The capacitated minimax location-allocation problem with probabilistic customer locations and border crossing constraints

Abstract

Minimax facility location allocation is a type of facility problem which is of prime importance for emergency situation, since it directly affects services response times to the customers and cost of transportation. The emergency facility can be a hospital, fire station, or relief room. This thesis intends to find the optimum or near optimum solution of new emergency facilities which minimize the maximum expected distance between facility and customer area. This study involves a fixed line barrier with some border crossing along it which divides the area into two subregions. Although some studies have recently been accomplished for the case problem in which the customer demand locations are known with certainty, much less attention has been devoted to developing a comprehensive mathematical model for probabilistic customer location in the restricted region that finds the optimum location of emergency facilities and their corresponding allocation clusters. The main focus of this research is developing a mixed integer nonlinear programming model for facility location allocation problem when the location of customers is not exactly defined. The weight of the customer demands has been evaluated based on qualitative and quantitative criteria. Two MINLP solvers, BARON and DICOPT, are applied to find the optimum location of new facilities and compared with each other in terms of solution quality. On task of flood disaster management organization in Amol district in Mazandaran is selected as a case study to demonstrate the proficiency and applicability of the proposed model. The computational results reveal that BARON solver performs better than DICOPT solver and able to achieve the global optimal solution for location of relief rooms.