Production and delivery scheduling problem with delivery times and costs dependent on batch-size

In this paper, we study a real‐industrial case of an integrated lot sizing and delivery scheduling problem with multi‐capacitated transporters, distinct due dates considerations and batch‐size‐dependent delivery times and costs. The objective is to find a coordinated lot sizing and scheduling scheme so that the total cost is minimised while guaranteeing a certain service level at the manufacturers. A mathematical formulation of the problem is given as a nonlinear model in a general way. We prove dominance properties among the solutions of the problem and propose two solving methods. The first one is a generalised dynamic programming scheme to solve this problem in the case of homogeneous and heterogeneous transporters, and the second one is a mixed integer programming formulation proposed to evaluate the performance of the dynamic programming method. Computational experiments show that the proposed approach is very efficient for solving from small to medium‐sized instances, especially for the identical transporter case.