Risk Analysis in a Production Inventory Model with Fuzzy Demand, Variable Production Rate and Production Time Dependent Selling Price

In this paper a production inventory model of a single item with a variable production rate and production time dependent selling price has been introduced. Realistically it is seen that for any business concern, demand is always uncertain. Henceforth, in this model, demand of an item has been assumed to be fuzzy but its membership function is not known in prior. It is also considered that the production rate is a decreasing function of the inverse efficiency of the system. Under these circumstances, a profit function of the model has been formulated. As demand is fuzzy with unknown membership function, hence to get expected maximum profit, the diffusion method including possibility probability distribution has been used and the risk estimation values for failure to attain different profit levels have been evaluated. Finally the proposed model has been demonstrated taking a numerical example and a comparison among different types of demand such as crisp, fuzzy with triangular and trapezoidal membership value and fuzzy with unknown membership value have been shown.