Production Smoothing of Economic Lot Sizes with Non-Decreasing Requirements

This paper considers the problem of finding a production schedule, in terms of how much to produce in each period, that minimizes the total cost of supplying known market requirements for a single product. The costs include a concave production cost, a concave inventory cost, and a piecewise concave cost of changing the production level from one period to the next. Assuming that there is no backlogging of requirements and that the market requirements are monotone increasing, i.e., not decreasing from period to period, the form of the minimum cost production schedule is obtained. This form is then exploited in a dynamic programming algorithm to provide an efficient means of exactly determining the minimum cost schedule. An interesting calculation reducing theorem is also developed to further enhance the efficiency of the dynamic programming algorithm.