Production strategies for a stochastic lot-sizing problem with constant capacity

This paper presents a single item capacitated stochastic lot-sizing problem motivated by a Dutch company operating in a Make-To-Order environment. Due to a highly fluctuating and unpredictable demand, it is not possible to keep any finished goods inventory. In response to a customer's order, a fixed delivery date is quoted by the company. The objective is to determine in each period of the planning horizon the optimal size of production lots so that delivery dates are met as closely as possible at the expense of minimal average costs. These include set-up costs, holding costs for orders that are finished before their promised delivery date and penalty costs for orders that are not satisfied on time and are therefore backordered. Given that the optimal production policy is likely to be too complex in this situation, attention is focused on the development of heuristic procedures. In this paper two heuristics are proposed. The first one is an extension of a simple production strategy derived by Dellaert for the uncapacitated version of the problem. The second heuristic is based on the well-known Silver–Meal algorithm for the case of deterministic time-varying demand. Experimental results suggest that the first heuristic gives low average costs especially when the demand variability is low and there are large differences in the cost parameters. The Silver–Meal approach is usually outperformed by the first heuristic in situations where the available production capacity is tight and the demand variability is low.