Arab J Sci Eng (2014) 39:5253–5264DOI 10.1007/s13369-014-1069-8

RESEARCH ARTICLE - SYSTEMS ENGINEERING

A Comparison Study of Replenishment Strategiesin Vendor-Managed Inventory

James T. Lin · Fu-Kwun Wang · Candice Wu

Received: 9 January 2013 / Accepted: 30 April 2013 / Published online: 30 March 2014© King Fahd University of Petroleum and Minerals 2014

Abstract In a vendor-managed inventory system, the sup-plier rents a third party provider’s warehouse which is closeto its buyer and the buyer shares the demand forecast infor-mation with the supplier. However, the relationship betweeninventory cost and service level is a trade-off problem. In thisstudy, we propose a forecast forward replenishment (FFR)strategy to improve the performance of the warehouse man-agement regarding inventory cost and service level. A sim-ulation study is conducted to compare our proposed FFRstrategy with other strategies, such as re-order point (ROP)and material requirement planning (MRP) under differentcombinations of demand pattern and distribution lead time.The results show that the FFR strategy outperforms the ROPand MRP strategies. A real data set is used to demonstratethe application of our proposed method. The FFR strategyyields lower inventory cost with a certain service level.

Keywords Vendor-managed inventory system ·Forecast forward replenishment · Re-order point ·Material requirement planning

J. T. Lin · C. WuDepartment of Industrial Engineering and EngineeringManagement, National Tsing Hua University, Hsinchu,Taiwan, ROC

F.-K. Wang (B)Department of Industrial Management, National TaiwanUniversity of Science and Technology, No. 43, Keelung Rd.,Sec. 4, Taipei 106, Taiwan, ROCe-mail: fukwun@mail.ntust.edu.tw

1 Introduction

In a vendor-managed inventory (VMI) system, the suppliermanages inventory replenishment for its buyers and the buy-ers share the demand forecast information with the supplier[1–8]. Both supplier and buyer agree on a defined mini-mum level per stock keeping unit. The supplier is respon-sible for replenishing buyers and for deciding when and howmuch to deliver. Disney and Towill [9] provided that VMIcomes in many different forms including quick response,synchronized consumer response, continuous replenishment,efficient consumer response, rapid replenishment, collabora-tive planning, forecasting and replenishment, and central-ized inventory management. Many studies in a VMI systemshowed that in all cases there is substantial reduction in Bull-whip effect [9–17].

In a VMI system, the supplier rents a third party provider’swarehouse which is close to its buyer and the buyer shares

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the demand forecast information with the supplier. The sup-plier decides and manages when and how much to deliver.Therefore, the measure of supplier performance is not deliv-ery time and preciseness, but it is the availability and inven-tory turnover. The business problem faced by the supplierin this type of VMI system is to effectively manage inven-tory at its warehouse for replenishing buyers. However, toreduce inventory cost at warehouse and maintain a certain ser-vice level is a trade-off problem. In addition, non-stationarydemand patterns are often occurred in business environ-ment. It is essential to develop dynamic inventory controlpolicies.

Several types of replenishment strategies dealing withdynamic inventory control policies under non-stationarydemand have been investigated. The first two types suchas re-order point (ROP) and kanban (KBN) aim at mini-mizing total inventory cost, including backlog penalties. Itconsiders non-stationary stochastic demands over periodsof an infinite horizon. Some researches focus on develop-ing dynamic order-up-to level policies where control para-meters are computed under certain service levels [18–22].Enns [23] investigated the total inventory and delivery per-formance of ROP and KBN under different demand rates andlot setup times using simulation approach. Results show thatthe ROP strategy under time-varying demand is slightly bet-ter, and the reduction of lot setup time for both strategies issimilar. The third type is based on the distribution/materialrequirement planning (DRP/MRP) strategy. Suwanruji andEnns [24] compared DRP/MRP with ROP and KBN strate-gies under different capacity constraints and demand pat-terns. With seasonal demand, DRP/MRP performs best,followed by ROP and KBN. Without seasonal demandand capacity constraint, ROP performs best, followed byDRP/MRP and KBN. With capacity constraint, the ranking isreversed. Other issues such as frozen order and future demandinformation in the inventory management can be found in[25–28].

Discrete-events simulation has been used to investigatethe performance of different replenishment strategies [29–31]. Dong and Leung [32] developed a dynamic rolling sim-ulation optimization model on the VMI-based replenishmentstrategy,the genetic algorithm (GA) of which is used to searchthe optimal replenishment quantity in each replenishmentcycle [16]. The experimental results show that the proposalreplenishment strategies can benefit the manufacturer withbalanced production and maintain the customer service levelat a certain degree. Lin et al. [33] developed a dynamicfuzzy system in a VMI supply chain with fuzzy demand.Furthermore, GA is used to search optimal parameters ofthe proposed model. The results show that the fuzzy VMImodel can simultaneously reduce the Bullwhip effect andinventory response in supply chain. Kristianto et al. [34] pro-posed an adaptive fuzzy control model to reduce the Bullwhip

effect by eliminating the Houlihan effect and the Burbidgeeffect.

