Online order acceptance and scheduling in a single machine environment

Abstract

We consider the online order acceptance and scheduling (OAS) problem, a widely studied problem in its offline counterpart, where orders arrive online sequentially with associated rewards, arrival times, and due dates in a finite planning horizon. The objective is to make real-time order acceptance and scheduling decisions so as to maximize the total profit. To tackle this problem, we derive an upper bound on the competitive ratio of any online algorithm for the online OAS problem and introduce three algorithms (online greedy, online learning, and delay). For the online greedy algorithm, we provide a performance guarantee under the mild conditions via theoretical analysis. Furthermore, through computational studies we highlight that both the urgency of due dates of the orders and the workload level of the system can significantly influence the performance of the online algorithms. Since each proposed algorithm has its advantages and disadvantages, we categorize different scenarios for using the suitable algorithm, aiming at offering managerial insights for firms to make informed decisions.