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Computer and Information Science » Numerical Analysis and Scientific Computing » "Efficient Decision Support Systems - Practice and Challenges in Multidisciplinary Domains", book edited by Chiang Jao, ISBN 978-953-307-441-2, Published: September 6, 2011 under CC BY-NC-SA 3.0 license. © The Author(s).

# Quick Response in a Continuous-Replenishment-Programme Based Manufacturer Retailer Supply Chain

By Shu-Lu Hsu and Chih-Ming Lee
DOI: 10.5772/20186

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## Overview

Figure 1. Inventory levels for a manufacturer and multiple retailers under a coordinated common shipment cycle time

Figure 2. The system window to input parameters

Figure 3. The replenishment and lead time reduction decisions under CRP provided by the decision support system

Figure 4. The coordinated replenishment decision under CRP provided by the decision support system

Figure 5. The “what-if analysis” function of the decision support system

# Quick Response in a Continuous-Replenishment-Programme Based Manufacturer Retailer Supply Chain

Shu-Lu Hsu1 and Chih-Ming Lee2

## 1. Introduction

With the widespread concept of partnership in supply chain management, the traditional replenishment process is fast giving way to the Quick Response (QR) and Continuous Replenishment Programme (CRP). QR is a movement in industries to shorten the replenishment lead time which is critical to reduce inventory level and improve the levels of customer service. Wal-Mart, Seven-Eleven Japan, and many other retailers apply tremendous pressure on their suppliers to reduce the replenishment lead time (Chopra and Mendil 2007). CRP is an efficient replenishment initiative which focuses on removing excess inventory throughout the pipeline and synchronizes demand with production (EAN International 2000). In CRP, the inventory of retailer is planned, monitored, and replenished by the supplier on behalf of the consumers. To enable CRP, sales data and inventory level of the retailer must be provided to the supplier via Electronic Data Interchange (EDI) or other electronic means. Thus, to successfully implement CRP requires the supplier and the retailer to work in a cooperative manner based on mutual trust and joint gains.

The study of inventory decision of CRP based inventory systems was initiated by Goyal (1976) by presenting a joint economic lot-size model for a supplier and a retailer. Subsequently, many researchers investigated this issue under various assumptions. For example, Banerjee (1986) generalized the model of Goyal (1976) by incorporating a finite replenishment rate for the supplier. Goyal (1988) extended Banerjee’s work by relaxing the lot-for-lot policy for the supplier and assumed that the supplier’s lot size is an integral multiple of retailer’s order quantity. Goyal and Srinivasan (1992) further extended the model by relaxing the assumption that the supplier can supply to the retailer only after completing the entire production lot. At the same time, Banerjee and Banerjee (1992) extended the study of integrated inventory control to a multiple-retailer case by considering that the supplier delivers items to several buyers at a coordinated common cycle time. Banerjee and Banerjee (1994) generalized their previous model by dealing with the normally distributed demand case and assuming a fixed shortage cost attributable to each stockout incident.

To understand the effects of QR on the CRP based supply chains, we build a formal model of lead time reduction and replenishment decisions for a supply chain consisting of a manufacturer and multiple retailers in which the inventory throughout the supply chain is managed in a CRP context. The model extends the work of Banerjee and Banerjee (1994) by including the ordering cost and adopting QR with the expenditure regarded as a function of the reduced lead time. In stead of explicitly estimating the shortage cost, a service level constraint (SLC) approach is applied to the problem for which may skirt the difficult practical issue of explicitly determining the shortage cost (Chen and Krass 2001). According to the definition in Ouyang and Chuang (2000), the service level in this study is measured by the expected fraction of demand met from inventory on hand in an inventory cycle. The objective of the model is to determine the common shipment cycle time and the replenishment lead time for the retailers, the manufacturer’s production cycle time, and the target levels of replenishment for the manufacturer and each retailer so that the expected total system cost can be minimized under the service level constraint.

## 2. Notations and assumptions

To develop the proposed models, we adopt the following notation which is principally the same as that in Banerjee and Banerjee (1994):

n= total number of retailers;

d i = demand rate of retailer i, which follows a probability density function (p.d.f.) f i (d i ) with mean D i and variance σi2 , i =1, 2,…, n;

h i = carrying cost per unit per year for retailer i ($/unit/year); h v = carrying cost per unit per year for the manufacturer ($/unit/year);

l= length of lead time for retailers (year), a decision variable;

x i = demand during the protection period (T+l) on retailer i, which has a p.d.f. fiT+L(xi) with the mean Di(T+l) and the variance σi2 (T+l);

y= demand during the production cycle time of KT on manufacturer, which has a p.d.f. g(y) with the mean KTi=1nDi and the variance KTi=1nσi2 ;

z i = safety factor for retailer i with z i ≥ 0;

z v = safety factor for the manufacturer with z v ≥ 0;

α i = the threshold of retailer i’s service level, 0 ≤ α i ≤1;

α v = the threshold of manufacturer’s service level, 0 ≤ α v ≤1;

A= setup cost for the manufacturer ($/per setup); C= common ordering cost shared by all retailers ($/per order);

#### Figure 2.

The system window to input parameters

#### Figure 3.

The replenishment and lead time reduction decisions under CRP provided by the decision support system

#### Figure 4.

The coordinated replenishment decision under CRP provided by the decision support system

#### Figure 5.

The “what-if analysis” function of the decision support system

decision maker clicks “Perform”. From the value of “Saving”, the benefit derived from implementing QR can be learned. As shown in Figure 4, the system also provides the inventory decision before QR (represented by the constant lead time option). One advantage of the system is that the decision maker can learn the sensitivity of replenishment and lead time decisions and the expected annual total cost of the chain by specifying the parameter with the variation range in the Window of “What-if Analysis”. Figure 5 illustrates the output of the what-if analysis of K *, l *, T *, S *, Sv* , ETC *, and the cost saving after QR against the variation of standard deviation of demand.