In this study, we propose a forecast forward replenishment(FFR) strategy to improve the performance of a VMI systemregarding inventory cost and service level. The remainder ofthis paper is organized as follows. Section 2 presents a VMIsystem based on a real case. The FFR strategy is reported inSect. 3 followed by the simulation study and analysis resultsin Sect. 4. A real example is demonstrated in Sect. 5. Conclu-sions and future research directions are presented in Sect. 6.

2 Description of the Model

A supply chain model consisting of one seller and one buyer(see Fig. 1) is developed from a real case of a company thatsupplies a heat sink to cool electronic components for high-power semiconductor devices, and optoelectronic devicesfor higher power lasers and light-emitting diodes. The com-pany’s plants are located in China and its customers arelocated in Taiwan, China, Japan, American, and European.According to its VMI system, the seller rents warehouse forreplenishing the buyers. If goods at warehouse are more than3 months, the seller initiates the mechanism of recycling idlegoods. All idle goods are sent back to its plant for otherprocesses. The buyer provides demand forecasts based onthe rolling forecast approach. The assumptions made in thisVMI system are given by:

1. The seller operates a warehouse for carrying inventory,eventually, to be shipped to buyers.

2. The system does not consider the production mode,capacity constraint, and production time. The capacityfor the seller is unlimited.

3. The demand forecasts by the buyer cannot be changedduring forecast horizon. All calculations are based onthe demand forecasts from the buyer.

Fig. 1 The replenishment concept for a vendor-managed inventorysystem

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4. The distribution lead time is constant and the systemdoes not consider the defective products.

5. The review period for inventory is constant based ontime bucket.

The demand variations come from rapidly changing mar-ket. For the stationary demand, the ROP strategy has beensuccessfully implemented in real inventory management sys-tems. However, non-stationary demand patterns are oftenoccurred in business environment. In the context of highlyvariable demand, the static ROP and the static order-up-to-level policies are not suitable to control inventory. Babaï andDallery [22] showed that the safety stock of the forecast-based inventory management is lower than that of the stan-dard inventory management under non-stationary demandin which the standard deviation of the demand is generallygreater than the standard deviation of the forecast uncer-tainty. Babaï et al. [28] showed that the forecast-based inven-tory approach can result in lower inventory cost under non-stationary demand. In addition, the parameters includingdemand forecasting method, replenishment strategy suchas safety stock, planning horizon, and frozen horizon, andtransportation policy such as full truckload and less-than-truckload are identified and affected the performance ofinventory systems under non-stationary demand.

To effectively manage inventory at its warehouse forreplenishing buyers in this VMI system, we will investigatethree replenishment strategies and provide the optimal levelsof the parameters under different demand patterns.

3 Replenishment Strategies

In this section, we present three different replenishmentstrategies: ROP, MRP, and FFR. Here, the replenishmentlogic is based on the rolling forecast approach [35]. The fol-lowing notation that is used throughout the paper:

ADt Actual demand at time period tDFt Demand forecast at time period tDFt,i Demand forecast at time period i based on the

Actual time period tFH Forecast horizonFT Frozen typeGITt Goods in transit at time period tLT Distribution lead time from supplier to buyerm Forecasting horizonIP Inspection periodPH Planned horizonPOHt Projected on hand at time period tPOLt Planned-order release at time period tPORt Planned-order receipt at time period t

PP Planning periodR Review periodSSt Safety stock at time period t

3.1 ROP Strategy

Several types of ROP strategy including order-point, order-quantity (s, Q), order-point, order-up-to-level (s, S),periodic-review, order-up-to-level (R, S), and can-order(R, s, S) have been studied by many researchers. In thisstudy, we adopt (R, s, S) strategy and assume that R =1 week. Four steps of this strategy are given as followings:Step 1 Calculate the order point using Eq. (1):

st = AD × LT + SSt , (1)

where AD = average demand, SSt = WOS ×∑PP

i=1 DFt,im and

WOS = the weeks of supply.Step 2 Calculate the order-up-to level using Eq. (2):

St = AD × (LT + IP) + SSt . (2)

Step 3 Make a planned-order release using the formula:

POLt

={

St−POHt−1−∑t+LTk=t+1 GITk if POHt−1 ≤ st

0 if POHt−1 > st. (3)

Step 4 Repeat steps 1–3 until the horizon has been adequatelyplanned.

3.2 MRP Strategy

The MRP strategy is based on the rolling forecastingapproach. Four steps of this strategy are given as follows:Step 1 Calculate the projected on hand quantity using Eq. (4):

POHt = POHt−1 + GITt − DFt . (4)

Step 2 If the projected on hand quantity is less than safetystock, then we initiate replenishment and calculate theplanned-order receipt. The formula is defined by:

PORt = (DFt + SSt ) − (POHt−1 + GITt ). (5)

Step 3 Make a planned-order release based on the planned-order receipt and the lead time requirements using Eq. (6):

POLt−LT = PORt . (6)

Step 4 Repeat steps 1–3 until the horizon has been adequatelyplanned.

