Impact of Forecast Errors in CPFR Collaboration Strategy 391

runs. According to Law and Kelton [10], “One of the

principal goals of experimental design is to estimate how

changes in input factors affect the results or responses of

the experiment”. Generally, a variety of experimental

designs can be used in the simulation experiments when

the objective is to explore the reactions of a system (re-

sponse variables) to changes in factors (control variables)

affecting the system. Some of the relevant experimental

designs include the full factorial, fractional factorial and

response surface designs. A factorial experiment is one in

which the effects of all factors and factor combinations in

the design are investigated simultaneously. Each combi-

nation of factor levels are used the same number of times.

This study employs a full factorial design to gain insight

on the impact of the control variables on the performance

measures.

Four control variables as shown in Table 1 and two

performance measures as shown in Table 2 are consid-

ered for this study. Demand variability plays an impor-

tant role in the supply chain collaboration. This study

considers the auto-correlated demand pattern with three

levels of demand variability. Auto-correlated demand is

generated using the following formula

tt1

Dd Dt

ε

−

=++ (1)

where, d = initial mean, ρ = correlation factor and εt =

i.i.d. normally distributed with mean zero and standard

deviation σ. The correlation factor is 0.5 and three levels

of demand variability are generated by varying σ in the

above equation. The average customer demand for the

retailer is 100 units per period. The demand forecast is

generated according to the following formula.

tt

FDBFERFEsnorml(a)=++ × (2)

where, Ft and Dt are forecast and demand during period t

(t = 1, 2, 3 …), BFE is the bias forecast error, and RFE is

the random forecast error, and snormal() is the standard

normal random number generator.

Table 1. Control variables for the experimental design.

Control

Variables Details for Variables Other Details

Demand

Variability

(DVR)

Low Demand Variability, σ = 05

Med Demand Variability, σ = 15

High Demand Variability, σ = 25

Average Demand

is 100 units per

period

Random

Forecast Error

(RFE)

Low Random Error, ε = 05

Med Random Error, ε = 10

High Random Error, ε = 15

Random Forecast

Error for

Demand Forecast

Bias Forecast

Error

(BFE)

Negative Bias Error = −10

Neutral Bias Error = 0

Positive Bias Error = +10

Bias Forecast

Error for

Demand Forecast

Back Order

Penalty

(BOP)

Low Backorder Penalty, 09

Med Backorder Penalty, 19

High Backorder Penalty, 32

Backorder

Penalty is factor

of Holding Cost

Table 2. Performance measures for the experimental de-

sign.

Performance Measures Performance Measure Details

Retailer Cost

per Period

Inventory Holding Cost for Retailer

plus Backorder Cost for the Retailer

Manufacturer Cost

per Period

Inventory Holding Cost for

Manufacturer plus Backorder Cost for

Manufacturer

Periodic order-up-to inventory policy is used to deter-

mine the target inventory levels for both the manufac-

turer and retailer. Generally, inventory holding cost and

backorder penalty cost are important parameters in de-

termining order-up-to inventory level. Instead of chang-

ing both the inventory holding cost and backorder pen-

alty cost at the same time, the inventory holding cost is

held steady and backorder penalty cost is changed as

shown in Table 1.

4. Results and Discussions

The output data from the simulation model is analyzed to

determine the impact of forecast errors in the CPFR col-

laboration strategy. In a supply chain, the consequences

of forecast error can either lead to increased inventory

holding cost or increased stockout/backorder penalty cost.

Some of the main results of this research study are shown

below.

4.1. Impact of Random Forecast Error and

Demand Variability

The impact of random forecast error and demand vari-

ability on the inventory management cost for both the

retailer and manufacturer in CPFR collaboration strategy

are shown in Figure 2. When demand variability is low,

the cost for both the manufacturer and retailer increases

as random forecast error increases. It is interesting to

note that when demand variability is high, the impact of

random forecast error is generally lower. This may be

due to the fact that when demand variability is high, gen-

erally higher level of inventory is carried which can off-

set any forecast error. Higher inventory levels can help in

reducing backorder penalty costs when demand variabil-

ity is higher. However, when demand variability is high,

the overall cost of inventory management is higher for

both the manufacturer and the retailer.

4.2. Impact of Bias Forecast Error and Demand

Variability

The impact of bias forecast error and demand variability

on the inventory management cost for both the retailer

and the manufacturer in CPFR collaboration strategy are

shown in Figure 3. It is interesting to note that positive

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