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

AboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to Section HomeINFORMS Journal on ComputingVol. 32, No. 4 Production and Transportation Integration for Commit-to-Delivery Mode with General Shipping CostsFeng Li , Zhou Xu , Zhi-Long Chen Feng Li , Zhou Xu , Zhi-Long Chen Published Online:4 May 2020https://doi.org/10.1287/ijoc.2019.0935AbstractWe 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 NP-hard when the planning horizon consists of an arbitrary number of days. For the two-day problem, we show that it is ordinarily NP-hard, but is unlikely to have a fully polynomial time approximation scheme (FPTAS) unless NP=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. Previous Back to Top Next FiguresReferencesRelatedInformation Volume 32, Issue 4Fall 2020Pages 855-1186, C2 Article Information Supplemental Materials Metrics Information Received:September 18, 2018Accepted:September 02, 2019Published Online:May 04, 2020 Copyright © 2020, INFORMSCite asFeng Li, Zhou Xu, Zhi-Long Chen (2020) Production and Transportation Integration for Commit-to-Delivery Mode with General Shipping Costs. INFORMS Journal on Computing 32(4):1012-1029. https://doi.org/10.1287/ijoc.2019.0935 Keywordsintegrated production and transportationcommit-to-delivery modegeneral shipping cost functionscomputational complexityalgorithm analysisinteger programmingcolumn generationPDF download