This study concerns the development of a nonlinear programming model capable of solving an adapted version of a single-objective nonlinear problem. The original problem was adapted via the inclusion of an additional constraint and term in the objective function. The resultant aim is twofold: to optimize a three-level supply chain so as to decrease objective costs (such as shortage periods) while simultaneously increasing customer service levels. Demand is random and the inventory control system continuous. Lost sales due to urgent demand are assumed. After evaluating the formulated mathematical model, a metaheuristic algorithm is developed capable of determining the number of open distribution centers and allocating retailers to these centers. Experiments to evaluate the proposed method's performance are conducted on small to medium-sized problems. Results are compared against those of e-constraint and None Dominated Sorting Genetic Algoritms (NSGA2) (whose parameters are adjusted using the Taguchi method). Final results indicate the superiority of the proposed metaheuristic in comparison to other, competing approaches.
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