A Smoothing SAA Method for Solving a Nonconvex Multisource Supply Chain Stochastic Optimization Model

Abstract

We construct a new multisource supply chain stochastic optimization model when the supply and demand are both uncertain. This model is nonconvex because the decision variables are truncated by the random variable in the objective function. It is a common technical challenge encountered in many operations management models. To address this challenge, we adopt a novel transformation technique to transform the nonconvex problem into an equivalent convex optimization problem. Then, we provide a smoothing sample average approximation (SAA) method to solve the transformed problem. The SAA model is a good approximation for the expected value function in the objective function when the number of samples is large enough. The smoothing technique can transfer the nonsmooth plus function into a smoothing function in the model, and thus, we can use the numerical methods for the common nonlinear integer programming to solve the transformed model. Numerical tests verify the effectiveness of the new model and the smoothing SAA method.