with a competitive product, Weiss’s expected profit is $40,000; if Weiss adds an assembly line and ATR follows suit, Weiss still expects $10,000 profit. If Weiss adds a new plant addition and ATR does not produce a competitive product, Weiss expects a profit of $600,000; if ATR does compete for this market, Weiss expects a loss of $100,000.Determine the EMV of each decision. For Problem A. 5, compute the expected value of perfect information. The following payoff table provides profits based on various possible decision alternatives and various levels of demand at Amber Gardner’s software firm: DEMAND LOW Alternative 1 Alternative 2 Alternative 3 $10,000 $ 5,000 $ 2,000 HIGH $30,000 $40,000 $50,000 P A. 5 P P A. 6 A. 7 a) b) c) The probability of low demand is 0. 4, whereas the probability of high demand is 0. 6. What is the highest possible expected monetary value? What is the expected value under certainty?Calculate the expected value of perfect information for this situation. Leah Johnson, director of Legal Services of Brookline, wants to increase capacity to provide free legal advice but must decide whether to do so by hiring another full-time lawyer or by using part-time lawyers. The table below shows the expected costs of the two options for three possible demand levels: STATES OF NATURE ALTERNATIVES Hire full-time Hire part-time Probabilities LOW DEMAND $300 $ 0 . 2 MEDIUM DEMAND $500 $350 . 5 HIGH DEMAND $ 700 $1,000 . 3 P A. 8 Using expected value, what should Ms.Johnson do? P A. 9 Chung Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosin g a process that is inappropriate. Chen Chung is VP of operations. He can choose among batch manufacturing or custom manufacturing, or he can invest in group technology. Chen won’t be able to forecast demand accurately until after he makes the process choice. Demand will be classified into four compartments: poor, fair, good, and excellent.The table below indicates the payoffs (profits) associated with each process/demand combination, as well as the probabilities of each long-term demand level. POOR Probability Batch Custom Group technology a) b) . 1 $ 200,000 $ 100,000 $1,000,000 FAIR . 4 $1,000,000 $ 300,000 $ 500,000 GOOD . 3 $1,200,000 $ 700,000 $ 500,000 EXCELLENT . 2 $1,300,000 $ 800,000 $2,000,000 Based on expected value, what choice offers the greatest gain? What would Chen Chung be willing to pay for a forecast that would accurately determine the level of demand in the future?Julie Resler’s company is considering expansion of its current facility to meet incre asing demand. If demand is high in the future, a major expansion will result in an additional profit of $800,000, but if demand is low there will be a loss of $500,000. If demand is high, a minor expansion will result in an increase in profits of $200,000, but if demand is low, there will be a loss of $100,000. The company has the option of not expanding. If there is a 50% chance demand will be high, what should the company do to maximize long-run average profits? P A. 10 P RO B L E M S 87 P A. 11 The University of Dallas bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 90 operations management students enrolled, but bookstore manager Curtis Ketterman has second thoughts, based on his intuition and some historical evidence. Curtis believes that the distribution of sales may range from 70 to 90 units, according to the foll owing probability model: Demand Probability 70 . 15 75 . 30 80 . 30 85 . 0 90 . 05 a) b) This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $36. Construct the table of conditional profits. How many copies should the bookstore stock to achieve highest expected value? Palmer Cheese Company is a small manufacturer of several different cheese products. One product is a cheese spread sold to retail outlets. Susan Palmer must decide how many cases of cheese spread to manufacture each month. The probability that demand will be 6 cases is . , for 7 cases it is . 3, for 8 cases it is . 5, and for 9 cases it is . 1. The cost of every case is $45, and the price Susan gets for each case is $95. Unfortunately, any cases not sold by the end of the month are of no value as a result of spoilage. How many cases should Susan manufacture each month? Ronald Lau, chief engineer at South Dak ota Electronics, has to decide whether to build a new state-of-the-art processing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, South Dakota Electronics could lose $180,000.At this time, Lau estimates a 60% chance that the new process will fail. The other option is to build a pilot plant and then decide whether to build a complete facility. The pilot plant would cost $10,000 to build. Lau estimates a 50-50 chance that the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plant does not work, there is only a 20% chance that the complete project (if it is constructed) will work. Lau faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision?Help Lau by analyzing this problem. Karen Villagomez, president of Wright Industries, is considering whether to build a manufacturing plant in the Ozarks. Her decision is summarized in the following table: ALTERNATIVES Build large plant Build small plant Don’t build Market probabilities FAVORABLE MARKET $400,000 $ 80,000 $ 0 0. 