Sub-group quadratic assignment problem: A variant Of quadratic assignment problem with model development and comparison - Syed Abdullah, Sharifah Shuthairah; Abdul Rahman, Syariza; Benjamin, Aida Mauziah; Ku-Mahamud, Ku Ruhana; Wibowo, Antoni (PennWell Corp., 2020)
Numerous research on Quadratic Assignment Problem (QAP) and its variants have been proposed in the past to reflect real-world problems. One of the real problems related to QAP is facilities are required to be assigned to certain locations due to their purposes. A set of assignment has to be made accordingly based on their requirements and allow complexities of the problem to be reduced. Hence, this study introduces a variant of QAP which is called as Sub-Group QAP (SGQAP) with the objective to minimize the assignment cost by taking into consideration the flow and distance between the facilities and locations. SGQAP represents real-world problem, especially in dealing with specific requirements of some facilities to a specific set of locations. In this study, mathematical model of the problem is developed and a data set of SGQAP with various sizes of group is introduced and solved. The results of SGQAP are compared with QAP and QAP with Fixed Assignment (QAPFA) in terms of objective function and running time in order to show variation in the solution quality when different condition is applied. The computational results show that the solution quality of SGQAP is better than QAPFA but not for QAP since the complexity was reduced by grouping facilities into a set of assignment. This isdue to the need to fulfill some preferences in the assignment which contribute to assignment cost. SGQAP is a new variant of QAP which is related to group assignment based on preferences, hence it contributes as a new practical problem which gives more flexibility and effectiveness in the assignment while maximizing the preferences.