MATP6620/ISYE6760 Final Project Stochastic Optimization Framework for Input Uncertainty in Inventory Management

In this project, we formulate a Stochastic optimization framework to manage the risk from input uncertainty in inventory management. In the classical inventory management, the stochastic programming is used to find an optimal policy that optimizes the risk-neutral expected cost over a certain planning horizon [3], or the risk from the randomness of the demand [7]. However, to the best of our knowledge, we have not found any study on the risk from the input uncertainty of the parameters in the demand distribution. Therefore, in this project, we develop a Stochastic optimization framework to control the risk from the input uncertainty in inventory management, and provide some numerical studies based on these framework. We use a coherent Conditional Vale at Risk (CVaR) [1] to measure the risk. Due to the difficulties of evaluate an analytical form of CVaR, we formulate a sample average approximation (SAA) for it, and transform the stochastic program into a linear program, which can be solved numerically. We develop the framework under a finite horizon periodic review inventory model without fixed order cost. The empirical study uses a statedependent Markovian demand process. However, our framework can also be generalized to other inventory models. Our report is organized as follows. In the next section, we will provide the theoretical formulation of the Stochastic program framework. In section 3, we transform the Stochastic program into a linear program using SAA. In section 4, we introduce the state-dependent Markovian demand process that will be used in the numerical study. And we provide the design of experiment and the result of the numerical study in section 5. We conclude the report and provide some discussions in section 6. We also list the notations in Appendix A and provide the matlab code for the empirical study in Appendix B for the readers’ convenience.