A Deterministic Inventory Model with Two Warehouses and a Finite Rate of Replacement for Deteriorating Products

Abstract

When demand is uniform, shortages are permitted, and the replenishment rate is finite, a deterministic inventory model for degrading items with two warehouses is created. It is anticipated that there may be differences in the rates of item deterioration between the two warehouses. An analysis of the model is conducted for the continuous release pattern situation. The variance in the ideal inventory level and optimum cost for changing shortage costs is illustrated with a numerical example and discussion of several unique instances.

Introduction

I. INTRODUCTION

The deterministic demand scenario involving a single storage facility is the primary scenario for which the classical inventory models are constructed. However, when considering the matter more practically, if a considerable supply needs to be held and the available facility, like the own warehouse (OW), has a limited capacity, then extra storage space may be needed. One possible option for this extra storage space may be a leased warehouse (RW), like a central warehouse equipped with advanced preservation technology. Hartley [3] provides an early explanation of an inventory model with two storage facilities. The holding cost in the RW is typically thought to be higher than the same in the OW. As a result, only extra stock is kept in the RW; all other products are kept in the OW. Additionally, the RW goods are released first, followed by the OW things.

A number of writers have recently thought about expanding on the fundamental two-storage inventory model covered. Constructed a deterministic inventory model with an infinite production rate and two layers of storage, with and without shortages. A case study of an extension to the finite production rate without shortages has been studied. The study is done for the scenario of bulk release pattern in the two models mentioned above. In the event of an unlimited pace of replenishment with shortages, explored expanding his previous model, assuming that the goods degrade in both warehouses. We create an order-level inventory model with two storage facilities for decaying items in this research. We presume that the deterioration rate of the products held might be different in the two warehouses due to the difference in the environmental conditions or preserving settings. Even in the event that the rate of deterioration in both warehouses is constant, the model is still relevant. For the situation of continuous release pattern, we formulate and assess the model assuming uniform demand and shortages are tolerated and the production rate is finite. We also infer an accurate form of the cost equation for the model without making any approximations, and we also make some observations on the 'single storage' version of this model.

II. NOTATIONS

R is the demand rate per time unit, which remains constant during the duration of the analysis.

P is the limited output rate.

There is no supply lead time and the scheduling period T is a set constant.

There is a backlog of shortages, and the cost per unit of time is pi for each shortage.

The unit holding cost is expressed as C1 per unit cost, where C1 denotes items in the OW as H and items in the RW as F.

The rates of OW and RW deterioration are a and b, respectively.

The inventory level in the OW at time point t is shown by Qo(t), and the inventory level in the RW at time point r is indicated by Qr(t).

The RW has an infinite capacity, but the OW has a limited capacity of W units.

C is the estimated cost of a degraded unit, which takes salvage value and disposal costs into account.

S is a decision variable that represents the amount of inventory in the RW at which production is halted.

References

[1] T.P.M. Pakkala. and K.K. Achary , \" A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate\", European Journal of Operational Research 57 (1992) 71-76. [2] Chowdhury M.R., and Chaudhuri, K.S., \"An order-level inventory model for deteriorating items with finite rate of replenishment\",Opsearch 20 (1983) 99-106. [3] Dave, U., \"On the EOQ models with two levels of storage\", Opsearch 25 (1988) 190-196. [4] Hartley, V.R., Operations Research - A managerial Emphasis, Goodyear, Santa Monica, CA, 1976, Chapter 12, 315-317. [5] Murdeshwar, T.M., and Sathe, Y.S., \"Some aspects of lot size models with two levels of storage\", Opsearch 22 (1985) 255-262. [6] Sarma, K.V.S., \"A deterministic inventory model with two levels of storage and an optimum release rule\", Opsearch 20 (1983) 175-180. [7] Sarma, K.V.S., \"A deterministic order-level inventory model for deteriorating items with two storage facilities\", European Journal of Operational Research 29 (1987) 70-72. [8] Sarma, K.V.S., and Sastry, M.P., \"Optimum inventory for systems with two levels of storage\", Industrial Engineering Journal 8 (1988) 12-19. [9] Shah, Y.K., and Jaiswal, M.C., \"An order-level inventory model for a system with constant rate of deterioration\" Opsearch 14 (1977) 174-184.

Copyright

Copyright © 2024 Dr. Kishor Y. Ingale, Mr. Avinash D. Rajegore. 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.