Inventory Control: Fuzzy Demand

Introduction

This chapter continues Chapter 20 on fuzzy inventory control. The first changes made in this chapter are to allow shortages and have demand $\overline{D}_i$ fuzzy. There will be no backlogging (back orders) so shortages result in lost sales and loss of customer’s goodwill. The penalty cost, due to shortages, is usually very difficult to estimate so it will be modeled by a fuzzy number $\overline{p}_i$ for the period i. We will still minimize the total fuzzy cost, with $\overline{D}_i$, $\overline{K}_i$, $\overline{h}_i$, $\overline{p}_i$ and also the $\overline{x}_i$ (i ≥ 2) all fuzzy, subject to fuzzy $\overline{x}_{N+1}$ approximately zero. We now discuss in more detail the changes from Chapter 20 to this chapter in order to handle fuzzy demand and shortages. Then we plan to apply our Monte Carlo method to a numerical example and compare its solution to a crisp solution and an evolutionary algorithm solution.