Applications of Parallel Computing for Facility Location-Transportation Problems for Disaster Response

Abstract

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.

A Comparison of Parallel Branch and Bound Algorithms for Location-Transportation Problems in Humanitarian Relief

“…Finally, shipping costs from distribution centres to demand points are restricted by post-disaster budgetary restrictions. The mathematical model formulation of this problem refers to [13]. The parameters and decision variables are defined as follows.…”

“…In order to analyse the effect of BR and HA on the performance of the PTBB1 algorithm, which is an PBB approach that was proposed in [13], for various sizes of FLTDR, a 3 4 full factorial design with single replication is used to carry out the numerical experiments. Two following hypotheses are tested.…”

“…The PTBB1 proposed in [13] is composed of 10 steps as follows. Parallel computing is applied in steps 2 to 10 using the "parfor" function in MATLAB.…”

“…The numerical experiments are implemented on an asynchronous shared memory system, which is constructed from a workstation with a CPU Intel Core i7-5820K 3.30 GHz 6-core processor with 16 GB RAM. The data sets of nine problem cases with the specific n and u in [13] are used. All algorithms are set to be prematurely terminated at 28,800 sec.…”

“…Much of the research in the PBB approach area has emphasized developing new or improving the existing computer architectures such as [10]- [12]. Little research has focused on developing new or improving PBB approaches such as [13]. However, the various strategies of the BB algorithm, which are used in sub-problem solving in the PBB algorithm and affect the branching sequence of the PBB algorithm, have not been studied.…”