Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

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We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

Original languageEnglish
Pages (from-to)79-97
Number of pages19
JournalJournal of Combinatorial Optimization
Issue number1
StatePublished - Jan 2022


  • Common flow-allowance
  • Convex resource allocation
  • Minmax
  • Position-dependent workloads
  • Single machine scheduling


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