For example, we assume that R = 1 week, FH = 3 weeks,LT = 2 weeks, and SS = 50 units. At period W 0, we havethat POH0 = 80 units, GIT1 = GIT2 = 100, and DF1 =110, DF2 = 120, DF3 = 130. According to Eq. (4), theprojected on hand quantities at periods W 1–W 3 are 70, 50,

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Table 1 Results of the MRP strategy at period W 0

Period W 0 W 1 W 2 W 3 W 4 W 5 W 6 W 7

Actual demand

Demand forecast 110 120 130

Goods in transit 100 100

Projected on hand 80 70 50 −80

Planned-order receipts 130

Planned-order release 130

Table 2 Results of MRP the strategy at period W 1

Period W 0 W 1 W 2 W 3 W 4 W 5 W 6 W 7

Actual demand 120

Demand forecast 110 125 115 130

Goods in transit 100 100 130

Projected on hand 80 60 35 50 −80

Planned-order receipts 15

Planned-order release 15

Planned-order release is not available at period W 0

and, −80, respectively. Since the projected on hand quantityat period W 3 is less than safety stock, then the replenishmentis initiated. According to Eq. (5), the planned-order receiptquantity at period W 3 is obtained as (130+50)−(50+0) =130. According to Eq. (6), the planned-order release quantityat period W 1 is 130. The results of MRP strategy are shownin Table 1.

When time is at period W 1, we can use the results fromTable 1 to update the information. Now, actual demand atperiod W 1 is already occurred and set at 120 units. Using therolling forecast approach, the demand forecasts at periodsW 2–W 4 are 125, 115, and 130, respectively. Since POL atperiod W 1 is 130 and LT is 2 weeks, we have that GIT atperiod W 3 is 130. The projected on hand quantity at periodW 1 is obtained as 80 + 100 − 120 = 60. Again, accordingto Eqs. (4)–(6), the replenishment results at period W 1 areshown in Table 2. From Table 2, we found that the projectedon hand quantity at period W 2 is 35 and less than safety stock.Also, the planned-order release quantity at period W 0 is 15.Unfortunately, this is at period W 1 and cannot be plannedfor order release at period W 0. Thus, the stock out situationis occurred.

3.3 FFR Strategy

We proposed the FFR strategy to avoid the stock out situ-ation of the MRP strategy. The FFR strategy includes twomajor factors: planning period and forecast horizon. If PPis <LT, then the demand forecasts in some periods are not

included in replenishment. Therefore, it could result in stockout situation. If PP is >FH, then the buyer cannot providethe demand forecasts after FH periods. So, it is useless forperiods (FH + 1 ∼ PP). That is, PP must be greater than orequal to LT and be less than forecast horizon. We developfour steps of this strategy.Step 1 Calculate the planned-order release quantity usingEq. (7):

POLt =(

t+PP−1∑

t

DFt + SSt

)

−(

POHt−1 +t+LT−1∑

t

GITt

)

.

(7)Step 2 Make a planned-order release based on the lead timerequirements using Eq. (8):

PORt+LT = POLt . (8)

Step 3 Calculate the projected on hand using the formula:

POHt = POHt−1 + GITt − DFt . (9)

Step 4 Repeat steps 1–3 until the horizon has been adequatelyplanned.

We considered the example in Sect. 3.2 and assumedthat FH = 5 weeks and PP = 4 weeks. At period W 0, wehave that POH0 = 80 units, GIT1 = GIT2 = 100, andDF1 = 110, DF2 = 120, DF3 = 130, DF4 = 125, DF5 =135. According to Eq. (7), the planned-order receipt quan-tity at period W 1 is obtained as [50 + (110 + 120 + 130 +125)]− [80+ (100+100)] = 255. According to Eq. (8) andLT = 2 weeks, the planned-order release quantity at period

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Table 3 Results of the FFR strategy at period W 0

Period W 0 W 1 W 2 W 3 W 4 W 5 W 6 W 7

Actual demand

Demand forecast 110 120 130 125 135

Goods in transit 100 100

Projected on hand 80 70 50

Planned-order receipts 225 135

Planned-order release 225 135

Table 4 Results of the FFR strategy at period W 1

Period W 0 W 1 W 2 W 3 W 4 W 5 W 6 W 7

Actual demand 120

Demand forecast 110 125 135 135 145 150

Goods in transit 100 100 225

Projected on hand 80 60 35 155

Planned-order receipts 175 150

Planned-order release 175 150

W 3 is 255. According Eq. (9), the projected on hand quantityat period W 1 is obtained as 80100110 = 70. The results ofFFR strategy are shown in Table 3.

