Mixed-Integer Nonlinear Programming Models and Algorithms for Large-Scale Supply Chain Design with Stochastic Inventory Management

An important challenge for most chemical companies is, to simultaneously consider inventory optimization and supply chain network design under demand uncertainty. This leads to a problem that requires integrating a stochastic inventory model with the supply chain network design model. This problem can be formulated as a large-scale combinatorial optimization model that includes nonlinear terms. Since these models are very difficult to solve. they require exploiting their properties and developing special solution techniques to reduce the computational effort. In this work, we analyze the properties of the basic model and develop solution techniques for a joint Supply chain network design and inventory management model for a given product. The model is formulated as a nonlinear integer programming problem. By reformulating it as a mixed-integer nonlinear programming (MINLP) problem and using an associated convex relaxation model for initialization. we first propose a heuristic method to quickly obtain good-quality solutions. Further. a decomposition algorithm based on Lagrangean relaxation is developed for obtaining global or near-global optimal solutions. Extensive computational examples with up to 150 distribution centers and 150 retailers are presented to illustrate the performance of the algorithms and to compare them with the full-space solution.