Question: Essentially, this type of problem can be tackled by using either exact solution techniques or heuristic/meta-heuristic methods. In the first approach, the model is

Essentially, this type of problem can be tackled by using either exact solution techniques or heuristic/meta-heuristic methods. In the first approach, the model is formulated and solved by stan- dard MIP software. However, in some problems, by increasing the problem size, computational time rises exponentially which shows the complexity and NP-hard property of the problem. In these cases, heuristic/meta-heuristic methods can be used to find a near-optimal solution. In fact, there would be a trade-off between solution quality and computational time. In this research context, since the prime objective is to allocate supplies to multiple loca- tions, it is a long-term planning problem without frequent changes once implemented. Therefore, a high quality solution is strongly preferred over a fast computational time. Moreover, our proposed model is computationally efficient and can reach the optimal/near- optimal solution in a reasonable time. The mathematical model was coded and executed in IBM ILOG CPLEX version 12.6 on an Intel Core i7 CPU @ 3.4 GHz with 16 GB RAM. More informa- tion about the characteristic, size and computational time for the problem of interest are presented in Section 6. To assess the performance of the proposed model, we first evaluated the system operating under the current conditions as a baseline in terms of the cost components and standard deviation of the objective function. Afterward, three improvement alternatives, denoted as A1, A2, and A3, are proposed and the expected cost of each alternative is compared against the baseline. The charac- teristics of each alternative in terms of the number of variables and constraints are presented in Table 3. We have also conducted extensive sensitivity analysis about the risk coefficient and main cost parameters to further evaluate the behavior of the model with respect to different values for these parameters. In the following subsections, we elaborate on the current con- figuration of the system and discuss each of the three proposed alternatives when the risk coefficient is fixed at 0 (i.e., = 0). We allowed the optimality gap (i.e., the relative gap between the corresponding lower and upper bounds) for each problem to be 3%.
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