Analysis of Some Stochastic Inventory System in Supply Chain

Analysis of Some Stochastic Inventory System in Supply Chain

Bakthavachalam Rengarajan (Alagappa University, India)
Copyright: © 2016 |Pages: 24
DOI: 10.4018/978-1-5225-0044-5.ch008


In this chapter we consider a three echelon inventory control system which is modeled as a warehouse, single distribute and one retailer system handling a single product. A finished product is supplied from warehouse to distribution center which adopts one-for-one replenishment policy. The replenishment of items in terms of packets from warehouse to distribution center with exponential lead time having parameter µ1. Then the product is supplied from distribution center to retailer who adopts (s, S) policy. Supply to the retailer in packets of Q (= S - s) items is administrated with exponential lead time having parameter µ0. The demand at retailer node follows a Poisson with mean lambda. The steady state probability distribution of system states and the measures of system performance in the steady state are obtained explicitly. The Cost function is computed by using numerical searching algorithms, the optimal reorder points are obtained for various input parameters. Sensitivity analysis are discussed for various cost parameter such as holding cost, setup cost etc.
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1. Introduction

In this chapter, we study some stochastic inventory control problems in Supply Chain Management System (SCMS). Our main objectives are to find steady state probabilities of the inventory levels and the optimum values of the decision variables that minimize the total excepted cost in the SCMS. Most of the results are illustrated with numerical examples and sensitivity analysis.

The major focus of our work is on operational decisions such as inventory control and distribution management in Supply Chain (SC). The motivation of our research lies with real life serially connected locations and the need of optimal policies for its efficient maintenance. Even though the numbers of models analyzed within the preview of Supply Chain are limited, we studied the flow of goods through the Supply Chain which are both perishable and non-perishable. Most of our models assume Poisson demand, exponential lead times and exponential life time. Since the demand is highly fluctuating the position inventory can be considered as a random process, to deal with real life problems we consider Supply Chain with random type demands and lead times only in this work.

1.1. The Importance of Supply Chain Management

Basically, the world is one of the biggest Supply Chain. The Supply Chain Management (SCM) touches major issues, including the rapid growth of multinational corporations and strategic partnerships; global expansion and sourcing; fluctuating gas prices and environmental concerns. Each of these issues dramatically affects corporate strategy and bottom line. Because of these emerging trends, Supply Chain management is the most critical business discipline in the world today.

A Supply Chain may be defined as an integrated process wherein a number of various business entities suppliers, distributors and retailers work together in an effort to (i) acquire raw materials (ii) process them and then produce valuable products and (iii) transport these final product to retailers.

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