Inventory Model with Genralized Pareto Rate of Replinishment Having Time Dependent Demand

K. Srinivasaro¹ , B. Punyavathi²

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.1 , pp.92-106, Feb-2020

Online published on Feb 28, 2020

Copyright © K. Srinivasaro, B. Punyavathi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Generalized Pareto distribution gained lot of importance in income analysis and life testing experiments due to its long upper tail. The characteristics of the life time of a commodity in production processes dealing with deteriorated items match with the statistical characteristics of the Generalized Pareto distribution. Hence, in this paper we develop and analyze an economic production quantity model with generalized Pareto rate of production and deterioration. Here it is assumed that the production quantity is random and follows a Generalized Pareto distribution. It is further assumed that the life time of the commodity is random and follows a Generalized Pareto distribution. Considering that the demand rate is time dependent and follows a power pattern the instantaneous state of inventory at any given time in the cycle length under the assumptions of shortages are allowed and fully backlogged is derived. With plausible cost considerations the total production cost of the system is derived and minimized with respect to production up time, production down time and production quantity. The sensitivity analysis of the model reveals that the random production and random life time have significant influence on production. It is further observed that the deteriorating distribution and life time distribution parameters have tremendous influence on optimal operate policies of the system. This model also includes the model without shortages as a limiting case. This model is useful for analyzing the production systems dealing with deteriorating items.

Key-Words / Index Term :
Generalized Pareto distribution, Random Production, Economic Production Quantity Model, Sensitivity Analysis, Production Scheduling, Deterioration

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