An Inventory Model for Weibull Distributed Deteriorating Items Under Ramp Type Demand and Permissible Trade Credit Policy

doi:10.7176/ejbm/13-19-03

Abstract

In a classical inventory economic order quantity (EOQ) model, the stock is depleted due to both market demand and deterioration. Many inventory models are developed for items under variable rate of deterioration. The two parameter Weibull distributed term is a representation of constant, time dependent linear and non-linear, increasing and decreasing rate of deterioration. Again the demand rate is assumed here as time dependent in beginning of cycle and then becomes constant as passage of time. Shortages are allowed and fully backlogged. Moreover the trade credit policy is a win-win payment strategy for sharing profit in the inventory system. This present paper deals with a replenishment policy assuming two parameter Weibull distributed deteriorating items, demand rate a ramp type function of time under permissible trade credit policy. Finally several numerical examples are given to illustrate the model and some particular cases are also discussed along with its’ illustrations along with concluding remarks. Keywords: Inventory, Weibull distribution, deterioration, ramp type, trade credit and shortages. Subject classification: AMS Classification No. 90B05 DOI: 10.7176/EJBM/13-19-03 Publication date: October 31 st 2021

Highlights

In a classical economic order quantity (EOQ) model and in view of a real life situation, inventory is depleted due to both market demand and deterioration
The deterioration rate is followed by two parameter Weibull distributed which is a representation of constant, time dependent linear and non-linear, increasing and decreasing function of time
Behera [2017], Biswaranjan Mandal[2021] etc. are noteworthy. This present study investigates a situation in which replenishment policy is assumed with two parameter Weibull distributed deteriorating items, demand rate a ramp type function of time under permissible trade credit policy

Summary

Introduction

In a classical EOQ model and in view of a real life situation, inventory is depleted due to both market demand and deterioration. Chakrabarty et al[1998], K.S.Wu (2002), Anil Kumar Sharma[2012], Biswaranjan Mandal[2010],[2020] and many are developing different inventory models assuming items which deteriorate at constant or vary over time. When a new brand of goods like new branded car, dolls, advanced computer devices etc come in the market, the initial demand is mostly increasing with time and stabilizes as constant. Beyond this period of time, the interest is charged by the supplier This trade credit policy is a win-win payment strategy for sharing profit in the inventory system. This present study investigates a situation in which replenishment policy is assumed with two parameter Weibull distributed deteriorating items, demand rate a ramp type function of time under permissible trade credit policy.

Model development

Numerical Examples

Concluding Remarks