Abstract
The proper allocation of facilities within Islamic holy places is barely studied. These places annually witness millions of pilgrims and guests. The number of people during pilgrimage has been growing recently and is expected to grow further in the future. Different facilities should be optimally allocated to properly serve this large number of people and efficiently respond to their requests. In this paper, we target the problem of optimally allocating facilities within the largest Islamic holy place, Arafat. We evaluate the current allocation with respect to distance, coverage, and cover inequality metrics. Average-case and worst-case values of the three metrics are considered for evaluation. Results show that the current allocation strategy is far from being optimal. For the three considered metrics, we use crowdedness-based techniques to allocate facilities within the area of Arafat. Optimal allocations are first obtained by solving integer programming (IP) models. Thereafter, two widely used metaheuristics, genetic algorithms (GA) and simulated annealing, are experimented and evaluated. Results show that the optimal solution could be easily obtained for coverage and cover inequality metrics. For the distance metric, the computation time of the IP technique is large and GA appears as a good candidate to balance between computation time and solution quality. Finally, we study allocating facilities from a multiobjective perspective. Both scalar-weighted formulation and nondominated sorting genetic algorithm II techniques are considered. Results show that the latter technique outperforms the former technique in the number of generated Pareto-optimal allocations as well as the quality of these allocations.