Profit Maximization Through Integrated Order Acceptance and Scheduling: A Metaheuristic Approach

The synchronization of production capacity with demand plays a significant role in maximizing profit. Firms attempt to align their activities, requiring that businesses be occasionally turned away. A trade-off exists between the revenue gained by a specific order and all related processing costs. We solve an important order acceptance and scheduling problem arising from this business model. A firm that receives multiple orders must determine: (i) whether to accept or reject any order, (ii) how to assign accepted orders to identical parallel machines, (iii) the sequence of accepted orders, and (iv) when to schedule order starting times. The objective is to maximize the total profit, measured as the difference between revenue and tardiness penalty costs. We propose an effective hybrid algorithm (GA-RP-TS) that combines a refining process (RP), a genetic algorithm (GA), and a tabu search (TS) step to tackle this NP-hard problem. The hybrid GA-RP-TS employs GA’s strong global search ability, uses RP to improve a solution, and performs exploitation with TS. In particular, the proposed GA-RP-TS balances the intensification and diversification ability of metaheuristics and evolutionary algorithms. We evaluate the performance of the proposed GA-RP-TS by testing benchmark instances. Results show that the proposed GA-RP-TS outperforms the state-of-the-art algorithm in solving large-sized instances. GA-RP-TS obtains 22 new best solutions out of the 54 tested benchmark instances, besides helping prove optimality for two instances. In addition, GA-RP-TS consumes less computation time. Sensitivity analysis shows that the excellent performance of GA-RP-TS comes from the hybridization of its three components, i.e., GA, RP, and TS.