When time is at period W 1, the actual demand at periodW 1 is already occurred and set at 120 units. Using the rollingforecast approach, the demand forecasts at periods W 2–W 6are 125, 135, 135, 145, and 150, respectively. Since POL atperiod W 1 is 255 and LT is 2 weeks, we have that GIT at timeperiod W 3 is 130. The projected on hand quantity at periodW 1 is obtained as 80 + 100 − 120 = 60. Again, accordingto Eqs. (7)–(9), the replenishment results at period W 1 areshown in Table 4. From Table 4, we found that there is nostock out; that is, the FFR strategy can avoid the stock outsituation during replenishment periods.

4 Simulation Study

The details of the simulation logic for the FFR strategy areshown in Fig. 2. In the replenishment process, we generatedthe planned-order releases based on several factors (forecastdemands, safety stock, planned-order receipts, and goods intransit) using the FFR strategy in Sect. 3.3. The discrete-eventsimulation model using VBA (visual basic for applications)from Microsoft Excel 2007 is shown in Fig. 3. From Fig. 3,we found that the input parameters setting and simulationresults are located in area #1, the replenishment time andquantity are located in area #2, and the simulation parametersare located in area # 3. The simulation procedure is validatedby the real data.

4.1 Design of Experiments

Two experiments with time bucket (week) are conducted inthis study. The first experiment is to compare the performanceof different replenishment strategies using the analysis ofvariance approach. The second experiment is to find the opti-mal parameters for inventory replenishment using responsesurface methodology. The details of these two methods canbe found in Myers and Montgomery [36].

Experiment-1 We investigated the performance of thethree replenishment strategies (ROP, MRP, and FFR) underdifferent combinations of demand patterns and distributionlead times. Each combination represents one operation envi-ronment. Thus, one can treat every operation environment asa scenario. Some pilot runs were performed to validate themodel and to determine a proper simulation warm-up period.Demand pattern from the buyer can be calculated using thefollowing formula [37,38]:

Demandt = base + slope × t + season

× sin

[(2π

season cycle

)

× t

]

+ noise (10)

× snormal(), (11)

where Demandt is the demand in time t , base is the averagedemand, season is a seasonal factor, noise is the coefficientof demand variation, and snormal() is a standard normal ran-dom number generator. Using the different combination ofparameters (base, slope, season, season cycle, noise), we cangenerate the demand patterns. In this study, base was selectedto ensure that the average demand was ∼1,000 units; the para-

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Fig. 2 The simulation logic ofFFR strategy

No

Yes

FFR

Start

Input

model parameters

Initilize model

t=1

Execute FFR i=1

Generate demandforecast

Update safety stock

Calculate planned order release

Forward planned order receipt

Is forecast horizon end?

Yes

Calculate projected on hand

Noi=i+1

Generate current actual demand

Calculate current stock level

Is simulation time end?

Yes

Stop

No t=t+1

Does stock level satisfy?

Record stock out

Record stock level

Update information

meters for six demand patterns are shown in Table 5. Level-LV produced the demand with no trend or seasonality andwith low variability; level-HV produced the demand with notrend or seasonality and with high variability; tendency-UPproduced the demand with trend up, tendency-DN producedthe demand with trend down, season produced the demand

with seasonality and mix produced the demand with season-ality and trend up. The levels of distribution lead time are setat 2, 4, and 8, respectively. Each combination of the simu-lation study is replicated five times for 104 periods. Consid-ering the simulation warm-up, we collected all performancemeasures during the simulation periods from 11 to 94. Thus,

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Fig. 3 The simulation model

Table 5 Parameter settings for six different demand patterns

Demand pattern Base Slope Season Season cycle Noise

Level-LV 1,000 0 0 26 100

Level-HV 1,000 0 0 26 400

Tendency-UP 1,000 10 0 26 100

Tendency-DN 1,000 −10 0 26 100

Season 1,000 0 200 26 100

Mix 1,000 10 200 26 100

the total number of simulation runs for experiment-1 is equalto 3 × 6 × 3 × 5 = 270.

Experiment-2 We considered three factors (planningperiod, forecast method, and frozen type) under the demandwith seasonality and trend up for the FFR strategy. The pur-pose of this experiment is to find the optimal levels for theFFR strategy under the demand with seasonality and trend up.The levels of planning period are set at 4, 5, 6, 7, and 8, respec-tively. The levels of forecasting method are the centered mov-ing average method, the centered maximum value method byTiacci and Saetta [39], and the simple exponential smooth-ing (EXP) method and their formulae are given by DFt =ADt−1+ADt−2+ADt−3

3 , DFt = Max(ADt−1, ADt−2, ADt−3),and DFt = DFt−1 + 0.5 × (ADt−1 − DFt−1), respec-tively. The levels of frozen type are set at zero and one,respectively. If the level of frozen type is one, then frozenperiod is set at 2 weeks. Each combination of the simulationstudy is replicated five times for 104 periods. Consideringthe simulation warm-up, we collected all performance mea-sures during the simulation periods from 11 to 94. Thus, the

total number of simulation runs for experiment-2 is equal to5 × 3 × 2 × 5 = 150.

