Developing a Fuzzy-Stochastic Multi Objectives Inventory Model

In this paper we developed an inventory model in mixed imprecise and uncertain environment. Presented model is developed form of (r,Q) and is a multi-items model with two objectives as minimizing costs (holding & shortage) and risk level under constraints including available budgetary, the least service level, storage spaces & allowable quantities of shortage. Demand distribution functions are assumed to be exponential and extra demands are supposed in two situations as lost sales and backlogging. At first we develop crisp model then fuzzy stochastic model with fuzzy budgetary, allowable quantities of shortage and shortage spaces (i.e. stochastic with normal distribution function) parameter. All of fuzzy numbers are triangular type. In methodology of solution we change model to a crisp multi-­objective by using difuzzification of fuzzy constraints and fuzzy chance-constrained programming methods, and then solve it by fuzzy logic method. Finally an illustrated example is taken and solved using LINGO package