Study on Re-entrant Flow-shop Scheduling Problem (Optimization by Mixed Integer Programming)

Abstract

A sophisticated formulation for re-entrant flow-shop scheduling problem is discussed in order to plan an optimum production schedule by mathematical programming. In the formulation, repeated operations by the same production resource are taken into account in the cyclic manufacturing process for mono-product. The general constraints of the problem are represented in linear equations composed by decision variables including both absolute starting times and relative starting times of the operations. The absolute starting times provide the sequence of the processing order in the manufacturing activity, while the relative starting times assure the appropriate handling in cyclic operation for each production resource. Since the complexity of the constraints affects the optimization, redundant decision variables have to be eliminated from the constraints. In this paper, we derive a new formulation in which the absolute starting times variables are represented implicitly by the relative starting time variables. The new formulation guides stepwise optimization approach, that is, the total number of cyclic terms is minimized before the search for the shortest complete time of the product, or the flow time. The result of the pre-optimization contributes enlargement of the problem size in optimization. The number of the total processes of the products is evaluated to verify the feasibility of the formulation and the optimization procedures by computational examinations.