Integrated production and transportation scheduling with order-dependent inventory holding costs

Abstract In this study, we consider an integrated production and transportation scheduling problem faced by make-to-order manufacturers that adopt a commit-to-delivery business mode and cooperate with third-party logistics providers to deliver processed products to customers. The third-party logistics providers typically offer multiple shipping modes chosen by the manufacturers to deliver products, each shipping mode with a shipping time guarantee and a shipping cost function that is non-increasing in shipping time and sub-additive, non-decreasing in shipping quantity. The problem involves inventory holding costs which not only depend on the time that the products spend in temporary storage but also depend on customer types. The problem is to determine an integrated production and shipping schedule that satisfies the committed delivery due date limitations for the customers, such that the total cost of shipping and inventory holding is minimized. We investigate two cases with and without split delivery. For both cases, we first show that both of them are ordinarily NP-hard, prove that there exist no polynomial-time approximation algorithms with constant worst-case ratios, propose exact algorithms to solve them, and finally design column generation-based heuristic algorithms to find feasible solutions. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions efficiently. We also consider two interesting practical variants of the problem.