Two criteria are used to measure the warehouse perfor-mance. The average inventory (AI) of warehouse is derivedby

AI =∑ub

t=lb POHt

lb − ub, (12)

where lb is the time period after simulation warm-up andub is the end of simulation period. The service level (SL) isderived by

SL =(

ub∑

t=lb

OFt

ADt

)

× 100 %, (13)

where OFt = the order fulfill quantity at time period t . Here,the service level is also called the probability of non-out-of-stock during simulation periods.

4.2 Analysis Results

Statistical tests on normality and homoscedasticity wereperformed to validate assumptions needed on the simula-tion results representing two performance measures of thereplenishment strategies. The residual analysis shows that theassumptions are satisfied for all scenarios, so further statis-tical analysis can be carried out. The results of experiment-1 are summarized in Table 6. The interaction plots of AIand SL are shown in Figs. 4 and 5. Regarding the perfor-mance of average inventory, the FFR strategy outperforms theMRP and ROP strategies under demand patterns, including

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Table 6 Summary of simulation results for all replenishment strategies

Demand pattern Distribution lead time FFR MRP ROP

AI SL AI SL AI SL

Level-LV 2 1,018.3 0.99 3,290.8 1.00 1,161.7 0.94

4 1,066.0 0.98 3,027.7 1.00 2,298.4 1.00

8 1,551.5 0.98 4,704.9 0.79 1,900.4 0.97

Level-HV 2 1,800.6 0.90 4,766.7 1.00 1,138.4 0.81

4 2,445.9 0.91 5,688.0 0.99 2,556.1 0.97

8 4,606.2 0.98 6,182.9 0.82 4,391.7 0.96

Tendency-UP 2 1,424.7 1.00 4,611.9 1.00 627.2 0.86

4 1,329.7 0.99 3,876.0 1.00 1,176.4 0.95

8 1,577.0 0.97 6,665.1 0.78 1,120.5 0.91

Tendency-DN 2 672.0 0.98 1,982.4 1.00 1,158.9 0.88

4 924.2 0.97 2,132.3 1.00 2,091.4 0.96

8 1,700.5 0.99 3,857.4 0.85 3,003.8 1.00

Season 2 1,071.9 0.99 3,369.6 1.00 2,929.5 1.00

4 1,257.5 0.96 3,356.9 0.99 1,409.1 0.97

8 2,109.5 0.94 6,418.6 0.82 1,770.1 0.94

Mix 2 1,436.4 0.99 4,657.9 1.00 875.2 0.91

4 1,516.5 0.97 3,737.2 1.00 702.8 0.94

8 2,153.5 0.95 8,319.7 0.76 1,177.0 0.90

Fig. 4 The interaction plots ofAI for experiment-1

842654321

6000

4000

2000

6000

4000

2000

Strategy

Demand patte

Lead time

6

5

4

3

2

1

3

2

1

Interaction Plot - Data Means for AI

level-LV, tendency-DN, and season. On the other hand, theROP strategy outperforms the FFR and ROP strategies underdemand patterns, including level-HV, tendency-UP, and mix.Regarding the performance of service level, the MRP strategyoutperforms the FFR and ROP strategies under all six differ-ent demand patterns. Table 7 provides guidance for decisionmakers in the selection of preferable strategy, based on thedifferent operational conditions.

For experiment-2, the quadratic response model wasobtained by the software Design-Expert [40]. The ANOVAresults for average inventory and service level are providedin Tables 8 and 9, respectively. Consequently, two generatedmodels are given as follows:

AI = 4, 510.19 − 2, 998.85×A [1] − 1, 573.66×A [2]

− 53.23×A [3] + 1, 523.02×A [4] − 243.48×B [1]

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Fig. 5 The interaction plots ofSL for experiment-1

842654321

1.0

0.9

0.8

1.0

0.9

0.8

Strategy

Demand patte

Lead time

6

5

4

3

2

1

3

2

1

Interaction Plot - Data Means for SL

Table 7 Suggested strategies under different operational conditions

Distribution lead time Demand pattern

Level-LV Level-HV Tendency-UP Tendency-DN Season Mix

2 FFR FFR/ROP FFR FFR FFR FFR

4 FFR FFR/ROP FFR FFR FFR FFR

8 FFR FFR/ROP FFR/ROP FFR FFR/ROP FFR/ROP

Table 8 ANOVA of response surface reduced quadratic model for AI

Source Sum of squares DF Mean square F value Prob > F

Model 7.219 × 108 19 9.023 × 107 11,811.74 <0.0001

Planning period 7.026 × 108 4 1.756 × 108 24,273.32 <0.0001

Forecasting method 1.793 × 107 2 8.966 × 106 1,239.13 <0.0001

Frozen type 5.635 × 105 1 5.635 × 105 77.88 <0.0001

PP × forecasting method 7.668 × 105 8 95,851.62 13.25 <0.0001

PP × frozen type 1.217 × 105 4 30,420.68 4.20 0.0031

Residual 9.407 × 105 130 7,235.94

Lack of fit 41,434.41 10 4,143.44 0.55 0.8489

Purr error 8.992 × 105 120 7,493.65

Corrected total 7.229 × 108 149

+ 488.98×B [2] − 61.29×C + 64.24×A [1] B [1]

