Scheduling in multi-scenario environment with an agreeable condition on job processing times

Miri Gilenson, Dvir Shabtay, Liron Yedidsion, Rohit Malshe

Research output: Contribution to journalArticlepeer-review


In the literature on multi-scenario scheduling problems, it is assumed that (i) each scenario defines a different possible realization of the job’s parameters; and (ii) the value of each parameter is arbitrary for any job in any scenario. Under these assumptions many multi-scenario scheduling problems have been proven to be NP-hard. We study a special case of this set of problems, in which there is an agreeable condition between scenarios on the processing-time parameters. Accordingly, the processing time of job Jj under scenario si is at most its value under scenario si+1, for i= 1 , … q- 1 , where q is the number of different possible scenarios. We focus on three classical scheduling problems for which the single-scenario case is solvable in polynomial time, while the multi-scenario case is NP-hard, even when there are only two scenarios. The three scheduling problems consist of minimizing either the total completion time or the number of tardy jobs on a single machine, and minimizing the makespan in a two-machine flow-shop system. We show that the multi-scenario version of all three problems remains NP-hard even when processing times are agreeable and there are only two scenarios. We also show that for a more specific structure of job processing times two out of the three problems become easy to solve, while the complexity status of the third remains open for future research.

Original languageAmerican English
Pages (from-to)153-173
Number of pages21
JournalAnnals of Operations Research
Issue number1-2
StatePublished - 1 Dec 2021


  • Agreeable condition
  • Flow-shop
  • Multi-scenario
  • NP-hard
  • Scheduling
  • Single-machine

All Science Journal Classification (ASJC) codes

  • General Decision Sciences
  • Management Science and Operations Research


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