Exact solution approaches for order acceptance and scheduling decisions in m-machine open shops

This paper considers an order acceptance and scheduling (OAS) problem in open shops with m-machines and the objective of maximizing the total net revenue, which is defined as the difference between the sum of revenues and the total weighted tardiness. Open shop scheduling problems occur in many different industries, like the production or the service industry, which show a great potential for the use of integrated OAS methods. However, these mostly NP-hard problems are computationally challenging. With this work, we are the first to consider the problem of OAS in an m-machine open shop and propose several exact solution approaches. We first develop two basic mixed integer linear programming (MIP) formulations. Second, we present several enhancements to allow more problem instances to be solved to optimality with a standard solver compared to the basic MIP formulations. Third, we propose a model-based branch-and-bound (B&B) approach. In an extensive numerical study, we compare the performance of a standard solver with all developed MIP formulations as well as the B&B approach. The results demonstrate the superior performance of the enhanced MIP formulations as well as the B&B approach in terms of CPU time and the number of verified optimal solutions found.