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Spreadsheet supplement for case UV6133.

Benecol Spread, a cholesterol-lowering margarine, was a product with unusual media-planning challenges. With a narrow target group and unproven market potential, Johnson & Johnson needed to get the most "bang for the buck" from its Benecol advertising. Would a media-planning model (optimizer) requiring executives to quantify their judgment on several key inputs be helpful in this process? A spreadsheet accompanying the case allows students to weight the target groups and to choose among different advertising vehicles to form the best possible media plan.

After years of development, William Krause knew that 2014 was the year to "go big or go home." His Flexible Herbert Screw, a medical device intended to support the healing of fractured collarbones (clavicles), was ready for launch, and he had accumulated the necessary cash?$1 million by his reckoning?needed to comfortably see him through the start-up phase. Although evidence in favor of the invasive device was still inconclusive, other key players were now entering the space with remarkably similar technologies.

Spreadsheet Supplement for UV2930.

We refer to a model that uses mathematical programming to find an optimal quantity as an optimization model. Thus, an optimization model differs from an evaluation model in that it goes beyond simply evaluating the consequences of proposed alternatives: It actually identifies the "optimal" alternative. How does an optimization model accomplish this impressive task? In this age of readily available computing power and ever more user-friendly software, it is possible to build and use optimization models without a detailed understanding of the mathematics that underlie the answer to this question. To truly take advantage of this capability, however, it is necessary to have a basic understanding of some core concepts. The primary objective of this note is to introduce these concepts. This note is highly pragmatic; the companion note "The Mathematics of Optimization" (UV4309) explores more deeply the mathematical foundations of the concepts and is designed for the user with the motivation and mathematical background to further explore the topic.

This technical note provides a mostly nontechnical introduction to analytical probability distributions. The distributions covered are: uniform, triangular, normal, Poisson, exponential, lognormal, and binomial.

This comprehensive technical note explains linear regression. It is intended for students with no prior knowlede of the topic. It is devided into nine sections, which may be assigned separately: 1. The simple linear model, 2. Fitting the model using least Squares, 3. Important properties of the least-squares regression line, 4. Summary regression statistics, 5. Assumptions behind the linear model, 6. Model-building Philosophy, 7. Forecasting using the linear model, 8. Using dummy variables to represent categorical variables, and 9. Useful data transformations. The sections correspond to stand-alone notes also available through Darden Business Publishing

The creator of special-event T-shirts has to decide how many shirts to order for an upcoming rock concert. Although she has a best guess and maximum and minimum estimates of attendance at the concert, her decision is complicated by this particular group's history of canceling at the last minute, in which case she would be stuck with all the T-shirts.

This note introduces simulation as a tool to analyze uncertainty in business decisions. It first observes the limitations of single point or simple range estimates of key uncertainties, thereby motivating the need to create a risk profile for any alternative that characterizes the full range of possible outcomes and their relative likelihoods. A simple example involving both a discrete and a continuous (triangle) distribution is used. The note is simulation software independent, although output from Crystal Ball is displayed.

The problem set contains three problems designed to help students practice their ability to build math programming models. Problem # 1 is a portfolio problem where the student is asked to find a portfolio that minimizes risk (variance) subject to a required rate of return; as such, it is nonlinear. Problem # 2 is aggregate production scheduling; hence, linear. Problem # 3 involves determining how to source a fixed quantity from a menu of vendors with differing fixed- ordering charges and per-unit prices; it is a mixed integer model. All are sufficiently small that they can be easily optimized with standard math programming software (such as Excel's standard Solver).

A road construction company needs a new asphalt plant and must decide between two options: a drum plant with a 10-year life or a batch plant with a 5-year life. In addition, the company must decide which of two offers to accept from local dealerships for heavy equipment to support the new plant. The case provides comparison of net present value, internal rate of return, payback, and profitability index as criteria for making investment decisions.

Supplement for case UV6133

At the core of this case is a distribution, or sourcing, problem that can be modeled and solved using linear programming (LP). There are also issues of whether to build (a) new plant(s)--and if so, what the capacity should be--and whether to expand or close one or more of the existing plants. These latter issues can be analyzed using a 0/1 LP facility-location model. Alternatively, because the number of options is limited, they can be analyzed using the straight LP model of the distribution problem as a tool to facilitate analysis.

This case describes the coal-procurement process of a small electric utility. The manager of the production fuel department must decide how much coal to purchase from each vendor and how to allocate the purchased coal among the utility's three coal-burning plants. The situation can be modeled and solved as a linear program. Sensitivity analysis can be used to help formulate a strategy for negotiating with the vendors and to address other special issues.

This case is a good introductory linear-programming case; it introduces the notion of constraint exploitation and provides practice in deciding between alternative forecasting techniques (including exponential smoothing). The case contains a decision-uncertainty structure. A production planner must determine whether or not to take a contract for future delivery of a specified product at a stated price. The decision will affect the production mix in future periods. Uncertainty surrounding the future market price of the product is crucial. In the B case (UVA-QA-0391) a second constraining resource is introduced to the decision environment.