Parameter | Value |
Number of customers | 17 |
Number of distribution centers | 3 |
Number of forbidden areas | 1 |
The radius of margin | 15 |
The coordinates of margin center | (50, 30) |
Number of corners of each of regions | 5 |
In this paper we propose a metaheuristic approach to solve a customer priority based location-allocation problem in presence of obstacles and location-dependent supplier capacities. In many network optimization problems presence of obstacles prohibits feasibility of a regular network design. This includes a wide range of applications including disaster relief and pandemic disease containment problems in healthcare management. We focus on this application since fast and efficient allocation of suppliers to demand nodes is a critical process that impacts the results of the containment strategy. In this study, we propose an integrated mixed-integer program with location-based capacity decisions that considers customer priorities in the network design. We propose an efficient multi-stage genetic algorithm that solves the problem in continuous space. The computational findings show the best allocation strategies derived from proposed algorithms.
Citation: |
Table 1. Sample instance from randomly generated instances
Parameter | Value |
Number of customers | 17 |
Number of distribution centers | 3 |
Number of forbidden areas | 1 |
The radius of margin | 15 |
The coordinates of margin center | (50, 30) |
Number of corners of each of regions | 5 |
Table 2. Summary of computational results on randomly generated instances
Objective Function | ||||||||
Instance | m | n | R-SCOLAP | SCOLAP | GCOLAP1 | GCOLAP2 | MIP gap | GA gap |
1 | 2 | 8 | 0.0435 | 19.41 | 25.44 | 26.96 | 0 | 0.31 |
2 | 2 | 10 | 0.0443 | 30.56 | 36.57 | 34.21 | 0 | 0.2 |
3 | 2 | 12 | 0.0424 | 33.26 | 39.18 | 47.41 | 0 | 0.18 |
4 | 2 | 15 | 0.0493 | 65.52 | 80.89 | 77.46 | 0 | 0.23 |
5 | 3 | 17 | 0.0443 | 65.5 | 87.34 | 105.68 | 0 | 0.33 |
6 | 3 | 20 | 0.0542 | 138.12 | 177.07 | 139.72 | 0.00009 | 0.28 |
7 | 3 | 25 | 0.0677 | 163.25 | 209.29 | 214.77 | 0.0001 | 0.28 |
8 | 3 | 30 | 0.0723 | 273.86 | 329.96 | 277.23 | 0.00254 | 0.2 |
9 | 4 | 35 | 0.0738 | - | 249.24 | 501.61 | - | - |
10 | 4 | 40 | 0.0881 | - | 387.83 | 500.64 | - | - |
11 | 4 | 44 | 0.0733 | - | 618.62 | 645.86 | - | - |
12 | 5 | 47 | 0.077 | - | 721.32 | 941.63 | - | - |
13 | 5 | 50 | 0.138 | - | 835.72 | 1122.76 | - | - |
14 | 5 | 55 | 0.0971 | - | 854.85 | 1025.11 | - | - |
15 | 6 | 60 | 0.1343 | - | 1542.82 | 1825.43 | - | - |
16 | 6 | 65 | 0.1067 | - | 1382.88 | 1738.93 | - | - |
17 | 7 | 70 | 0.1536 | - | 1699.78 | 2836.1 | - | - |
18 | 7 | 74 | 0.1206 | - | 2021.15 | 2590.2 | - | - |
19 | 8 | 78 | 0.1088 | - | 2145.16 | 3079.13 | - | - |
20 | 8 | 82 | 0.1156 | - | 3210.13 | 3450.84 | - | - |
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Obstacle and the marginal area
Alternative connecting paths around an obstacle
Visibility graph method around the obstacles
Type two chromosome crossover
Supplier and demand network in the sample
Convergence of GCOLAP1 and GCOLAP2 on the sample