Production and transportation integration for a make-to-order manufacturing company with a commit-to-delivery business mode

When a make-to-order manufacturing company adopts a commit-to-delivery business mode, it commits a delivery due date for an order and is responsible for the shipping cost. Without loss of generality, we consider that transportation is done by a third-party logistics company, such as FedEx or UPS, which provides multiple shipping modes such as overnight, one-day, two-day delivery, and more. When the transportation time has to be short, clearly, shipping cost is more expensive than it could have been. How should a company schedule production for accepted orders so that the company can leave enough transportation time for orders to take slow shipping modes to reduce the shipping cost? We study this problem of integrating the production and transportation functions for a manufacturing company producing a variety of customized products in a make-to-order environment with a commit-to-delivery mode of business. Various realistic scenarios are investigated in increasing order of complexity. When partial delivery is allowed by customers, we provide both a mixed-integer programming (MIP) model and a minimum cost flow model. We show that nonpreemptive earliest due date (NEDD) production schedules are optimal when partial delivery is allowed and shipping cost is a decreasing convex function with transportation time. When partial delivery is not allowed, we develop an MIP model and prove that the problem is NP-hard. An efficient heuristic algorithm with polynomial computation time is provided for the NP-hard problem. It gives near-optimal production schedules, as shown via thousands of numerical experiments. We also provide models and analysis for other scenarios where shipping cost accounts for customer locations and quantity discounts.