 K* T* l* S1* S2* S3* Sv* ETC* K 0 a T 0 a ΔETC(%)b Base example 2 0.0709 0.005 708 760 1276 3574 19455.3 2 0.0711 0.73 σi (i=1,2,3) +100% 2 0.0568 0.002 895 1086 1384 3789 27806.2 2 0.0577 2.59 P +100% 1 0.0877 0.005 827 874 1320 2357 18822.3 1 0.0880 0.71 C +100% 2 0.0779 0.005 758 808 1208 3885 20799.7 2 0.0781 0.67 Ci (i=1,2,3) +100% 1 0.1024 0.005 930 970 1488 2691 23410.0 1 0.1027 0.54 A +100% 3 0.0705 0.005 705 757 1291 5108 20696.8 2 0.0781 1.16 hi (i=1,2,3) +100% 3 0.0507 0.005 560 616 886 3803 26567.3 3 0.0513 1.88 hv +100% 1 0.0704 0.005 704 756 1120 1958 23078.6 1 0.0705 0.62 1-αi (i=1,2,3) +100% 2 0.0733 0.01 705 741 1128 3681 18548.2 2 0.0735 0.32 1-αv +100% 2 0.0727 0.005 721 772 1147 3467 18897.2 2 0.0728 0.75

#### Table 1.

a: K 0 and T 0 represent the optimal K and T, respectively, before QR is implemented.b: ΔETC(%)=(1－ETC * /ETC 0)×100%, where ETC 0 represents the optimal ETC before QR is implemented.Sensitivity analysis for parameters

The sensitivity of the optimal solution has been further examined by conducting several numerical experiments. The results are illustrated by a base case and are shown in Table 1. Some findings are summarized as follows:

1. The amount of ΔETC(%) measures the improvement rate of expected annual total system cost after implementing QR. The behavior of ΔETC(%) reveals that the supply chain may benefit from shortening the replenishment lead time.

2. The value of ΔETC(%) is especially sensitive to the variation of σ i or h i . As σ i or h i increases, the value of ΔETC(%) increases. The results mean that the return of investment in QR is especially significant for a system with high uncertainty in demand or with high carrying costs incurred to the retailers.

3. The common shipment cycle time is more sensitive to the variance of demand, the variation of manufacturer’s production rate, the individual ordering cost, and the retailer’s carrying cost.

4. The shipment cycle time, T * , will be reduced after implementing QR in which the replenishment lead time for retailers has been shortened. Moreover, the target levels of replenishments for the manufacturer and the retailers may become lower after bringing QR into practice.

5. The number of shipments per production cycle, K * , after implementing QR is always no less than that before implementing QR. When the values of K for the two situations are equal, the optimal shipment cycle time, T * as well as the protection period, T * +l * , after QR is always no large than those before QR. The result implies that under a fixed number of shipments during a production cycle, the protection period for the retailer will be reduced after implementing QR.

6. The increase of production rate will result in a longer shipment cycle time and higher target levels of replenishments for the retailers. In contrast, as the value of P increases, the number of shipment per production cycle and the target level of production for the manufacturer will become smaller.

7. When the ordering cost increases, the shipment cycle time and the target levels of replenishments for each party will increase.

8. The value of α i specifies the minimal fraction of demand met per cycle for the retailer and directly relates with the length of protection period (T+l). It can be found that the amount of ΔETC(%) decreases as the retailer’s maximal fraction of demand unfilled per cycle increases. The result implies that the benefit from implementing QR is significantly related to the retailer’s service level threshold and the benefit is substantial for a supply chain requesting a high customer service level.

9. The numerical example shows that as 1－α v increases from 1% to 2%, the length of common shipment cycle time increases by 2.54% (from 0.0709 to 0.0727) but the lead time is unaffected. The result implies that the effect of manufacturer’s service level threshold is more significant on the common shipment cycle time than on the reduction of lead time.

## 5. Conclusions

Speed, service, and supply chain management have been core capabilities for business competition. The reduction of overall system response time with a satisfied service level has received a great deal of attention from researchers and practitioners. In this study, we investigated the effect of investing in QR on a CRP based supply chain where a manufacturer produces and delivers items to multiple retailers at a coordinated common cycle time with the minimized expected total system cost and satisfied service levels. Extending the work of Banerjee and Banerjee (1994) by involving ordering costs and the reducible replenishment lead time, a model and an algorithm are proposed to simultaneously determine the optimal shipment cycle time, target levels of replenishments, lead time, and number of shipments pre production cycle under service level constraints for the supply chain.

A numerical experiment along with sensitivity analysis was performed and the results explain the effect of QR on the replenishment decisions and the total system cost. The results provide the following findings about our model:

1. The system can reduce the stocks throughout the pipeline and remain service levels of retailers via investing in QR initiative.

2. The benefit from implementing QR is especially significant for a supply chain with high uncertainty in demand or the retailers requesting high service levels or incurring high carrying costs.

3. The shipment cycle time will decrease after QR implemented. Additionally, the shipment cycle time is especially sensitive to the variation of manufacturer’s production rate, the individual ordering cost, the variance of demand, and the retailer’s carrying cost.

4. The decision of adopting QR is mainly influenced by the variance of demand and the retailer’s service level threshold. The higher the demand uncertainty or the higher the retailer’s service level threshold, the more beneficial to implement QR in supply chains.

## Acknowledgements

This research was partially supported by the National Science Council, Taiwan ROC (Plan No. NSC 98-2410-H-415 -007).

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