Two-Machine Stochastic Flow Shops With Blocking and the Traveling Salesman Problem

Authors:
Pawel Jan Kalczynski;Jerzy Kamburowski
Affiliations:
Department of Information Operations and Technology Management, College of Business Administration, MS #103, The University of Toledo, Toledo, USA 43606-3390;Department of Information Operations and Technology Management, College of Business Administration, MS #103, The University of Toledo, Toledo, USA 43606-3390
Venue:
Journal of Scheduling
Year:
2005

Citing 3
Cited 1

Rearrangement, majorization and stochastic scheduling

Mathematics of Operations Research
Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

SIAM Review
Minimizing variation in stochastic flow shop

Operations Research Letters

On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices

Journal of Heuristics

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Abstract

The paper deals with the problem of minimizing the expected makespan in a two-machine flow shop with blocking and random job processing times. It is well known that it reduces to an instance of the traveling salesman problem (TSP). Assuming that the job processing times can be stochastically ordered on both machines, we show that the problem under study is equivalent to TSP on a permuted Monge matrix. This allows us to prove that it is NP-hard for the independently and exponentially distributed job processing times, and identify a new class of efficiently solvable special cases.