Heuristic procedures for a stochastic lot-sizing problem in make-to-order manufacturing

We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-to-order company producing steel pipes. Since no finished goods inventory is kept, a delivery date is fixed upon arrival of each order. The objective is to determine the optimal size of production lots so that delivery dates are met as closely as possible with a limited number of set-ups. Orders that are not satisfied on time are backordered and a penalty cost is incurred in those cases. We formulate the problem as a Markov Decision Process and determine the optimal production policy by dynamic programming. Since this approach can only be applied to very small examples, attention is given to the development of three simple lot-sizing rules. The first strategy consists of producing the orders for a fixed number T of periods whenever the demand for the current period reaches a pre-specified limit x. A simple set of tests is proposed leading to cost improvements in situations where the best combination for the decision variables x and T deviates from the optimal policy. The second lot-sizing rule is based on the well-known Silver-Meal heuristic for the case of deterministic time-varying demand. A fixed cycle production strategy is also derived. Numerical examples taking into account different demand patterns are provided. The analysis of the results suggests that the first heuristic is particularly suitable for the problem under consideration. Finally, the model is incorporated in the operations control level of the hierarchical production planning system of the Dutch company and assists the management in the evaluation of the quality of the aggregate decisions. A consequence of this feedback mechanism is the modification of the aggregate plans.

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