A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) 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. It is also assumed that backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. The computational results from a set of simulation experiments are also presented.