Operations Research Proceedings 2005

A Two-echelon Model for Inventory and Returns ( p. 131)

Allen H. Tai and Wai-Ki Ching

Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China. h0150695@graduate.hku.hk, wkc@maths.hku.hk

Summary.

We consider an Markovian model for a two-echelon inventory/return system. The system consists of a supply plant with in.nite capacity and a central warehouse for inventory and returns. There is also a number of local warehouses which are also able to re-manufacture products. To obtain a high service level of handling inventory and returns, lateral transshipment of demands is allowed among the local warehouses.

1 Introduction

The efficiency of product/service delivery is one of the major concerns in many industries including re-manufacturing industry. Since customers are usually scattered over a large regional area, a network of locations (local warehouses) for inventory of products and handling of returns is necessary to maintain a high service level. In our study, Lateral Transshipment (LT) is allowed among the local warehouses to enhance the service level. LTs are also very practical in many organizations having multiple locations linked by computers.

Substantial savings can be realized by the sharing of inventory in the local warehouses [15]. A number of research publications have been appeared in this area. Kukreja et. al [9] developed a single-echelon and multi-location inventory model for slow moving and consumable products. Moinzadeh and Schmidt [12] studied the emergency replenishment for a single-echelon model with deterministic lead times.

Aggarwal and Moinzadeh [2] then extended the idea to a two-echelon model. Ching [5] considered a multi-location inventory system where the process of LT is modelled by Markov-modulated Poisson Process (MMPP). Both numerical algorithm and analytic approximation have been developed to solve the steady-state probability distribution of the system [5, 8]. Lee [10] and Axsäter [3] considered a two-echelon system in which the local warehouses are grouped together. Within the group, the warehouses were assumed to be identical.

Simulation study of a two-echelon system can also be found in [14]. Alfredsson and Verrijdt [1] considered a two-echelon inventory system for service parts with emergency supply options in terms of LT and direct delivery. In this paper, we consider an inventory/returns model based on the framework and analysis discussed in [1, 10].

The model of the system consists of a supply plant with infinite capacity, a central warehouse and a number of local warehouses with re-manufacturing capacity. Here we consider a queueing model for a two-echelon inventory system. Queueing model is a useful tool for many inventory models and manufacturing systems [4, 5, 7, 8].

2 The Two-echelon System

In this section, we present a two-echelon system based on the framework discussed in [1, 10]. The system consists of a supply plant with infinite capacity, a central warehouse (maximum capacity C) and n identical local warehouses (each has a capacity of L), see Fig. 1.