Joint production-inventory-location problem with multi-variate normal demand

This paper develops a mixed integer nonlinear programming formulation for the production-inventory-location problem with correlated demands across the retailers. Several structural results for special cases of the problem are derived and studied. A solution method based on the outer approximation of the nonlinear terms is developed to solve the problem. The efficiency of the proposed model and solution approach is investigated through extensive numerical studies. Ignoring correlations can increase the total costs of a production-location-inventory system. Accounting for correlations may lead to changes in supply chain configuration. The effect of capacity on computational times was more pronounced in lower correlations than higher correlations. In addition, we show that the efficiency of the solution method increases significantly for two special cases - when all products have the same holding cost and when the number of orders for different products at each warehouse is constrained to be the same.