The no-wait two-machine flow shop scheduling problem with convex resource-dependent processing times

Dvir Shabtay, Moshe Kaspi, George Steiner

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We extend the classical no-wait two-machine flow shop scheduling problem to the case where job-processing times are controllable through the allocation of a common, limited and nonrenewable resource. Our objective is to simultaneously determine the sequence of the jobs and the resource allocation for each job on both machines in order to minimize the makespan. By using the equivalent load method to obtain the optimal resource allocation on a series-parallel graph, we reduce the problem to a sequencing one and show that it is equivalent to a new special case of the Traveling Salesman Problem (TSP). We prove that although the reduced problem forms a subclass of the TSP on permuted Monge matrices, it is still strongly NP-hard. We provide an approximation result and present three special cases which are polynomially solvable. We have also tested two different subtour-patching heuristics in large-scale computational experiments on randomly generated instances of the problem. Both heuristics produced close-to-optimal solutions in most cases.

Original languageEnglish
Pages (from-to)539-557
Number of pages19
JournalIIE Transactions (Institute of Industrial Engineers)
Volume39
Issue number5
DOIs
StatePublished - 1 May 2007

Keywords

  • Convex resource consumption function
  • Flow shop scheduling
  • No-wait
  • Series-parallel graph
  • TSP on k-root cost matrices

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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