Abstract
We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.
Highlights
[1] introduced the standard quadratic assignment problem (QAP)
QAPLIB instances: Instances of this family are generated from some classical QAP instances available in the QAPLIB library
We tried to solve the uncertain instance of the RQAP using CPLEX applied to mixed integer programming (MIP) model (24)–(27) with time limit 7,200 s, and if proven optimality was achieved for all 10 instances and all tested values of Γ, we classified these instances as ‘‘easy’’
Summary
[1] introduced the standard quadratic assignment problem (QAP). Standard QAP deals with choosing an optimal way to assign n facilities to n locations to minimize the total material handling cost, given all distances between locations and the amount of material flow between each pair of facilities. It is assumed that input data (e.g. flows between facilities and distances between locations in QAP) are precisely known in advance. This assumption can be true in some applications, it is not realistic in many others [39]. [43] studied integration of facility layout design and flow assignment problem under demand uncertainty. For an uncertain mixed integer programming (MIP) problem with interval data, solving robust counterparts for budgeted uncertainty sets is much easier than finding the minmax regret solution. We consider a generalization of the QAP where the flows are uncertain for some subset J of pairs of facilities.
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