The design and optimization of combined location-inventory model for deteriorating products are a main focus in supply chain management. There were many combined location-inventory design models in this field, but these models are under the assumptions of adequate capacity facilities, invariable lead time, unique product, and uncorrelated retailer’s demands. These assumptions have a big gap in the practical situation. In this paper, we design a combined location-inventory model for deteriorating products under capacitated facilities, stochastic lead time, multiple products, and correlated retailers’ stochastic demands assumptions. These constraints are near to actual supply chain circumstance. The problem is modeled as conic quadratic mix-integer programming (CQMIP) to minimize the total expected cost. We explain how to formulate these problems as conic quadratic mixed-integer problems, and in order to obtain better computational results we use extended cover cuts. Simultaneously we compare our method with the previous Lagrange methods; the result is that the new CQMIP method can get better solution.
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