Minimizing tardiness in a two-machine flow-shop

Abstract

The two-machine flow-shop scheduling problem with the objective of minimizing total tardiness is considered in this paper. Dominance criteria are developed to establish the precedence constraints between jobs in an optimal schedule. A lower bound on the total tardiness of the problem is derived by constructing the sequence of jobs from front to back to simplify the bounding procedure. A branch-and-bound algorithm incorporating these properties is proposed to expedite the search for an optimal sequence. Computational experiments are conducted and the results demonstrate that the proposed algorithm surpasses an existing one in terms of both computation times and sizes of the problems solved. Scope and purpose An m-machine flow-shop requires all the n jobs to be processed following the same path from one to another on these m machines. For a two-machine flow-shop problem, however, one needs to consider only permutation schedules [1] on which both machines process the jobs in the same order. Besides the flow-shops that actually consist of two machines, there are many occasions in which a large complex facility can be viewed as though it performs two major operations. Even if a shop has several machines, two of them may be so restrictive and function as bottleneck ones. Total tardiness is a widely used scheduling performance measure in practical production environments for which there is no benefit for finishing jobs early, and the tardiness penalty is proportional to the delay over all jobs. The two-machine flow-shop problem with total tardiness as the scheduling criterion is NP-complete [2] and has been solved by branch-and-bound algorithms. However, more properties of the problem can be exploited and developed to enhance the computational efficiency of the algorithm.