Determining the Optimum Ordering Policy in Multi-Item Joint Replenishment Problem Using a Novel Method

Wen-Tsung Ho

doi:10.1155/2013/469794

Abstract

This work investigates the joint replenishment problem (JRP) involving multiple items where economies exist for replenishing several items simultaneously. The demand rate for each item is known and constant. Shortages are not permitted and lead times are negligible. Many heuristic algorithms have been proposed to find quality solutions for the JRP. In this paper, cycle time division and recursive tightening methods are developed to calculate an efficient and optimal replenishment policy for JRP. Two theorems are demonstrated to guarantee that an optimal solution to the problem can be derived using cycle time division and recursive tightening methods. Restated, cycle time division and recursive tightening methods theoretically yield the optimal solution in 100% of instances. The complexity of cycle time division and recursive tightening methods is justO(NlogN), whereNrepresents the number of items involved in the problem. Numerical examples are included to demonstrate the algorithmic procedures.

Highlights

The joint replenishment problem (JRP) is an inventory problem involving multiple items where economies exist for replenishing several items simultaneously
The author of [11] was the first to present an optimal algorithm for the inventory problem involving multiple items supplied by a single supplier with the assumption of purchase orders placed at equal time intervals
This work studies the joint replenishment problem involving multiple items where economies can be achieved by replenishing several items simultaneously

Summary

Introduction

The joint replenishment problem (JRP) is an inventory problem involving multiple items where economies exist for replenishing several items simultaneously. A heuristic method was proposed for determining order quantities in joint replenishments with deterministic demand in [14]. The author of [21] pointed out that the lower bound of the Goyal method [11] cannot guarantee to yield an optimal solution He recommended the correct lower bound on T and demonstrated a heuristic algorithm for deriving the optimal among the various cyclic policies. The bounds on the basic cycle time are derived and a global optimization procedure is proposed to solve the JRP with constraints. A heuristic method based on a spreadsheet technique for solving joint replenishment problems with strict cycle policies was proposed in [31]. This study proposes the cycle time division (CTD) and recursive tightening (RT) methods to calculate an efficient and optimal strict cyclic policy for JRP.

Cycle Time Division Method

Recursive Tightening Method

Optimization Algorithm

Numerical Examples

Findings

Concluding Remarks