Multi-item Inventory Control: the K-Curve Methodology

Author: Maike Schwarz

Abstract: This article deals with the problem of optimally coordinating the replenishment in a multi-item stock-keeping environment.  The K-Curve Methodology represents a way to classify all items into a given number of classes with a common order frequency.  A theoretical investigation of the K-Curve Methodology however show that this methodology does not achieve an optimal grouping of the items in respect to the cost function considered in most articles.  Practical experience shows that the K-Curve Methodology fits the objectives of management and represents a good decision aid in practice.


A multi-item inventory system is considered which has the property that, for each single item, a reorder policy using the EOQ formula would be appropriate.  The ordering costs can not be reduced by ordering items jointly.

In real-life procurement processes it is often desirable to form a number of classes of items where all items of one class share the same order cycle.  This yields simplified stock control, better supplier relations, more reliable deliveries and improved warehouse planning.  Practitioners who are responsible for the management of thousands of items have to define objectives regarding inventory level, workload, and customer service and furthermore simple methodologies are needed to take decisions.

The question which items should have the same order cycle in order to minimize the total costs associated with ordering and holding the items given a desired number of groups has been studied by several authors.  Page and Paul were the first to consider a coordinated replenishment of items and proposed an algorithm for classifying the items.  Chakravarty showed that the optimal groups possess a constructiveness property and hence can be found by using a dynamic programming recursion or a shortest path algorithm. Donaldson suggested to choose the ordering frequencies in geometric progressions.  Aggarwal assumed that the cumulative distribution by values of the inventory can be characterized by a Pareto function of a certain type and established optimal boundaries of the groups in closed form.  Aggarwal studied in the sensitivity of the optimal group boundaries so obtained.  The results demonstrate the availability of flexibility in the partition boundaries.

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