Scheduling in a Multi-Stage Flow Shop with Parallel Machines to Minimize Average Flow Time

Abstract

In this paper, a heuristic algorithm is proposed for solving the scheduling problem in a multi-stase flow shop with parallel machines to minimize the average flow time. The problem is presented by an Integer Programming formulation and optimal or near-optimal solutions can be obtained by the following iterative procedure : (1) to produce a Lagrangean problem and solve it by decomposition; (2) using a heuristic algorithm to find a feasible solution based on the solution of (1); (3) to evaluate the optimality of the feasible solution and adjust the Lagrangean multipliers. Finally a numerical example is given to illustrate the proposed approach.