Integrated production and delivery scheduling with disjoint windows

Yumei Huo, Joseph Y.T. Leung, Xin Wang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Consider a company that manufactures perishable goods. The company relies on a third party to deliver goods, which picks up delivery products at regular or irregular times. At each delivery time, there is a time window that products can be produced to be delivered at that delivery time. The time windows are disjoint. Suppose we have a set of jobs with each job specifying its delivery time, processing time and profit. The company can earn the profit if the job is produced and delivered at its specified delivery time. From the company point of view, we are interested in picking a subset of jobs to produce and deliver so as to maximize the total profit. The unpicked jobs will be discarded without penalty. We consider both the single machine case and the parallel and identical machine case. In this article we consider three kinds of profits: (1) arbitrary profit, (2) equal profit, and (3) profit proportional to its processing time. In the first case, we give a fully polynomial time approximation scheme (FPTAS) for a single machine with running time O (frac(n3, ε{lunate})). Using the bound improvement technique of Kovalyov, the running time can be further reduced to O (frac(n2, ε{lunate}) + n2 log n). In the second case, we give an O (n log n)-time optimal algorithm for a single machine. In the third case, we give an FPTAS for a single machine with running time O (frac(n2, ε{lunate})). All of our algorithms can be extended to parallel and identical machines with a degradation of performance ratios.

Original languageEnglish (US)
Pages (from-to)921-931
Number of pages11
JournalDiscrete Applied Mathematics
Volume158
Issue number8
DOIs
StatePublished - Apr 28 2010

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Fully polynomial time approximation schemes
  • NP-hard and strongly NP-hard
  • Parallel and identical machines
  • Perishable goods
  • Single machine

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