+ 36×A [2] B [1] + 8.61×A [3] B [1] − 43.37

×A [4] B [1] − 132.57×A [1] B [2] − 89.41

×A [2] B [2] − 0.41×A [3] B [2] + 93.63

×A [4] B [2] + 6×A [1] C − 19.93×A [2] C

− 25.91×A [3] C − 12.98×A [4] C,

and

SL = 1.00 − 0.01×A [1] + 2.067×10−3 A [2] + 2.733

×10−3 A [3] + 2.733×10−3 A [4] − 1.067×10−3 B [1]

+ 7.333×10−4×B [2] − 1.8×10−3C − 4.933

×10−3×A [1] B [1] + 1.733×10−3 A [2] B [1]

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Table 9 ANOVA of response surface reduced quadratic model for SL

Source Sum of squares DF Mean square F value Prob > F

Model 6.626 × 10−3 19 3.487 × 10−4 17.76 <0.0001

Planning period 3.963 × 10−3 4 9.907 × 10−4 50.44 <0.0001

Forecasting method 8.933 × 10−5 2 4.467 × 10−5 2.27 0.1070

Frozen type 4.860 × 10−4 1 4.860 × 10−4 24.74 <0.0001

PP × forecasting method 4.773 × 10−4 8 5.967 × 10−5 3.04 0.0037

PP × frozen type 1.611 × 10−3 4 4.027 × 10−4 20.50 <0.0001

Residual 2.553 × 10−3 130 1.964 × 10−5

Lack of fit 1.133 × 10−4 10 1.133 × 10−5 0.56 0.8455

Purr error 2.440 × 10−3 120 2.033 × 10−5

Corrected total 9.179 × 10−3 149

+ 1.067×10−3 A [3] B [1] + 1.067×10−3 A [4] B [1]

+ 2.267×10−3 A [1] B [2] − 6.667×10−5 A [2] B [2]

− 7.333×10−4 A [3] B [2] − 7.333×10−4 A [4] B [2]

− 6.533×10−3 A [1] C + 1.133×10−3 A [2] C

+ 1.8×10−3 A [3] C + 1.8×10−3 A [4] C,

where A = planning period, B = forecasting method,C = frozen type. The adjusted R2 values of the two responsemodels are 0.9987 and 0.6812, respectively. The residualanalysis validates the model assumptions. Myers and Mont-gomery [36] described a multiple response method calleddesirability. The method uses an objective function, D(X),called the desirability function. It reflects the desirable rangesfor each response. The desirable ranges are from zero to one(the least to the most desirable in that order). The simultane-ous objective function is a geometric mean of all transformedresponses:

D =(

n∏

i=1

di

)1/n

, (14)

where n is the number of responses in the measure. If anyresponses fall outside their desirability range, the overallfunction becomes zero. The present study treats all responsevariables as the same important measures. Using the sameweight for AI and SL, the optimum solution for the desirabil-ity function is 0.965, where PP = 4, forecasting method = EXPand frozen type = 0. The confirmatory runs at this optimalset showed that all responses satisfy the requirements.

4.3 Managerial Implications

The study performed in this work has two important man-agerial implications such as replenishment strategy decisionand the optimal levels of the parameters.

1. Replenishment strategy decision: the FFR strategy givesa lower inventory cost under demand patterns such aslevel-LV, tendency-DN, and season. On the other hand,the ROP strategy gives a lower inventory cost underdemand patterns such as level-HV, tendency-UP, andmix. Table 7 provides guidance for decision makers inthe selection of preferable strategy under different oper-ational conditions to meet lower inventory cost at a cer-tain service level.

2. The optimal levels of the parameters: to meet lowerinventory cost at a certain service level, the optimal lev-els of the parameters for replenishment strategy can beobtained using the response surface models.

5 Illustrative Example

In this section, we considered a real demand data. The histor-ical demand data of the product F in 2009–2011 are providedin Fig. 6. The minimum service level for the buyer is set at95 %. The distribution lead time from plant to warehouse is5 weeks. The review period of warehouse is set at 1 week.Safety stock is set at 3 weeks. The buyer provides demandforecasts for 13 weeks. That is, forecast horizon is 13 weeks.Currently, the company selects the MRP strategy to manageits inventory at its warehouse. In Fig. 6, we found that thedemand pattern is a mix type of seasonality and tendencydown.

