Order Acceptance and Scheduling Problem: A Proposed Formulation and the Comparison with the Literature

Abstract

In classical scheduling problem, it is assumed that all orders must be processed. In the order acceptance and scheduling (OAS) problem, some orders are rejected due to limited capacity. In make-to-order production environment, in which the OAS problem occurs, accepting all orders may cause overloads, delay in deliveries and unsatisfied customers. Oğuz et al. (2010) introduced the OAS problem with sequence-dependent setup times and release dates. In this paper, we propose a new mixed integer programming formulation with O(n²) decision variables and O(n²) constraints for the same problem. We conduct a computational analysis comparing the performance of our formulation with Oğuz et al. (2010) formulation. We use the benchmark instances, which are available in the literature. We observe that our formulation can solve all the instances up to 50 orders in a reasonable time, while Oğuz et al. (2010) formulation can solve only the instances with 10 orders in the same time limit.