Abstract
In this chapter we shall consider applications of mathematical programming arising in various contexts. We shall examine the problem faced by the client, the model built, and the use to which it would be put. Problems will be ones that require financial modeling, modeling of the closing and opening of facilities, modeling across time periods, discounting over time, using opening and closing balances, and using hard and soft constraints in model development. Each case will demonstrate the need for a model of a particular type. A formulation of each model is provided in MCOL, so that the reader may solve the problem and investigate the results. In some cases it will be possible to formulate the problem in several contrasting ways. Some of the benefits of the alternative formulations will be discussed. In the second half of the chapter the focus will be on difficulties that commonly arise when we try to run models and solve problems. We discuss how to get around infeasibilities and illuminate certain aspects of sensitivity analysis.
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Notes
- 1.
The expression \(\left \lfloor x\right \rfloor \) means return the largest integer number not exceeding x. If x is a positive number, then \( \left \lfloor x\right \rfloor \) yields the integral part of x, i.e. , \(\left \lfloor 4.5\right \rfloor =4.\)
- 2.
An IIS facility is available, for instance, cplex or xpress-optimizer .
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Kallrath, J. (2021). Case Studies and Problem Formulations. In: Business Optimization Using Mathematical Programming. International Series in Operations Research & Management Science, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-030-73237-0_8
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DOI: https://doi.org/10.1007/978-3-030-73237-0_8
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