Linear Programming and Sequential Decisions

Using an illustration drawn from the area of inventory control, this paper demonstrates how a typical sequential probabilistic model may be formulated in terms of (a) an initial decision rule and (b) a Markov process, and then optimized by means of linear programming. This linear programming technique may turn out to be an efficient alternative to the functional equation approach in the numerical analysis of such problems. Regardless of computational significance, however, it is of interest that there should be such a close relationship between the two traditionally distinct areas of dynamic programming and linear programming.