We conducted a small experiment for this data set usingthe FFR strategy. The optimal levels of planning period, fore-casting method, and frozen type are obtained as 5 weeks,SMV, and zero, respectively. The comparison results of thethree different strategies including FFR, ROP, and MRP areprovided in Table 10. Regarding the performance of AI, wefound that the ROP strategy outperforms the other two strate-gies (FFR and MRP). But, regarding the performance of SL,the ROP strategy only provides 91 % that it is less than the

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Fig. 6 The demand data ofproduct F

Table 10 Comparison results for example

Strategy AI SL (%)

FFR 218,252 99.00

ROP 122,095 91.00

MRP 462,405 100.00

requirement level (=95 %). The service levels of both FFRand MRP strategies are obtained as 99 and 100 %, respec-tively. We found that the FFR strategy can provide lowerinventory cost with 99 % service level.

6 Conclusions

In a VMI system, the supplier rents a third party provider’swarehouse which is close to its buyer and the buyer sharesthe demand forecast information with the supplier. The sup-plier decides and manages when and how much to deliver.The business problem faced by the supplier in this type ofVMI sytem is to reduce inventory cost at warehouse andmaintain a certain service level for replenishing buyers. Wepropose a FFR strategy to obtain lower inventory cost with acertain service level. A simulation study is conducted to com-pare our proposed FFR strategy with other strategies, suchas ROP and MRP under different combinations of demandpattern and distribution lead time. The results show that theFFR strategy outperforms the ROP and MRP strategies underthe demand patterns (level-LV, tendency-DN, and season)regarding inventory cost. Our proposed approach has beentested on a real data set. The results show that the FFR strat-egy provides lower inventory cost with 99 % service level.

There are many issues that can be addressed in the futurestudies. First, we may consider a supply chain model consist-

ing of multiple warehouses and multiple buyers. The alloca-tion policy from the plants to multiple warehouses will bea research topic. Second, other demand forecasting methodssuch as exponential smoothing model and neural networkmodel may improve the accuracy of demand forecasts. As aresult, the inventory costs of warehouses will be significantlyreduced. Finally, we may consider the impact of a variety ofinventory/production policies that should be included in thereplenishment strategy.

Acknowledgments The authors gratefully acknowledge two review-ers of this paper who helped clarify and improve this presentation.

References

1. Waller, M.; Johnson, M.E.; Davis, T.: Vendor-managed inventoryin the retail supply chain. J. Bus. Logist. 20, 183–195 (1999)

2. Dong, Y.; Xu, K.: A supply chain model of vendor managed inven-tory. Transp. Res. Part E Logist. Transp. Rev. 38, 75–95 (2002)

3. George, K.: Effectiveness of vendor-managed inventory in the elec-tronics industry: determinants and outcomes. Inf. Manag. 41, 645–654 (2004)

4. Rusdiansyah, A.; Tsao, D.B.: Coordinating deliveries and inven-tories for a supply chain under vendor managed inventory system.JSME Int. J. Ser. A Solid Mech. Mater. Eng. 48, 85–90 (2005)

5. Bookbinder, J.H.; Gumus, M.; Jewkes, E.M.: Calculating the ben-efits of vendor managed inventory in a manufacturing-retailer sys-tem. Int. J. Prod. Res. 48, 5549–5571 (2010)

6. Marquèsab, G.; Thierryb, C.; Lamothea, J.; Gourca, D.: A reviewof vendor managed inventory (VMI): from concept to processes.Prod. Plan. Control. 21, 547–561 (2010)

7. Niranjan, T.T.; Wagner, S.M.; Thakur-Weigold, B.: Are you readyfor VMI. Ind. Eng. 43, 39–44 (2010)

8. Hohmann, S.; Zelewski, S.: Effects of vendor-managed inventoryon the Bullwhip effect. Int. J. Inf. Syst. Supply Chain Manag. 4,1–17 (2011)

9. Disney, S.M.; Towill, D.R.: The effect of vendor managed inventory(VMI) dynamics on the Bullwhip effect in supply chains. Int. J.Prod. Econ. 85, 199–215 (2003)

123

5264 Arab J Sci Eng (2014) 39:5253–5264

10. Disney, S.M.; Towill, D.R.: Vendor-managed inventory and Bull-whip reduction in a two-level supply chain. Int. J. Oper. Prod.Manag. 23, 625–651 (2003)

11. Disney, S.M.; Towill, D.R.: On the Bullwhip and inventory varianceproduced by an ordering policy. Omega. 31, 157–167 (2003)

12. De Toni, A.F.; Zamolo, E.: From a traditional replenishment systemto vendor-managed inventory: a case study from the householdelectrical appliances sector. Int. J. Prod. Econ. 96, 63–79 (2005)

13. Gronalt, M.; Rauch, P.: Vendor managed inventory in woodprocessing industries—a case study. Silva Fenn. 42, 101–114(2008)

14. Kiesmuller, G.P.; Broekmeulen, R.A.C.M.: The benefit of VMIstrategies in a stochastic multi-product serial two Echelon system.Comput. Oper. Res. 37, 406–416 (2010)

15. Mutlu, F.; Cetinkaya, S.: An integrated model for stock replen-ishment and shipment scheduling under common carrier dispatchcosts. Transp. Res. Part E 46, 844–854 (2010)

