Scheduling experiments on a nuclear reactor using mixed integer programming

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.