Dynamic lot sizing for multiple products with a new joint replenishment model

This paper studies a new multi‐product dynamic lot sizing problem, where the inventories of all products are replenished jointly with the same quantity whenever a production occurs. Such problems may occur in poultry and some chemical industries. We first introduce the general problem that allows for demand rejection with lost sales cost, and prove that the problem is NP‐hard. Then we study a special case where all demands have to be satisfied immediately, and show that it can be solved in polynomial time. Finally, we develop two heuristic algorithms for the general problem. Through computational experiments, we demonstrate the effectiveness of the heuristics and investigate some insights related to the decision of lost sales.