Integrated production and delivery with single machine and multiple vehicles

Kai Li, Chao Zhou, Joseph Y.T. Leung, Ying Ma

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


This paper considers a class of multi-objective production-distribution scheduling problem with a single machine and multiple vehicles. The objective is to minimize the vehicle delivery cost and the total customer waiting time. It is assumed that the manufacturer's production department has a single machine to process orders. The distribution department has multiple vehicles to deliver multiple orders to multiple customers after the orders have been processed. Since each delivery involves multiple customers, it involves a vehicle routing problem. Most previous research work attempts at tackling this problem focus on single-objective optimization system. This paper builds a multi-objective mathematical model for the problem. Through deep analysis, this paper proposes that for each non-dominated solution in the Pareto solution set, the orders in the same delivery batch are processed contiguously and their processing order is immaterial. Thus we can view the orders in the same delivery batch as a block. The blocks should be processed in ascending order of the values of their average workload. All the analysis results are embedded into a non-dominated genetic algorithm with the elite strategy (PD-NSGA-II). The performance of the algorithm is tested through random data. It is shown that the proposed algorithm can offer high-quality solutions in reasonable time.

Original languageEnglish (US)
Pages (from-to)12-20
Number of pages9
JournalExpert Systems with Applications
StatePublished - Sep 15 2016

All Science Journal Classification (ASJC) codes

  • General Engineering
  • Computer Science Applications
  • Artificial Intelligence


  • PD-NSGA-II algorithm
  • Pareto optimization
  • Production-distribution scheduling
  • Vehicle routing


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