16. Goh, S.A.; Ponnambalam, S.G.; Jawahar, N.: Evolutionary algo-rithms for optimal operating parameters of vendor managed inven-tory systems in a two-Echelon supply chain. Adv. Eng. Softw. 52,47–54 (2012)

17. Hariga, M.A.; Al-Ahmari, A.: An integrated retail space alloca-tion and lot sizing models under vendor managed inventory andconsignment stock arrangements. Comput. Ind. Eng. 64, 45–55(2013)

18. Heath, D.C.; Jackson, P.I.: Modeling the evolution of demandforecasts with application to safety-stock analysis in produc-tion/distribution systems. IIE Trans. 26, 17–30 (1994)

19. Lee, H.L.; Padmanabhan, P.; Whang, S.: Information distortion in asupply chain: the Bullwhip effect. Manag. Sci. 43, 546–558 (1997)

20. Graves, S.C.: A single-item inventory model for a nonstationarydemand process. Manuf. Serv. Oper. Manag. 1, 50–61 (1999)

21. Chen, F.Z.; Drezner, J.; Ryan, J.K.; Simchi-Levi, D.: Quantifyingthe Bullwhip effect in a simple supply chain: the impact of forecast-ing, lead times, and information. Manag. Sci. 46, 436–443 (2000)

22. Babaï, M.Z.; Dallery, Y.: Inventory management: forecast basedapproach vs. standard approach. In: Proceedings of InternationalConference on Industrial Engineering and Systems Management,Marrakech, pp. 1–10 (2005)

23. Enns, S.T.: Pull replenishment performance as function of demandrate and setup times under optimal settings. In: Proceedings of theWinter Simulation Conference, pp. 1624–1632 (2007)

24. Suwanruji, P.; Enns, S.T.: Evaluating the effects of capacity con-straints and demand patterns on supply chain replenishment strate-gies. Int. J. Prod. Res. 44, 4607–4629 (2006)

25. Hariharan, R.; Zipkin, P.: Customer order information, lead-timesand inventories. Manag. Sci. 41, 1599–1607 (1995)

26. Gallego, G.; Ozer, O.: Integrating replenishment decisions withadvance order information. Manag. Sci. 47, 1344–1360 (2001)

27. Karaesmen, F.; Liberopoulos, G.; Dallery, Y.: The value of advancedemand information in production/inventory systems. Ann. Oper.Res. 126, 135–158 (2004)

28. Babaï, M.Z.; Syntetos, A.A.; Dallery, Y.; Nikolopoulos, K.:Dynamic re-order point inventory control with lead-time uncer-tainty: analysis and empirical investigation. Int. J. Prod. Res. 47,2461–2483 (2009)

29. Ingalls, R.G.: The value of simulation in modeling supply chains.In: Proceedings of the 30th Conference on Winter Simulation,pp. 1371–1376. IEEE Computer Society Press, Washington, D.C.(1998)

30. Persentili, E.; Alptekin, S.E.: Product flexibility in selecting manu-facturing planning and control strategy. Int. J. Prod. Res. 38, 2011–2021 (2000)

31. Masuchun, W.; Davis, S.; Patterson, J.W.: Comparison of push andpull control strategies for supply network management in a make-to-stock environment. Int. J. Prod. Res. 42, 4401–4419 (2004)

32. Dong, A.H.; Leung, S.Y.S.: A simulation-based replenishmentmodel for the textile industry. Text. Res. J. 79, 1188–1201 (2009)

33. Lin, K.P.; Chang, P.T.; Hung, K.C.; Pai, P.F.: A simulation of ven-dor managed inventory dynamics using fuzzy arithmetic operationswith genetic algorithm. Expert Syst. Appl. 37, 2571–2579 (2010)

34. Kristianto, Y.; Helo, P.; Jiao, J.; Sandhu, M.: Adaptive fuzzy vendormanaged inventory control for mitigating the Bullwhip effect insupply chains. Eur. J. Oper. Res. 216, 346–355 (2012)

35. Nordhasu, W.: Forecasting efficiency: concepts and applications.Rev. Econ. Stat. 69, 667–674 (1987)

36. Myers, R.H.; Montgomery, D.C.: Response Surface Methodology.Wiley, New York (1995)

37. Zhao, X.; Lee, T.S.: Freezing the master production schedule formaterial requirements planning systems under demand uncertainty.J. Oper. Manag. 11, 185–205 (1993)

38. Zhao, X.; Xie, J.; Lau, R.S.M.: Improving the supply chain perfor-mance: use of forecasting models versus early order commitments.Int. J. Prod. Res. 39, 3923–3939 (2001)

39. Tiacci, L.; Saetta, S.: An approach to evaluate the impact of interac-tion between demand forecasting method and stock control policyon the inventory system performances. Int. J. Prod. Econ. 118, 63–71 (2009)

40. STATE-EASE: Design-Expert Version 5.0.8. State-Ease, Min-neapolis (1997)

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