Flow Shop Scheduling by a Lagrangian Relaxation and Network Flow Approach

By using advanced optimization methods, a production scheduling algorithm is developed for discrete-part, make-to-order type of flexible flow shops. The goal of scheduling is to meet due dates and the problem is formulated as a large-scale integer programming problem. The scheduling algorithm includes four parts: decomposition by Lagrangian relaxation into subproblems, a minimum cost linear network flow algorithm for solving subproblems, a subgradient algorithm for solving the dual problem, and a heuristic to obtain a near-optimal and feasible schedule. The algorithm is then compared with a heuristic rule that is considered effective by some local manufacturing firms. Preliminary results show that the scheduling algorithm not only is better in optimality but also provides more insights into scheduling complicated operations