A risk-averse multi-item inventory problem with uncertain demand

The observed values of demands in real-life inventory problems are sometimes imprecise due to the lack of information and historical data, thus a growing research is committed to study the properties of risk measures in fuzzy inventory optimization problems. In this paper, a risk-averse fuzzy optimization method is adopted for the multi-item inventory problem, in which the demands are described by common possibility distributions. Firstly, three classes of fuzzy inventory optimization models are built by combining the absolute semi-deviation with expected value operator and then model analysis is given for the min-max inventory models. To make the inventory problem tractable and computable, the equivalent forms of the proposed optimization models are discussed. Subsequently, several useful absolute semi-deviation formulas are presented under triangular, trapezoidal and Erlang possibility distributions. Finally, some numerical experiments are performed to highlight the modeling idea, and the computational results demonstrate the effectiveness of the solution method.