A Three-level Location-inventory Problem with Correlated Demand
Avinash Unnikrishnan
Civil and Environmental Engineering, Portland State University
ABSTRACT:Supply chain networks serve as the basis of operation for many industries. In today’s competitive market, with its risky and uncertain operational environment, it is important to design supply chain networks in a cost-effective, efficient, and responsive manner. Unnikrishnan considers a three-level supply chain comprising plants, warehouses, and retailers, and presents a three-level location-inventory problem with correlated demand, which simultaneously minimizes the total cost for three types of decisions: (i) location of warehouses and plants, (ii) assignment of warehouses to the plants and the assignment of retailers to the warehouses, and (iii) optimal inventory level and safety stock cost at the warehouses. The initially-proposed binary nonlinear integer program (BNIP) formulation is transformed into a mixed integer conic quadratic program (MICQP). This transformation is performed to exploit the advances made by solvers such as CPLEX in solving second order conic integer programs. A solution approach based on an outer approximation strategy is proposed and the algorithmic advantage of such a framework for this class of programs is demonstrated. The results from numerical experiments show that the proposed solution procedure clearly outperforms state-of-the-art commercial solvers. In addition, the research shows that neglecting the effect of correlation can lead to substantially sub-optimal solutions.
