Multi-item two storage inventory models for breakable items with fuzzy cost and resources based on different defuzzification techniques

Abstract

This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock and selling price dependent demand under imprecise space and budget constraints with two storage facilities. There are one rented warehouse called own warehouse (OW) at the market place and another rented warehouse (RW) at a little distance away from the market place. The sale is conducted from OW and the sold items are replaced continuously by the items at RW. The units at RW are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function i.e. rate of breakability per unit time be linear function of current stock level. Here shortages are not allowed. Normally inventory models involve imprecise parameters or resources like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation etc. Here, main emphasis has been given on the different defuzzification techniques such as min operator method, average operator method, two-phase approach and compromise technique for the fuzzy programming problems having fuzzy technical coefficients and fuzzy resources and the application of these techniques to a two-storage inventory problems for breakable items. Two two-warehouse fuzzy inventory models have been formulated as maximization problems with the above assumptions and solved using various defuzzification techniques and a gradient based non-linear programming technique - Generalised Reduced Gradient (GRG) method. The models are illustrated with numerical examples. Results from different techniques are graphically compared and some sensitivity analyses have been presented.