The permutation flow shop problem with sum-of-completion times performance criterion

In this article the authors address the non-preemptive flow shop scheduling problem for minimization of the sum of the completion times. They present a new modeling framework and give a novel game-theoretic interpretation of the scheduling problem. A lower-bound generation scheme is developed by solving appropriately defined linear assignment problems. This scheme can also be used as a heuristic approach for the solution of the problem with satisfactory results. Its main use, however, is as a bounding scheme within a branch-and-bound procedure. The present branch-and-bound procedure improves significantly upon the best available enumerative procedures in the current literature. Extensive computational results are used to qualify the above statements.