Multi-item imperfect production inventory model in Bi-fuzzy environments

Abstract

In this paper, we propose a mathematical model for a single period multi-product production inventory model producing stochastically imperfect items with continuous stochastic demand under budget and limited shortage constraints in Bi-fuzzy environment. The stochastic constraints are first converted into corresponding crisp values using expected value method. Here, we have considered the model as single period’s inventory for each item and the cycle lengths for different items are constant but different. Total demand for a cycle and the rate of production of defective units is considered as stochastic. The model is formulated and the expected average profits for each product are calculated from density function of demand and percentage of imperfectness in general form and then particular expressions are obtained by using appropriate boundary conditions. Here, all the constraints are Bi-fuzzy in nature and represented by possibility constraints. The deterministic problem is then solved by using generalized reduced gradient method. The model is illustrated through numerical examples. Sensitivity analysis on profit functions due to different aspiration and confidence level is presented via graphically.