A class of bifuzzy model and its application to single-period inventory problem∗

In this research we concentrate on developing a bifuzzy model for a Single-period inventory problem. The conventional studies have focused on the cases that the demands are probabilistic and follow certain distribution function; or the demands are considered as fuzzy variables; or the demands is expressed by random fuzzy variable. Recently, fuzzy random variables have been applied to some decision-making problems in such situations. However, there is no research about decision-making including a bifuzzy variable and such problems do exist in real-lift. In this paper, we analyze the single-period inventory problem in the presence of uncertainties and the demands are considered as bifuzzy variables. A method for the ordering of fuzzy numbers with respect to their total integral values is adopted to find the optimal quantity of maximizing the expected profit function. If the profit gained from selling one unit is less than the loss incurred for each item left unsold, then the inventory policy should be conservative to reduce the leftover. On the contrary, if the profit gained is greater than the loss incurred, then the inventory policy should be aggressive to satisfy the possible demand. When the profit gained is equal to the loss incurred, the order quantity should be equal to the most likely demand and correspond to the quantity with membership grade 1. The proposed model and algorithm, which can solve perfectly the uncertain Single-period inventory problem, provide significant solutions to construct other inventory models with bifuzzy variables in real-life.