TABLE OF CONTENTS With the first significant use of operations research during World War II, academicresearchers were eager to begin tackling corporate operations problems in the late 1940s and 1950s.There were immediate gains in better theories for inventory management (see the section oninventory above), scheduling algorithms, and mathematical programming approaches to operationsplanning (see Manne [19]).
A mathematical program is a formally structuredmathematical problem in which an objective function of many variables and their coefficients isto be minimized (if we want to minimize, say, cost) or maximized (if we want to maximize profit)subject to constraints that are also composed of many variables and their coefficients. Theseproblems have true mathematically optimal solutions: There is no lower cost solution (or higherprofit) than the optimal solution. In linear programs, all of the terms in both the objectivefunction and constraints are simply sums of the individual variables times their coefficients, withno variables squared or cubed and no variables multiplied times each other. Linear programvariables can typically take on any positive value, whole numbers or fractions. Integer programsrestrict variable values to integers (whole numbers) and are often used as switches to indicatethat you will or will not undertake a certain activity (I will make some of a product this week andincur the entire setup cost for it, or I will not). Mixed integer linear programs restrict somevariables in a problem to integer values, but not most of the variables. Nonlinear programs havevariables taken to other powers (squared, for example, in a...