4 UNFAVORABLE MARKET $300,000 $ 10,000 $ 0 0. 6 P A. 12 A. 13 P A. 14 a) b) c) A. 15 Construct a decision tree. Determine the best strategy using expected monetary value (EMV). What is the expected value of perfect information (EVPI)?Deborah Kellogg buys Breathalyzer test sets for the Denver Police Department. The quality of the test sets from her two suppliers is indicated in the following table: PERCENT DEFECTIVE 1 3 5 PROBABILITY LOOMBA TECHNOLOGY . 70 . 20 . 10 PROBABILITY STEWART-DOUGLAS ENTERPRISES . 30 . 30 . 40 FOR FOR a) b) For example, the probability of getting a batch of tests that are 1% defective from Loomba Technology is . 70. Because Kellogg orders 10,000 tests per order, this would mean that there is a . 7 probability of getting 100 defective tests out of the 10,000 tests if Loomba Technolo gy is used to fill the order.A defective Breathalyzer test set can be repaired for $0. 50. Although the quality of the test sets of the second supplier, Stewart-Douglas Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Loomba. Develop a decision tree. Which supplier should Kellogg use? 688 MODULE A D E C I S I O N -M A K I N G T O O L S Deborah Hollwager, a concessionaire for the Des Moines ballpark, has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd).STATES OF NATURE (SIZE OF CROWD) ALTERNATIVES Large inventory Average inventory Small inventory LARGE $20,000 $15,000 $ 9,000 AVERAGE $10,000 $12,000 $ 6,000 SMALL $2,000 $6,000 $5,000 P A. 16 a) b) If the probabilities associated with the states of nature are 0. 3 for a large crowd, 0. 5 for an average crowd, and 0. 2 for a small crowd, determine: The alternative that provides the greatest expected monetary value (EMV). The e xpected value of perfect information (EVPI). Joseph Biggs owns his own sno-cone business and lives 30 miles from a California beach resort. The sale of sno-cones is highly dependent on his location and on the weather.At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. Construct Joseph’s decision tree. What decision is recommended by the expected value criterion? Kenneth Boyer is considering opening a bicycle shop in North Chicago. Boyer enjoys biking, but this is to be a business endeavor from which he expects to make a living. He can open a small shop, a large shop, or no shop at all.Because there will be a 5-year lease on the building that Boyer is thinking about using, he wants to make sure he makes the correct decision. Boyer is also thinking about hiring his old market ing professor to conduct a marketing research study to see if there is a market for his services. The results of such a study could be either favorable or unfavorable. Develop a decision tree for Boyer. Kenneth Boyer (of Problem A. 18) has done some analysis of his bicycle shop decision. If he builds a large shop, he will earn $60,000 if the market is favorable; he will lose $40,000 if the market is unfavorable.A small shop will return a $30,000 profit with a favorable market and a $10,000 loss if the market is unfavorable. At the present time, he believes that there is a 50-50 chance of a favorable market. His former marketing professor, Y. L. Yang, will charge him $5,000 for the market research. He has estimated that there is a . 6 probability that the market survey will be favorable. Furthermore, there is a . 9 probability that the market will be favorable given a favorable outcome of the study. However, Yang has warned Boyer that there is a probability of only . 12 of a favorabl e market if the marketing research results are not favorable.Expand the decision tree of Problem A. 18 to help Boyer decide what to do. Dick Holliday is not sure what he should do. He can build either a large video rental section or a small one in his drugstore. He can also gather additional information or simply do nothing. If he gathers additional information, the results could suggest either a favorable or an unfavorable market, but it would cost him $3,000 to gather the information. Holliday believes that there is a 50-50 chance that the information will be favorable. If the rental market is favorable, Holliday will earn $15,000 with a large section or $5,000 with a small.With an unfavorable video-rental market, however, Holliday could lose $20,000 with a large section or $10,000 with a small section. Without gathering additional information, Holliday estimates that the probability of a favorable rental market is . 7. A favorable report from the study would increase the probabil ity of a favorable rental market to . 9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to . 