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Optimization Modeling with Spreadsheets, 3rd Edition by Kenneth R. Baker

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2LINEAR PROGRAMMING: ALLOCATION, COVERING, AND BLENDING MODELS

The linear programming model is a very rich context for examining business decisions. A large variety of applications has been reported in the 50 years or so that computers have been available for this type of decision support. Some of the routine early uses of linear programming appeared in operations management and led, for example, to the optimization of transportation and distribution plans, production schedules, and make/buy decisions. Later, linear programming moved into other business functions. Examples of such applications included the optimization of investment portfolios, advertising expenditures, procurement decisions, and staffing plans. Opportunities for applying linear programming continue to occur, and linear programming may therefore represent the most valuable optimization tool available today.

Our first task in this chapter is to describe the features of linearity in optimization models. We then begin our survey of linear programming models, which carries through the next three chapters as well. Appendix 2 provides a graphical perspective on linear programming. This material may help with an understanding of the linear programming model, but it is not essential for proceeding with spreadsheet-based approaches.

The term linear refers to properties of the objective function and the constraints. A linear function exhibits proportionality, additivity, and divisibility. Proportionality means that the contribution ...

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