A linear time–cost tradeoff problem with multiple milestones under a comb graph

  • Byung-Cheon Choi
  • Changmuk KangEmail author


We consider a linear time–cost tradeoff problem (LTCTP) with multiple milestones under a comb graph. A time–cost tradeoff problem decides whether and how much to spend a cost to compress processing time of a job in order to meet promised due dates. This is common in managing a project because additional labors or resources are expensive. It is called linear where the compression cost linearly increases with reduced time. An objective of the LTCTP that this study addresses is to minimize the weighted number of tardy milestones plus the total compression cost. This study considers a special precedence structure, which is called a comb graph. A chain of jobs that sequentially precede each other forms a main process of a project, and other chains of jobs, corresponding to sub processes, precede each job in the main process. For this structure, we developed a strongly-polynomial-time algorithm. This is the first result of unveiling complexity of the multi-milestone LTCTP under a non-chain structure.


Project scheduling Time–cost tradeoff Multiple milestones Comb graph 



This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5B8070344).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Business AdministrationChungnam National UniversityDaejeonSouth Korea
  2. 2.Department of Industrial and Information Systems EngineeringSoongsil UniversitySeoulSouth Korea

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