This note introduces four analytical probability distributions and the underlying uncertain processes from which they can be derived. It demonstrates that, when we can build a reasonable model of an uncertain process, we can use the model to derive the probability distribution from fundamental principles and forgo the chore of estimating the distribution subjectively by assessing fractiles. The probability distributions discussed are the binomial, normal, Poisson, and exponential. The associated processes discussed include counting, accumulation, Poisson, and memoryless. The note emphasizes that, although these probability distributions have many legitimate applications, they are applicable only when the specific assumptions about the underlying processes are satisfied--that is, when the uncertain quantity is obtained from a process similar to the one used to drive the probability distribution in the first place.
Used in conjunction with UV0697 and UV0698. Three couples, all good friends, rent a beach house for the week. They all have different financial circumstances and different beliefs about what's fair. They need to find a way to decide who sleeps where, and how to divide the costs of the beach house.
Avion is interested in a new valve to manage the highly volatile phenol in its production process. Avion and Orion strike a deal for Orion to try to produce these valves. There are time, engineering, and software constraints that make the valve-redesign project a risky endeavor. The A case (UVA-QA-0602) consists of a basic decision tree that has been used as an introductory case in decision analysis and in the core material for an exam. The A case is a rewrite of two earlier cases (QA-0480 and QA-0481). In those cases, the key issues surround the scheduling of the projects, leading to insights about which to schedule first. Here, the scheduling is fixed and the issues are less calculation-intensive and more interesting. In the A case, there are two options: one the students usually see and one they don't. The B case consists of a quick series of changes in the situation that leads to a totally different decision structure and requirement for simulation modeling (or some other technique to handle the introduction of continuous uncertainties). This case also has a wonderful real option embedded in the problem around which an entire class can be built. Because the estimate is continuous, the option problem becomes one of finding the optimal estimated-performance value at which one aborts the software redesign.
Avion is interested in a new valve to manage the highly volatile phenol in its production process. Avion and Orion strike a deal for Orion to try to produce these valves. There are time, engineering, and software constraints that make the valve-redesign project a risky endeavor. The A case uses the basic decision tree that has been used in an introductory case in decision analysis to the core material for an exam. The A case is a rewrite of two earlier cases (QA-0480 and QA-0481). In those cases, the key issues were scheduling of the projects, and in this case, the scheduling is fixed and the issues are less calculation-intensive and more interesting. Also in the A case, there are two options: one the students usually see and one they don't. This case also has a real option embedded in the problem around which an entire class can be built. Followed by the B case, QA-0603.
Sparta Glass Products has been losing significant market share over the last several quarters in the non-glare-glass market, with a price 10% above the competition. Lowering the price is under consideration. Unfortunately, fully allocated costs are such that the lower price results in a loss. Issues to be discussed and analyses to be conducted include the relevant costs for the decision and the reactions from competitors.
This set of three cases represents a mediation involving three professionals at a consulting firm: two disputants (a new MBA consultant and the manager of a group of programmers) both working on a client team, and an "interested" mediator with his own pressures and agenda, who would prefer to focus on business issues and resolve the dispute quickly. The dimensions of the dispute are both professional (whether changes should be made to a computer system being installed by the team) and personal (issues of respect and authority). The cases are designed to be used as part of a unit on mediation. We use the cases in a series of cases that permits each student to serve in disputant and mediator roles. Class discussion (see Teaching Note) focuses on skills, the process of mediation, resolutions reached, and the role of the "interested mediator," a role in which MBA graduates frequently find themselves.
This set of three cases represents a mediation involving three professionals at a consulting firm: two disputants (a new MBA consultant and the manager of a group of programmers) both working on a client team, and an "interested" mediator with his own pressures and agenda, who would prefer to focus on business issues and resolve the dispute quickly. The dimensions of the dispute are both professional (whether changes should be made to a computer system being installed by the team) and personal (issues of respect and authority). The cases are designed to be used as part of a unit on mediation. We use the cases in a series of cases that permits each student to serve in disputant and mediator roles. Class discussion (see Teaching Note) focuses on skills, the process of mediation, resolutions reached, and the role of the "interested mediator," a role in which MBA graduates frequently find themselves.
This set of three cases represents a mediation involving three professionals at a consulting firm: two disputants (a new MBA consultant and the manager of a group of programmers) both working on a client team, and an "interested" mediator with his own pressures and agenda, who would prefer to focus on business issues and resolve the dispute quickly. The dimensions of the dispute are both professional (whether changes should be made to a computer system being installed by the team) and personal (issues of respect and authority). The cases are designed to be used as part of a unit on mediation. We use the cases in a series of cases that permits each student to serve in disputant and mediator roles. Class discussion (see Teaching Note) focuses on skills, the process of mediation, resolutions reached, and the role of the "interested mediator," a role in which MBA graduates frequently find themselves.
The Liquid Gold cases (see also the B case, UVA-QA-0588) are an adaptation of the earlier Calambra Olive Oil cases (UVA-QA-0440 and UVA-QA-0442). This version supports a modified classroom experience. The cases describe the start-up of Calambra, a company built to sell a premier brand of olive oil. Frank Lockfeld, the founder, has to determine how much olive oil to make for the second year's production. Unfortunately, he has to make this decision before learning the results of the first year's sales. Thus, there is enormous uncertainty around the decision. The A case tells the start-up story and presents enough information for students to do a sensitivity analysis to decide which of the many uncertainties are most important, which leads to a discussion of tornado diagrams. The B case provides information on those critical uncertainties, which leads to a discussion of spreadsheet modeling and simulation modeling, searching for an optimal order quantity, adjusting for risk, etc. It also affords a discussion of a key general business issue: the difference between make-to-order and make-to-inventory businesses and the fundamental flaw in most business plans that leads to gross overestimates of potential profitability. Student spreadsheet files are available.