4. Of course, Holliday could ignore these numbers and do nothing. What is your advice to Holliday? P A. 17 a) b) A. 18 A. 19 A. 20 A. 21 a) b) A. 22 Problem A. dealt with a decision facing Legal Services of Brookline. Using the data in that problem, provide: The appropriate decision tree showing payoffs and probabilities. The best alternative using expected monetary value (EMV). The city of Segovia is contemplating building a second airport to relieve congestion at the main airport and is considering two potential sites, X and Y. Hard Rock Hotels would like to purchase land to build a hotel at the new airport. The value of land has been rising in anticipation and is expected to skyrocket once the city decides between sites X and Y. Consequently, Hard Rock would like to purchase land now.Hard Rock will sell the la nd if the city chooses not to locate the airport nearby. Hard Rock has four choices: (1) buy land at X, (2) buy land at Y, (3) buy land at both X and Y, or (4) do nothing. Hard Rock has collected the following data (which are in millions of euros): SITE X Current purchase price Profits if airport and hotel built at this site Sales price if airport not built at this site 27 45 9 SITE Y 15 30 6 a) b) Hard Rock determines there is a 45% chance the airport will be built at X (hence, a 55% chance it will be built at Y). Set up the decision table. What should Hard Rock decide to do to maximize total net profit?C A S E S T U DY A. 23 689 Louisiana is busy designing new lottery â€Å"scratch-off† games. In the latest game, Bayou Boondoggle, the player is instructed to scratch off one spot: A, B, or C. A can reveal â€Å"Loser, † â€Å"Win $1,† or â€Å"Win $50. † B can reveal â€Å"Loser† or â€Å"Take a Second Chance. † C can reveal â€Å"Loserâ⠂¬  or â€Å"Win $500. † On the second chance, the player is instructed to scratch off D or E. D can reveal â€Å"Loser† or â€Å"Win $1. † E can reveal â€Å"Loser† or â€Å"Win $10. † The probabilities at A are . 9, . 09, and . 01. The probabilities at B are . 8 and . 2. The probabilities at C are . 999 and . 001. The probabilities at D are . 5 and . 5.Finally, the probabilities at E are . 95 and . 05. Draw the decision tree that represents this scenario. Use proper symbols and label all branches clearly. Calculate the expected value of this game. INTERNET HOMEWORK PROBLEMS See our Companion Web site at www. prenhall. com/heizer for these additional homework problems: A. 24 through A. 31. CASE STUDY Tom Tucker’s Liver Transplant Tom Tucker, a robust 50-year-old executive living in the northern suburbs of St. Paul, has been diagnosed by a University of Minnesota internist as having a decaying liver. Although he is otherwise healthy, Tucker ’s liver problem could prove fatal if left untreated.Firm research data are not yet available to predict the likelihood of survival for a man of Tucker’s age and condition without surgery. However, based on her own experience and recent medical journal articles, the internist tells him that if he elects to avoid surgical treatment of the liver problem, chances of survival will be approximately as follows: only a 60% chance of living 1 year, a 20% chance of surviving for 2 years, a 10% chance for 5 years, and a 10% chance of living to age 58. She places his probability of survival beyond age 58 without a liver transplant to be extremely low.The transplant operation, however, is a serious surgical procedure. Five percent of patients die during the operation or its recovery stage, with an additional 45% dying during the first year. Twenty percent survive for 5 years, 13% survive for 10 years, and 8%, 5%, and 4% survive, respectively, for 15, 20, and 25 years. Discussion Q uestions 1. Do you think that Tucker should select the transplant operation? 2. What other factors might be considered? CASE STUDY Ski Right Corp. After retiring as a physician, Bob Guthrie became an avid downhill skier on the steep slopes of the Utah Rocky Mountains.As an amateur inventor, Bob was always looking for something new. With the recent deaths of several celebrity skiers, Bob knew he could use his creative mind to make skiing safer and his bank account larger. He knew that many deaths on the slopes were caused by head injuries. Although ski helmets have been on the market for some time, most skiers consider them boring and basically ugly. As a physician, Bob knew that some type of new ski helmet was the answer. Bob’s biggest challenge was to invent a helmet that was attractive, safe, and fun to wear.Multiple colors and using the latest fashion designs would be musts. After years of skiing, Bob knew that many skiers believe that how you look on the slopes is more im portant than how you ski. His helmets would have to look good and fit in with current fashion trends. But attractive helmets were not enough. Bob had to make the helmets fun and useful. The name of the new ski helmet, Ski Right, was sure to be a winner. If Bob could come up with a good idea, he believed that there was a 20% chance that the market for the Ski Right helmet would be excellent. The chance of a good market should be 40%.Bob also knew that the market for his helmet could be only average (30% chance) or even poor (10% chance). The idea of how to make ski helmets fun and useful came to Bob on a gondola ride to the top of a mountain. A busy executive on the gondola ride was on his cell phone trying