Scheduling experiments on a nuclear reactor using mixed integer programming

Abstract

This paper describes an approach for scheduling a nuclear reactor that irradiates samples as required by customers. The environment involves a flowshop that consists of two stations, each composed of a set of parallel machines. Some jobs may be preempted, while others may not. Some jobs have deadlines, while others have due-dates. Some jobs require special tooling, while others do not. The problem is modeled as a time-indexed, mixed integer program with the objective of minimizing weighted tardiness. Pre-processing eliminates unnecessary variables and five solution strategies — four optimizing and one heuristic — are devised to utilize the options provided by a commercial solver. The strategies are compared on a set of 25 ten-job test instances. Jobs were selected randomly from a database of 103 actual jobs. One particular optimizing strategy worked especially well — it optimized 80% of the test problems within a predetermined time limit and did so with an average run-time of less than 1 min. Scope and purpose This paper has two primary purposes. The first purpose is to propose a structure to prescribe schedules in an actual environment, showing how classical assumptions can fall short of modeling practical problems. For example, in the environment studied in this paper some jobs have due dates while others have deadlines; some jobs can be pre-empted but others cannot; and some jobs require special tooling while others may not. The machine configuration is a two-station flowshop with parallel non-identical machines at each station. Machines have up times and down times each week. The second purpose is to propose a practical solution method based on a mixed integer programming formulation, using the capabilities of a commercial solver. The scope of the paper requires testing the solution method over a one-week horizon, which is required to support operations. While the long-term goal of this line of investigation is a decision support system to assist schedulers, the scope of this paper does not address implementation and attendant issues.