Solution Strategies in Short-term Scheduling for Multitasking Multipurpose Plants

Abstract

This thesis addresses challenges in short-term scheduling of multipurpose facilities using mathematical optimization. Such approach involves the formulation of a predictive model and an objective function, and the development of a solution strategy around such scheduling model formulation in order to obtain an operating schedule that achieves certain objectives, such as maximization of throughput or minimization of makespan. There are many choices that must be made in these aspects of short-term scheduling, and these choices often lead to a trade-off between the solution quality and computational time. This thesis presents two studies analyzing the quality-CPU time trade-off in two major aspects: time representations in model formulation, and the strategy for handling multiple conflicting objectives. The ultimate goal is to develop bi-objective short-term scheduling approaches to tackle industrial-sized problems for multitasking multipurpose plants that are computationally inexpensive, but provide practical schedules with a good balance between throughput and makespan.

The first study addresses the first aspect of interest and compares two different time representation approaches: discrete-time and continuous-time approaches. This comparison is made considering maximization of throughput as the sole objective. We show that, for the modeling framework implemented in this work, the selected discrete-time formulation typically obtained higher quality solutions, and required less time to solve compared to the selected continuous-time formulation, as the continuous-time formulation exhibited detrimental trade-off between computational time and solution quality. We also show that within the scope of this study, non-uniform discretization schemes typically yielded solutions of similar quality compared to a fine uniform discretization scheme, but required only a fraction of the computational time.

The second study builds on the first study and develops a strategy around an efficient non-uniform discretization approach to handle the conflicting objectives of throughput maximization and makespan minimization, focusing on a priori multi-objective methods. Two main contributions are presented in this regard. The first contribution is to propose a priori bi-objective methods based on the hybridization of compromise programming and the U+03B5-constraint method. The second is to present short-term operational objective functions, that can be used within short-term scheduling to optimize desired long term objectives of maximizing throughput and minimizing makespan. Two numerical case studies, one in a semiconductor processing plant and an analytical services facility, are presented using a rolling horizon framework, which demonstrate the potential for the proposed methods to improve solution quality over a traditional a priori approach