A general approach to multi-item capacitated dynamic lot-sizing problems

In this paper, we solve the multi-item capacitated dynamic lot-sizing problems, where each item faces a series of dynamic demand and in each period, multiple items share limited production resources. The objective is to find the optimal production plan so as to minimize the total cost, including production cost, inventory holding cost, and fixed setup cost. We consider both single-level and multi-level cases; in the multi-level case, some items are consumed in order to produce some other items and therefore, items face internally generated demands in addition to external demands. We propose a simple two-stage approach, which is applicable to both classes of problems. Extensive experiments show that the approach gives very good performance compared with the existing methods. We then provide an analysis on how the superior performance is achieved. Besides its performance, one appealing feature of our method is its simplicity and general applicability.