The Scheduling of Continuous Flow Prodcution: A Separable Programming Approach

Zero-one integer programming formulations have been described in the literature to solve a wide range of problems in areas as diverse as capital budgeting, allocation, machine sequencing, etc., but as yet large-scale realistic problems can be very expensive to compute using the standard branch-and-bound extensions to linear programming packages. Many authors, noting that there are many situations in which low-cost approximate solutions may be very acceptable, suggest the use of approximating methods, such as the corresponding linear programme or "effective gradients". This paper describes a complex production scheduling problem for which a near-optimal solution is obtained using a separable programming algorithm.By utilizing the special features of separable programming, the model is able to include considerations of setup times in the optimization. Computational experience suggests that the method is a considerable improvement on heuristic attempts, giving improvements in throughput of approximately 30 per cent.