This study extends the capability and increases the performance of a traditional Branch and Bound (BB) algorithm to solve Facility Location-Transportation problems for Disaster Response (FLTDR) using parallel computing. A Two-Stage Branch and Bound (TBB) algorithm was developed to support two parallel computing approaches. This algorithm divides problems into two small sub-problems, which are a facility location sub-problem and a transportation sub-problem. All possible numbers of distribution centers are determined. All possible locations relating to any number of distribution centers are explicitly explored. The transportation sub-problem corresponding to any selected location is then solved. Two parallel approaches for the TBB algorithm (PTBB) differ in partitioning the list of sub-problems. The first approach (PTBB1) solves both sub-problems in parallel. The other (PTBB2) explores the locations in sequence and solves only the transportation sub-problems in parallel. The numerical experiments were conducted on various sizes of generated problems. The quality of the solution and the computing time of both approaches were compared with a BB algorithm with premature termination by time. The experimental experiences showed that both PTBB1 and PTBB2 are more efficient and effective than a BB algorithm. However, the PTBB1 should be suggested for the FLTDR because of the least computational time usage.
In this paper, a squared-Euclidean distance multifacility location problem with inseparable demands under balanced transportation constraints is analyzed. Using calculus to project the problem onto the space of allocation variables, the problem becomes minimizing concave quadratic integer programming problem. The algorithm based on extreme point ranking method combining with logical techniques is developed. The numerical experiments are randomly generated to test efficiency of the proposed algorithm compared with a linearization algorithm. The results show that the proposed algorithm provides a better solution on average with less processing time for all various sizes of problems
This paper studies the effect of branching rules (BR) and heuristic algorithms (HA) to find feasible solutions for a branch and bound (BB) algorithm used to solve sub-problems in a parallel two-phase branch and bound (PTBB) approach. The nine PTBB algorithms, which are developed by varying 3 2 combinations of BR and HA strategies, are tested on the facility location-transportation problem for disaster response (FLTDR). The mathematical model for the problem determines the number and location of distribution centres in a relief network, the amount of relief supplies to be stocked at each distribution centre and the vehicles to take the supplies in order to maximize the percentage of needs coverage of disaster victims under capacity restriction, transportation and budgetary constraints. To examine the performance of the algorithms, computational experiments are conducted on the various sizes of generated problems. Three strategies of BR and HA provided in the "intlinprog" function of MATLAB were applied for these problems. The objective function values and the computational times of all algorithms were collected and analyzed. The results showed that all PTBB algorithms can solve problem sizes of four candidate locations with fifteen demand points without premature termination by time. The PTBB algorithm using "maxfun" branching rules and "rss" heuristic to find a feasible solution is recommended for FLTDR because of the least computational time usage.
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