Abstract
In this paper we developed a fuzzy inventory model for deteriorating items with time dependent demand rate. Shortages are allowed and completely backlogged. The backlogging rate of unsatisfied demand is assumed to be a decreasing exponential function of waiting time. The demand rate, deterioration rate and backlogging rate are assumed as a triangular fuzzy numbers. The purpose of our study is to defuzzify the total profit function by signed distance method and centroid method. Further a numerical example is also given to demonstrate the developed crisp and fuzzy models. A sensitivity analysis is also given to show the effect of change of the parameters.
Highlights
In many inventory models uncertainty is due to fuzziness and fuzziness is the closed possible approach to reality
In this paper we studied a fuzzy inventory model for deteriorating items with time dependent demand rate and partial backlogging
As we increase the parameters α, σ and θ in the crisp model the total profit increases and due to the uncertainties in the demand rate, deterioration rate and backlogging rate the parameters α, σ and θ are consider as triangular fuzzy numbers
Summary
In many inventory models uncertainty is due to fuzziness and fuzziness is the closed possible approach to reality. In recent years some researchers gave their attention towards a time dependent rate because the demand of newly launched products such as fashionable garments, electronic items, mobiles etc. Increases with time and later it becomes constant. Deterioration is defined as damage, decay or spoilage of the items that are stored for future use always loose part of their value with passage of time, so deterioration cannot be avoided in any business scenarios. F. Harris (1915) [1] developed first inventory model. Zadeh (1965) [2] introduced the concept of fuzzy set theory in inventory modeling. Zadeh [3] and R.
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