Integrated Production and Transportation Problem With Order Waiting

ABSTRACT We study production and transportation integration in a make‐to‐order environment with time‐dependent waiting and inventory holding costs. In this problem, manufacturers receive orders from customers, produce and then transport the products to customers, resulting in associated production and transportation costs. Orders, upon receipt, are not immediately produced, and likewise, once produced, they are not instantly transported. This delay in processes incurs additional costs, specifically order waiting costs resulting from the gap between receipt and transportation, and inventory holding costs due to the storage of products preceding their transportation. The objective is to determine an integrated plan of production and transportation that minimizes the total cost of production, waiting, inventory holding, and transportation. We first show that the problem is strongly NP‐hard, and then develop a primal‐dual heuristic algorithm with a worst‐case bound of two. The computational results demonstrate that our algorithms perform well based on randomly generated instances. Finally, we incorporate both limited production capacity and unit production cost into the problem, and extend the proposed algorithm to solve the problem. Additionally, we conduct computational experiments to demonstrate the efficiency and efficacy of the algorithm.