Multi-stage order acceptance model and the heuristic algorithm based on simulated annealing

This paper studies the order acceptance problem with tardiness penalties faced by firm who has a pool of potential orders waiting to be accepted and processed through a single production line with multiple processing stages. We present an order acceptance decision model, named the multistage order acceptance model, to handle this problem, which is an extension of the Slotnick-Morton version of single-stage order acceptance model, aiming at maximizing the total profit of these potential orders to be processed through a multi-stage production line. Because of the complexity of the problem that integrates the operations of order acceptance and multi-stage job scheduling, we propose a heuristic algorithm, named Simulated Annealing Based on Partial Optimization (SABPO) algorithm, to solve the model with feasible solutions and acceptable computational time. Empirical experiments on synthetic datasets are carried out to examine the proposed algorithm and also to compare the performances between multi-stage model and single-stage model. The comparisons show that the multi-stage model can always suggest a better decision on order acceptance problem; some potential orders rejected by single-stage model are in fact profitable and will be accepted by multi-stage model.