to complete a complicated merger. When the executive got off the gondola, he dropped the phone and it was crushed by the gondola mechanism. Bob decided that his new ski helmet would have a built-in cell phone and an AM/FM stereo radio. All the electronics could be operated by a co ntrol pad worn on a skier’s arm or leg.Bob decided to try a small pilot project for Ski Right. He enjoyed being retired and didn’t want a failure to cause him to go back to work. After some research, Bob found Progressive Products (PP). The company was willing to be a partner in developing the Ski Right and sharing any profits. If the market was excellent, Bob would net $5,000 per month. With a good market, Bob would net $2,000. An average market would result in a loss of $2,000, and a poor market would mean Bob would be out $5,000 per month. Another option for Bob was to have Leadville Barts (LB) make the helmet.The company had extensive experience in making bicycle helmets. Progressive would then take the helmets made by Leadville Barts and do the rest. Bob had a greater risk. He estimated that he could lose $10,000 per month in a poor market or $4,000 in an average market. A good market for Ski Right would result in $6,000 profit for Bob, and an excellent market wou ld mean a $12,000 profit per month. (continued) 690 MODULE A D E C I S I O N -M A K I N G T O O L S Cellular to make the phones, and TalRad to make the AM/FM stereo radios. Bob could then hire some friends to assemble everything and market the finishedSki Right helmets. With this final alternative, Bob could realize a net profit of $55,000 a month in an excellent market. Even if the market was just good, Bob would net $20,000. An average market, however, would mean a loss of $35,000. If the market was poor Bob would lose $60,000 per month. A third option for Bob was to use TalRad (TR), a radio company in Tallahassee, Florida. TalRad had extensive experience in making military radios. Leadville Barts could make the helmets, and Progressive Products could do the rest of production and distribution. Again, Bob would be taking on greater risk.A poor market would mean a $15,000 loss per month, and an average market would mean a $10,000 loss. A good market would result in a net profit of $7,000 for Bob. An excellent market would return $13,000 per month. Bob could also have Celestial Cellular (CC) develop the cell phones. Thus, another option was to have Celestial make the phones and have Progressive do the rest of the production and distribution. Because the cell phone was the most expensive component of the helmet, Bob could lose $30,000 per month in a poor market. He could lose $20,000 in an average market.If the market was good or excellent, Bob would see a net profit of $10,000 or $30,000 per month, respectively. Bob’s final option was to forget about Progressive Products entirely. He could use Leadville Barts to make the helmets, Celestial Discussion Questions 1. What do you recommend? 2. Compute the expected value of perfect information. 3. Was Bob completely logical in how he approached this decision problem? Source: B. Render, R. M. Stair, and M. Hanna, Quantitative Analysis for Management, 9th ed. Upper Saddle River, N. J. : Prentice Hall (2006). Re printed by permission of Prentice Hall, Inc.ADDITIONAL CASE STUDIES See our Companion Web site at www. prenhall. com/heizer for these additional free case studies: †¢ Arctic, Inc. : A refrigeration company has several major options with regard to capacity and expansion. †¢ Toledo Leather Company: This firm is trying to select new equipment based on potential costs. BIBLIOGRAPHY Brown, R. V. â€Å"The State of the Art of Decision Analysis. † Interfaces 22, 6 (November–December 1992): 5–14. Collin, Ian. â€Å"Scale Management and Risk Assessment for Deepwater Developments. † World Oil 224, no. 5 (May 2003): 62. Hammond, J. S. , R.L. Kenney, and H. Raiffa. â€Å"The Hidden Traps in Decision Making. † 76, no. 5 Harvard Business Review (September–October 1998): 47–60. Jbuedj, C. â€Å"Decision Making under Conditions of Uncertainty. † Journal of Financial Planning (October 1997): 84. Keefer, Donald L. â€Å"Balancing Drug Safety and Efficacy for a Go/NoGo Decision. † Interfaces 34, no. 2 (March–April 2004): 113–116. Kirkwood, C. W. â€Å"An Overview of Methods for Applied Decision Analysis. † Interfaces 22, 6 (November–December 1992): 28–39. Perdue, Robert K. , William J. McAllister, Peter V. King, and Bruce G. Berkey. Valuation of R and D Projects Using Options Pricing and Decision Analysis Models. † Interfaces 29, 6 (November 1999): 57–74. Raiffa, H. Decision Analysis: Introductory Lectures on Choices Under Certainty. Reading, MA: Addison-Wesley (1968). Render, B. , R. M. Stair, Jr. , and R. Balakrishnan. Managerial Decision Modeling with Spreadsheets. 2nd ed. Upper Saddle River, NJ: Prentice Hall (2006). Render, B. , R. M. Stair Jr. , and M. Hanna. Quantitative Analysis for Management, 9th ed. Upper Saddle River, NJ: Prentice Hall (2006). Schlaifer, R. Analysis of Decisions Under Certainty. New York: McGraw-Hill (1969).