Facility layout problem with QAP formulation under scenario-based uncertainty

ABSTRACT

The facility layout problem is usually treated as a deterministic problem and uncertainty regarding problem parameters has seldom been addressed. This study aims to investigate different ways of dealing with uncertainty to design a facility layout which attains robust and efficient performance under a finite number of possible scenarios. For this purpose, several mathematical models based on the quadratic assignment problem (QAP) formulation are developed. These formulations cover alternative approaches in stochastic programming and robust optimization literature such as: minimizing expected cost, maximum cost and maximum regret. Proposed models are solved using genetic algorithms incorporating operators and schemes that are specially selected and adapted for the models. Finally, a novel approach, where the optimization problem under scenario-based uncertainty is transformed into a multi-objective optimization problem by considering each scenario as a separate objective, is proposed. By solving the multi-objective counterpart of scenario-based QAP (mQAP), optimal solutions with respect to different robust performance measures can be obtained simultaneously in a Pareto optimal set. A multi-objective evolutionary algorithm is developed to solve the mQAP. Extensive numerical analysis enables comparison of the performance of these approaches and provides important insights about dealing with uncertainty in the facility layout problem.

KEYWORDS:

• Scenario-based uncertainty
• robust optimization
• stochastic programming
• genetic algorithm
• multi-objective optimization
• quadratic assignment problem

Acknowledgments

This research is supported by Boğaziçi University Research Fund [grant number 13843].

Disclosure statement

No potential conflict of interest was reported by the authors.