Stochastic lot-sizing: Solution and heuristic methods

The authors consider a single item stochastic lot-sizing model motivated by a Dutch company operating in a make-to-order environment. Since there is no possibility for having stocks on hand, every customer’s order received a fixed delivery date upon arrival. The objective is to determine the optimal size of production lots so the delivery dates are met as closely as possible at the expense of minimal costs. These include set-up costs, holding costs for orders that are finished before their delivery date and penalty costs for orders that are not satisfied on time and therefore backordered. The authors model this problem as a Markov Decision Process. Given that the optimal production policy is likely to be too complex, attention is focused on the development of heuristic procedures. In this paper three lot-sizing rules are proposed for both the uncapacitated and capacitated versions of the problem. The first one is a simple production strategy where the orders for a certain number of periods are produced whenever the demand for the current period is above a given value. The second lot-sizing strategy is based on the well-known Silver-Meal algorithm for the case of deterministic time-varying demand. The third rule is a fixed cyclic strategy. Numerical results are presented for some test problems with demand distribution close to real situations. The performance of the lot-sizing rules is analysed considering several capacity levels.