Integrated production and transportation scheduling problem under nonlinear cost structures

We consider an integrated production and transportation scheduling problem arising in several make-to-order settings, where customer orders have release times and pre-specified delivery time windows. These orders are first processed in a plant and, thereafter, delivered to their customer sites by transporters (e.g., freight trains, ships, or air flights) with fixed departure times and nonlinear transportation cost functions. If the processing of an order is completed but not immediately delivered, it will be stored temporarily, incurring inventory holding costs. The objective is finding an integrated schedule for production and transportation such that the total cost of inventory holding and transportation is minimized. In this study, we consider the following two cases: one where partial delivery is not allowed, and the other where partial delivery is allowed. For each case, we propose an exact algorithm to find optimal solutions for small-scale instances, and a heuristic algorithm to find near-optimal solutions for large-scale instances. For the randomly generated test instances, the computational results reveal that the exact algorithms significantly outperform a commercial optimization solver in terms of the computational times and the number of instances solved within a specified time limit, and the heuristic algorithms are capable of generating near-optimal solutions within a reasonable computational time. Finally, we incorporate considerations of sequence-dependent setup time into the problem and apply the approaches for designing the algorithms to address the more general problem.