A Lagrangian-based heuristic algorithm for multi-product capacitated lot sizing with time-varying transportation costs

This paper addresses multi-product, multi-period, dynamic lot sizing problem with time-varying transportation costs, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. The carrying capacity of single container and number of containers available for use in each period is limited. The objective of this study is to simultaneously determine the lot sizes and the transportation policy that minimizes the total costs, which consist of ordering cost, inventory cost, and freight cost. Because this problem is NP-hard, a lagrangian-based heuristic algorithm is proposed to compute lower and upper bounds, of which comprehensive computational experiments show the compelling performance in terms of quality and speed.