An effective approach to multi-item capacitated dynamic lot-sizing problems

In this study we solve the multi-item capacitated dynamic lot-sizing problem, where each item faces a series of dynamic demands, and in each period multiple items share limited production resources. The objective is to find the optimal production plan so as to minimise 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 demand in addition to external demands. We propose a simple three-stage approach that is applicable to both classes of problems. In the first stage we perform preprocessing, which is designed to deal with the difficulty due to the joint setup cost (a fixed cost incurred whenever production occurs in a period). In the second stage we adopt a period-by-period heuristic to construct a feasible solution, and in the final stage we further improve the solution by solving a series of subproblems. Extensive experiments show that the approach exhibits very good performance. We then analyse how the superior performance is achieved. In addition to its performance, one appealing feature of our method is its simplicity and general applicability.