Linear programming, or so-called "solver" PC software, can be used to figure out the best answer to an assortment of questions expressed in terms of functional relationships. In a fundamental sense, linear programming is a straightforward development from the more basic "what if" approach to problem solving. In a traditional "what-if" approach, one simply enters data or a change in input values in a computer spreadsheet and uses spreadsheet formulas and macros to calculate resulting output values. A prime advantage of the "what if" approach is that it allows managers to consider the cost, revenue, and profit implications of changes in a wide variety of operating conditions. An important limitation of the "what if" method is that it can become a tedious means of searching for the best answer to planning and operating decisions.

Linear programming can be thought of as performing "what-if in reverse." All you do is specify appropriate objectives and a series of constraint conditions, and the software will determine the appropriate input values. When production goals are specified in light of operating constraints, linear programming can be used to identify the cost-minimizing operating plan. Alternatively, using linear programming techniques, a manager might find the profit-maximizing activity level by specifying production relationships and the amount of available resources.

Linear programming has proven to be an adept tool for solving problems encountered in a number of business, engineering, financial, and scientific applications. In a practical sense, typically encountered constrained optimization problems seldom have a simple rule-of-thumb solution. This chapter illustrates how linear programming can be used to quickly and easily solve real-world decision problems.1

1 Kornelia Heusener and Gesa Von Wichert, "Profit Pressure in the Cargo Industry," The Wall Street Journal Online, March 18, 2002 (

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