Solving Quadratic Assignment Problem with Fixed Assignment (QAPFA) using Branch and Bound Approach

Abstract

Quadratic Assignment Problem (QAP) has been a very popular problem to be solved among researchers due to its practical applications. Several variants of QAP have been proposed by researchers in the past in order to reflect the real situations of QAP. One of the real problems of QAP is related with facilities which are required to be assigned to certain locations due to its function. In solving this problem, a fixed assignment has to be made thus allowing for the complexity of the problem to be reduced. Hence, this study introduces Quadratic Assignment Problem with Fixed Assignment (QAPFA) with the objective to minimize the assignment cost between the facility and location. This assignment takes into account the flow and distance between facility and location. QAPFA represents the real-world situation of the problem especially in dealing with specific requirement of some facilities to specific locations. Dataset of QAPFA is introduced and is solved using branch and bound approach. As for validation, the results of QAPFA are compared with QAP in terms of objective function and running time. The computational results show that the solution quality of QAPFA is lower when compared with the QAP, while the running time for QAPFA is lower than the QAP. Since the complexity of the problem is reduced by fixing the assignment, thus there is possibility that QAPFA has lower quality than QAP due to the fixed assignment. Nevertheless, in terms of running time QAPFA is better than QAP. It can be concluded that this problem reflect the real problem and practical to be used.