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Dynamic Programming Models

Many planning and control problems in manufacturing, telecommunications and capital budgeting call for a sequence of decisions to be made at fixed points in time. The initial decision is followed by a second, the second by a third, and so on perhaps infinitely. Because the word dynamic describes situations that occur over time and programming is a synonym for planning, the original definition of dynamic programming was “planning over time.” In a limited sense, our concern is with decisions that relate to and affect phenomena that are functions of time. This is in contrast to other forms of mathematical programming that often, but not always, describe static decision problems. As is true in many fields, the original definition has been broadened somewhat over the years to connote an analytic approach to problems involving decisions that are not necessarily sequential but can be viewed as such. In this expanded sense, dynamic programming (DP) has come to embrace a solution methodology in addition to a class of planning problems. It is put to the best advantage when the decision set is bounded and discrete, and the objective function is nonlinear.