Production and Transportation Integration for Commit-to-Delivery Mode with General Shipping Costs

Feng Li (), Zhou Xu () and Zhi-Long Chen ()
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Feng Li: School of Management, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China;
Zhou Xu: Department of Logistics and Maritime Studies, Faculty of Business, Hong Kong Polytechnic University, Kowloon, Hong Kong;
Zhi-Long Chen: Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742

INFORMS Journal on Computing, 2020, vol. 32, issue 4, 1012-1029

Abstract: We study an integrated production and transportation problem for a make-to-order manufacturing company that operates under the commit-to-delivery mode and uses third-party logistics service providers to deliver products to customers on or before certain committed delivery dates. Such third-party logistics service providers often provide various shipping modes with quantity discounts and different guaranteed shipping times. As a result, the company’s shipping costs need to be represented by general shipping cost functions that are typically nondecreasing, subadditive, and piecewise linear with shipping quantities, and nonincreasing with guaranteed shipping times. To the best of our knowledge, this paper is the first attempt to solve such an integrated production and transportation problem for the commit-to-delivery mode with general shipping costs. We prove that with general shipping costs, the problem is strongly N P -hard when the planning horizon consists of an arbitrary number of days. For the two-day problem, we show that it is ordinarily N P -hard, but is unlikely to have a fully polynomial time approximation scheme (FPTAS) unless N P = P . Interestingly, we find that when the unit inventory holding cost is relatively small, which is often true in practice, there exists an FPTAS for the two-day problem, the development of which hinges on a newly discovered property for minimizing the sum of two general piecewise linear functions. For the multiday problem, we develop a heuristic algorithm based on column generation, which novelly uses a dynamic program for a variant of the problem with a single customer. Results from computational experiments demonstrate that the heuristic algorithm can find near-optimal solutions with optimality gaps less than 1% in a short running time.

Keywords: integrated production and transportation; commit-to-delivery mode; general shipping cost functions; computational complexity; algorithm analysis; integer programming; column generation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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