Optimal Policies for a Multi-Echelon Inventory Problem

TLDR

Recent work on inventory problems has focused on single-location optimal purchasing, often assuming fixed or size‑independent lead times, but real‑world multi‑echelon systems violate this assumption because lead times depend on upstream stock availability. The study aims to determine optimal purchasing quantities in a multi‑installation inventory model where lead times depend on upstream stock availability. The authors analyze a multi‑installation model that incorporates size‑dependent lead times to derive optimal purchasing policies.

Abstract

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment of stock, this shipment will be delivered in a fixed or perhaps random length of time, but at any rate with a time lag which is independent of the size of the order placed. There are, however, a number of situations met in practice in which this assumption is not a tenable one. An important example arises when there are several installations, say 1, 2, …, N, with installation 1 receiving stock from 2, with 2 receiving stock from 3, etc. In this example, if an order is placed by installation 1 for stock from installation 2, the length of time for delivery of this stock is determined not only by the natural lead time between these two sites, but also by the availability of stock at the second installation. In this paper we shall consider the problem of determining optimal purchasing quantities in a multi-installation model of this type.