(BQ) Part 2 book "Mechanical engineering systems" has contents: Integer programming, nonlinear programming, game theory, decision analysis, markov chains, queueing theory, the application of queueing theory, inventory theory, markov decision processes, simulation. | 12 Integer Programming In Chap. 3 you saw several examples of the numerous and diverse applications of linear programming. However, one key limitation that prevents many more applications is the assumption of divisibility (see Sec. ), which requires that noninteger values be permissible for decision variables. In many practical problems, the decision variables actually make sense only if they have integer values. For example, it is often necessary to assign people, machines, and vehicles to activities in integer quantities. If requiring integer values is the only way in which a problem deviates from a linear programming formulation, then it is an integer programming (IP) problem. (The more complete name is integer linear programming, but the adjective linear normally is dropped except when this problem is contrasted with the more esoteric integer nonlinear programming problem, which is beyond the scope of this book.) The mathematical model for integer programming is the linear programming model (see Sec. ) with the one additional restriction that the variables must have integer values. If only some of the variables are required to have integer values (so the divisibility assumption holds for the rest), this model is referred to as mixed integer programming (MIP). When distinguishing the all-integer problem from this mixed case, we call the former pure integer programming. For example, the Wyndor Glass Co. problem presented in Sec. actually would have been an IP problem if the two decision variables x1 and x2 had represented the total number of units to be produced of products 1 and 2, respectively, instead of the production rates. Because both products (glass doors and wood-framed windows) necessarily come in whole units, x1 and x2 would have to be restricted to integer values. Another example of an IP problem is provided by the prize-winning OR study done for the San Francisco Police Department that we introduced (and referenced) in Sec. . As .