The Liquid Gold cases are an adaptation of the original Calambra Olive Oil cases (UV3774 and UV3777). This version has been written to support a modified classroom experience. The cases describe the start-up of Calambra, a company built to sell a premier brand of olive oil. Frank Lockfeld, the founder, has to determine how much olive oil to make for the second year's production. Unfortunately, he has to make this decision before learning the results of the first year's sales. Thus, there is enormous uncertainty around the decision. The A case (UV3849) tells the start-up story and presents enough information for students to do a sensitivity analysis to decide which of the many uncertainties are most important. This leads to a discussion of tornado diagrams. The B case provides information on those critical uncertainties. This leads to a class on spreadsheet modeling and simulation modeling, searching for an optimal order quantity, adjusting for risk, etc. It also enables a discussion of a key general business issue: the difference between make-to-order and make-to-inventory businesses and the fundamental flaw in most business plans that leads to gross overestimates of potential profitability.
This case focuses on a fictional company's satellite launch vehicle decision. The basis analysis requires the student to construct a decision tree using discrete probabilities. Further analysis can include the value of information and the value of control. The scope of the decision can include Monte Carlo simulation once continuous probabilities are added to the base case. This case has been used as a quiz.
exciting mystery movie. Walsh has the final say on the development and production of movie scripts for major box-office release. This new movie idea, like so many others in the film industry, is risky. It could become a blockbuster hit, but it could also become a costly failure. Alternatively, Anderson could recommend that Walsh forgo production of the movie drama and use the studio's currently available resources to produce a film from another script for Home Box Office (HBO). Anderson has to determine the best use of the studio's current production resources. The HBO option would provide fairly certain profits. Conversely, a huge hit at the box office could put High Places on the map as a major contender among the Hollywood studios, but a flop could incur significant losses, which High Places could ill afford. See also the B case, UVA-QA-0547.
In the B case, a question arises concerning what type of contract to offer the film's star. Should the studio offer a standard fixed-fee contract, or should it offer a smaller fixed fee plus a percentage of the gross? Moreover, which alternative would the star prefer? See also the A case, UV6214.
Emergency Vehicle Positioning, Inc. (EVPI) has developed a satellite-based tracking system that continuously updates and displays the location of every vehicle in its network. A recently signed contract presents new technical challenges that may make the normally installed system inadequate. While it is possible to augment the system so that it will definitely work, doing so would entail considerable cost. This case is a modified version of "Integrated Siting Systems, Inc." [UV0355]. The only difference is that the latter case provides all possible conditional probabilities, offering a slightly different introduction to Bayes Theorem. In this case, only the recent conditional probabilities are provided. Indeed, except for the name, date, final paragraph (which mentions the other probabilities), and the exhibit on conditional probabilities, the cases are identical. Therefore, the teaching note for the Integrated Siting Systems case [UV0356] is also appropriate for this case.
Harimann International, a small producer of finished textiles, receives a large, unexpected order at the beginning of the off-season. Unfortunately, none of the available embroiderers (subcontractors) can commit to finishing the goods in time for internal processing (bleaching, cutting, sewing, washing, and packing) to be completed in time to guarantee the shipping date. This case offers a rich context for analyzing problem solving under uncertain conditions and exploring risk-reduction opportunities.
TourAmerica is negotiating a master contract with Voyager Inn International (Bethesda) for hotel rooms during the 1995 tourist season. Issues under consideration include number of rooms during peak, mid-, and off-periods, room rates, breakfast prices, and the cost of ancillary services. While the hotel manager is evaluated on the basis of several criteria, including adjusted daily rates, occupancy rates, and food and beverage profitability, and is also provided with a utility scheme to facilitate trade-offs among the criteria, TourAmerica uses an effective cost per registrant (adjusted for intangibles). These two approaches provide an opportunity to contrast measurement schemes and to justify the use of utility functions. This case is a role-play exercise and must be used in conjunction with "Voyager Inn International" (UV0357).
Voyager Inn International (Bethesda) is negotiating a master contract with TourAmerica, an international tour operator, for hotel rooms during the 1995 tourist season. Issues under consideration include number of rooms during peak, mid-, and off-periods; room rates; breakfast prices; and the cost of ancillary services. The hotel manager is evaluated on the basis of several criteria, including adjusted daily rates, occupancy rates, and food and beverage profitability. To facilitate trade-offs among the various criteria, the manager articulates a utility scheme. This case is a role-play exercise, and must be used in conjunction with "TourAmerica" (UV0679). Reporting forms for the evaluation of alternative contracts are provided with each case.
The B case describes Frank Lockfeld building a spreadsheet model that captures the essence of the discussion in the A case. Since this is a difficult model to build, we recommend using the B case when teaching the Calambra Olive Oil sequence early in a module on Monte Carlo simulation. The model, which is also available electronically and should be distributed with the B case, is set up to evaluate scenarios and compare (in multiple columns) the affect of different order quantities for the specified scenario. To turn the model into a simulation model, all the students need do is replace the scenario drivers with probability distributions. Note: the C case may be used in place of--NOT IN ADDITION TO--the B case. Rather than evaluate different order quantities in columns, the C case uses data tables.