An application of robust optimization in inventory theory

Abstract

Inventory is very important for a company, as with the lowest possible stock levels, a company has to meet customer demands. By having in stock the right and an appropriate amount of products, a good plan will help the company to save money and space and also satisfy customers while making the largest possible profits. However, it is very difficult to predict what and how much the customers would like to buy and therefore all models are based on forecasts. Many techniques have been studied to improve the forecasts but they can never be exact. Thus, a technique called robust optimization has been studied that is based on the worst-case demand uncertainty. This dissertation focuses on a robust optimization technique where without making any distributional assumptions, this approach is easy to implement and understand. Moreover, this also simplifies to a linear programming model that offers protection against constraint violation and seeks the highest possible solutions. In order to obtain a feasible solution in the presence of variations in the data, this procedure is prepared to accept suboptimal solutions. In addition, probabilistic guarantees are also provided in order to show that the robust solution is feasible with high probability. Later, this technique is applied to the problem of inventory management, where without any distributional knowledge of the demands, this provides good solutions in the presence of stochastic demands. It is also shown that the form of the robust optimal policy is base-stock and is equivalent to the nominal policy for a sequence of modified demands. The resulting mathematical model is then applied to some data obtained from a local hotel and also from a local manufacturing company.