Taking advantage of a diverse set of efficient production schedules: A two-step approach for scheduling with side concerns

Abstract

In many practical scheduling problems, the concerns of the decision-maker may not be all known in advance and therefore may not be included in the initial problem definition as an objective function and/or as constraints. In such a case, the usual techniques of multi-objective optimization become inapplicable. To cope with this problem and to facilitate handling the concerns of the decision-maker, which can be implicit or qualitative, a dedicated methodological framework is needed. In this paper we propose a new two-step framework. First, we aim at obtaining a set of schedules that can be considered efficient with respect to a performance measure and at the same time different enough from one another to enable flexibility in the final choice. We formalize this new problem and suggest to address it with a multimodal optimization approach. Niching considerations are discussed for common scheduling problems. Through the flexibility induced with this approach, the additional considerations can be taken into account in a second step, which allows decision-makers to select an appropriate schedule among a set of sound schedules (in contrast to common optimization approaches, where usually a single solution is obtained and it is final). The proposed two-step approach can be used to handle a wide range of underlying scheduling problems. To show its potential and benefits we illustrate the framework on a set of hybrid flow shop instances that have been previously studied in the literature. We develop a multimodal genetic algorithm that employs an adapted version of the restricted tournament selection for niching purposes in the first step. The second step takes into account additional concerns of the decision-maker related to the ability of the schedules to absorb the negative effects due to random machine breakdowns. Our computational experiments indicate that the proposed framework is capable of generating numerous high-performance (mostly optimal) schedules. Additionally, our computational results demonstrate that the proposed framework provides the decision-maker a high flexibility in dealing with subsequent side concerns, since there are drastic differences in the capabilities of the efficient solutions found in Step 1 to absorb the negative impacts of machine breakdowns