Batch delivery scheduling with batch delivery cost on a single machine

Min Ji, Yong He, Edwin Tai Chiu Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

50 Citations (Scopus)


We consider a scheduling problem in which n independent and simultaneously available jobs are to be processed on a single machine. The jobs are delivered in batches and the delivery date of a batch equals the completion time of the last job in the batch. The delivery cost depends on the number of deliveries. The objective is to minimize the sum of the total weighted flow time and delivery cost. We first show that the problem is strongly NP-hard. Then we show that, if the number of batches is B, the problem remains strongly NP-hard when B ≤ U for a variable U ≥ 2 or B ≥ U for any constant U ≥ 2. For the case of B ≤ U, we present a dynamic programming algorithm that runs in pseudo-polynomial time for any constant U ≥ 2. Furthermore, optimal algorithms are provided for two special cases: (i) jobs have a linear precedence constraint, and (ii) jobs satisfy the agreeable ratio assumption, which is valid, for example, when all the weights or all the processing times are equal.
Original languageEnglish
Pages (from-to)745-755
Number of pages11
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 16 Jan 2007


  • Batch delivery cost
  • Computational complexity
  • Optimal algorithm
  • Single machine scheduling

ASJC Scopus subject areas

  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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