Abstract

A novel clusteringalgorithm is proposed and applied to the multi-item replenishment processing.This new algorithm has two distinguished features: non-binary hierarchical treeand the feature of overlapping clustering. A non-binary hierarchical tree ismuch smaller than the binary-trees constructed by most traditional algorithmsand, therefore, it clearly highlights meaningful clusters which significantlyreduce further manual efforts for cluster selections. The feature ofoverlapping clustering provides a better replenishment strategy for some singleitem that shares inventory patterns with more than one cluster. A simulationexample for comparison illustrates the effectiveness of the proposed algorithm.
Keywords: Cluster, Can-order Policy,Joint Replenishment Problem

1.  Introduction

Joint replenishment problem (JRP) is an extensively studied topic insupply chain management. It requires the coordination of replenishment strategyfor several items so that the cost savings can be achieved. Many mathematicalmodels and algorithms have been proposed to find the quality solutions of thisproblem. In [2], Loo Hay Lee and Ek Peng Chew classified these models andalgorithms into two broad categories, the deterministic and the stochasticjoint replenishment policies. Most of the deterministic problems in recentyears have focused on finding efficient computational algorithms to derive goodheuristic solutions for a large number of stock keeping units[3, 4, 5]. Goyaland Satir [6] gave an overview of the many heuristic procedures that haveappeared in the literature up to 1989, and then Moutaz Khouja and Suresh Goyal [7]review and summarize the literature on the joint replenishment problem from1989 to 2005. The stochastic problems, on the other hand, attempt to optimizethe parameters for a given assumed inventory policy. Refer to [8] for a moredetailed instruction to this problem.

As one of the existing joint replenishment policies,the can-order policy, which was originally suggested by Balintfy [9], hasreceived considerable attention in the inventory management literature in the pastdecades. This policy is characterized by three parameters: (). When the inventory position drops to or below themust-order level , an order is placed to bring the inventory position upto .