Multi-item EOQ model with hybrid cost parameters under fuzzy/fuzzy-stochastic resource constraints: A geometric programming approach

In this paper, a multi-item economic order quantity (EOQ) model is considered in which the cost parameters are of fuzzy/hybrid nature under two types of resources — (a) resources as fuzzy quantities; (b) resources as fuzzy and fuzzy-random quantities. The unit cost depends on demand rate. The time horizon is taken to be infinite. We find the average cost for the model, which is a function of order quantity and demand rate and also of some hybrid parameters. When the resources are fuzzy quantities, the problem is transformed into its equivalent unconstrained deterministic form by using a surprise function for the constraints. The problem involving hybrid number is again equivalently rewritten as a multi-objective (minimization of the mean of the objective function and variance function of the distribution) inventory problem. Introducing new variables we transform the terms of the functions into signomial types. Using fuzzy multi-objective solution procedure we solve the problem through Geometric Programming approach. Sensitivity analysis has been performed to study the effect of different weights considered for mean objective function and variance function.