Optimization Letters

, Volume 11, Issue 7, pp 1257–1271 | Cite as

Single-machine serial-batching scheduling with a machine availability constraint, position-dependent processing time, and time-dependent set-up time

  • Jun PeiEmail author
  • Xinbao Liu
  • Panos M. Pardalos
  • Kai Li
  • Wenjuan Fan
  • Athanasios Migdalas
Original Paper


This article considers the single-machine serial-batching scheduling problem with a machine availability constraint, position-dependent processing time, and time-dependent set-up time. The objective of this problem is to make the decision of batching jobs and sequencing batches to minimize the makespan. To solve the problem, three cases of machine non-availability periods are considered, and the structural properties of the optimal solution are derived for each case. Based on these structural properties, an optimization algorithm is developed and an example is proposed to illustrate this algorithm.


Scheduling Availability constraint Serial-batching Single-machine Position-dependent processing time 



This work is supported by the National Natural Science Foundation of China (Nos. 71601065, 71231004, 71501058, 71131002, 71471052, 71521001, 71571058), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167), and the Fundamental Research Funds for the Central Universities (Nos. JZ2016HGTA0709, JZ2016HGTB0727). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jun Pei
    • 1
    • 2
    Email author
  • Xinbao Liu
    • 1
    • 3
  • Panos M. Pardalos
    • 2
  • Kai Li
    • 1
    • 3
  • Wenjuan Fan
    • 1
    • 3
  • Athanasios Migdalas
    • 4
    • 5
  1. 1.School of ManagementHefei University of TechnologyHefeiChina
  2. 2.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA
  3. 3.Key Laboratory of Process Optimization and Intelligent Decision-making of Ministry of EducationHefeiChina
  4. 4.Division of Industrial Logistics, Department of Industrial EngineeringLulea University of TechnologyLuleåSweden
  5. 5.Division of Transportation, Construction Management and Regional Planning, Department of Civil EngineeringAristotle University of ThessalonikiThessalonikiGreece

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