A perishable inventory optimization model for two commodities in multi-echelon system

Authors

  • Prabaharan Kathiresan Mathematics (Alagappa University, Karaikudi); pharansouc@gmail.com
  • Bakthavachalam Rengarajan Government Arts and Science College for Women, Paramakudi); bakthaa@yahoo.com

DOI:

https://doi.org/10.23755/rm.v48i0.1201

Keywords:

Multi-echelon system, Markov process, Optimization. two commodity perishable inventory System,

Abstract

In this article, we delve into the quest for an optimal solution within the realm of a practical inventory system, which serves as an integral component of a larger Multiechelon inventory system. Our study focuses on a warehouse (WH) that houses a single Distribution Center (DC) and a sole retailer (R) tasked with managing two distinct yet interconnected perishable products. This setup is modeled as a three-stage continuous review inventory system. At the retailer node, we implement an (s, S) inventory system, accommodating Poisson demand and exponentially distributed lead times. It’s important to note that the primary products are susceptible to perishing exclusively at the retailer node, characterized by a rate ζ, whereas the sub-products are non-perishable in nature. Deliveries to retailers occur in packs of Qi(= Si − si) units, originating from the distribution center (DC) with immediate replenishment capabilities sourced from the well-stocked warehouse (WH). Throughout our analysis, we rigorously maintain steady-state probability distributions and behavioral insights. Furthermore, we diligently collect and analyze performance measurements for the system under steady-state conditions. Our findings are showcased through numerical examples, shedding light on the practical implications of our inventory management approach.

References

N. Anbazhagan and G. Arivarignan. "Two-commodity continuous review inventory system with coordinated reorder policy." International Journal of Information and Management Sciences, 11(3):19–30, 2000.

S. Axsater. "Simple solution procedures for a class of two-echelon inventory problems." Operations Research, 38(1):64–69, 1990.

R. Bakthavachalam, Navaneethakrishnan, and C. Elango. "Stochastic perishable inventory control systems in supply chain with partial backorders." International Journal of Mathematics Sciences & Applications, 2(2):680–708, May 2012.

B. Benita, M. "Supply chain design and analysis: Models and methods." International Journal of Production Economics, 55(3):281–294, 1998.

J. Clark, A and H. Scarf. "Optimal policies for a multi-echelon inventory problem." Management Science, 6(4):475–490, 1960.

C. Elango. "A continuous review perishable inventory system at service facilities." 2001.

F. Harris. "Operations and costs, factory management series." Pages 48–52, 1915.

Q. He, E. Jewkes, and J. Buzacott. "An efficient algorithm for computing the optimal replenishment policy for an inventory-production system." Pages 381–402, 1998.

S. Kalpakam and G. Arivarignan. "A coordinated multicommodity (s, s) inventory system." Mathematical Computer Modelling, 18:69–73, 1993.

C. Kartheeswari and R. Bakthavachalam. "Analysis of integrated inventory control system in supply chain with partial backloggin." International Journal of Computational and Applied Mathematics, 12(1), 2017.

A. Krishnamoorthy, R. Iqbal, Basha, and B. Lakshmy. "Analysis of a two commodity problem." International Journal of Information and Management Sciences, 5(1):127–136, 1994.

K. Krishnan. "Stochastic modeling in supply chain management system." 2007.

S. Kumaresan, R. Bakthavachalam, and K. Krishnan. "Perishable inventory system with (s, q) policy in supply chain." International Journal of Mathematics and Soft Computing, 4(2):213–224, 2014.

C. Sherbrooke. "Metric: A multi-echelon technique for recoverable item control." Operations Research, 16(1):122–141, 1998.

V. Yadavalli, C. Van Schoor, J. Strasheim, and S. Udayabaskaran. "A single product perishing inventory model with demand interaction." ORiON, 20(2):109–124, 2004.

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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