Computational Studies in Multi-Criteria Scheduling and Optimization

Multi-criteria scheduling provides the opportunity to create mathematical optimization models that are applicable to a diverse set of problem domains in the business world. This research addresses two different employee scheduling applications using multi-criteria objectives that present decision makers with trade-offs between global optimality and the level of disruption to current operating resources. Additionally, it investigates a scheduling problem from the product testing domain and proposes a heuristic solution technique for the problem that is shown to produce very high-quality solutions in short amounts of time.

Chapter 2 addresses a grant administration workload-to-staff assignment problem that occurs in the Office of Research and Sponsored Programs at land-grant universities. We identify the optimal workload assignment plan which differs considerably due to multiple reassignments from the current state. To achieve the optimal workload reassignment plan we demonstrate a technique to identify the n best reassignments from the current state that provides the greatest progress toward the utopian solution. Solving this problem over several values of n and plotting the results allows the decision maker to visualize the reassignments and the progress achieved toward the utopian balanced workload solution.

Chapter 3 identifies a weekly schedule that seeks the most cost-effective set of coach-to-program assignments in a gymnastics facility. We identify the optimal assignment plan using an integer linear programming model. The optimal assignment plan differs greatly from the status quo; therefore, we utilize a similar approach from Chapter 2 and use a multiple objective optimization technique to identify the n best staff reassignments. Again, the decision maker can visualize the trade-off between the number of reassignments and the resulting progress toward the utopian staffing cost solution and make an informed decision about the best number of reassignments.

Chapter 4 focuses on product test scheduling in the presence of in-process and at-completion inspection constraints. Such testing arises in the context of the manufacture of products that must perform reliably in extreme environmental conditions. Each product receives a certification at the successful completion of a predetermined series of tests. Operational efficiency is enhanced by determining the optimal order and start times of tests so as to minimize the make span while ensuring that technicians are available when needed to complete in-process and at-completion inspections We first formulate a mixed-integer programming model (MILP) to identify the optimal solution to this problem using IBM ILOG CPLEX Interactive Optimizer 12.7. We also present a genetic algorithm (GA) solution that is implemented and solved in Microsoft Excel. Computational results are presented demonstrating the relative merits of the MILP and GA solution approaches across a number of scenarios.