IV. Analysis of Double-Ordering Contract
4.2 Double-Ordering Contract Model Formulation
Double-ordering contract (DOC) is widely used in fast fashion industry. For example, Benetton , used in the 1980, provides second order opportunity around the start of the season and can significantly reduce markdowns and leftover inventory.
In our study of DOC, we consider a single supplier and a single buyer. The buyer
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placed a DOC order to the supplier. Figure 9 introduces the timeline sketch of DOC.
Figure 9 Timeline sketch of DOC
We assume that the market demand of DOC for the first half sales period is , and the second half sales period is . Both and are normal distributed, ~ N( , ) and ~ N( , ), with a mean of and and a standard deviation of
and respectively. The buyer place the first order before the sales season, and place the second order afetr observing the market demand. The buyer improves his or her forecast accuracy for the second order after observing some of the season’s demand.
As the result, the buyer is able to reduce the standard deviation of the forecast.
To write more detailed DOC model formulation, we now define the following notations of DOC.
Realized demand quantity of the first half sales period Realized demand quantity of the second half sales period SL Service level
F-1 The inverse of the standard normal distribution pD Selling price per unit
cD Wholesale price per unit.
Sales season begins
Double-ordering contract place 2nd order Ordering Q’ty: = max (0, – )
6 weeks 1 week
Single-ordering contract place order Ordering Q’ty : OX = F-1(SLX, , )
Double-ordering contract place 1st order Ordering Q’ty : = F-1(SL, , )
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mD Production cost per unit.
sD The buyer’s salvage value per unit. pD > cD > mD > sD > 0 Cost of overstocking by one unit, = cD - sD
Cost of understocking by one unit, = pD - cD Supplier profit of the first sales period
Supplier profit of the second sales period Supplier profit of the entire sales period
Buyer profit of the first sales period
Buyer profit of the second sales period Buyer profit of the entire sales period Total profit
The formulas of our DOC simulation model are described as follows.
The buyer’s first order quantity is
= F-1(SL, , ) (15)
The order-up-to level of the second half period is
= F-1(SL, , ) (16)
Buyer’s overstock quantity of first half period is
= max(0, – ) (17)
The buyer’s second order quantity is
= max(0, – ) (18)
Buyer’s overstock quantity of second half period is
= max(0, – ) (19)
Buyer’s understock quantity is
= max(0, – ) (20)
Supplier profit of the first sales period is
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= × (cD – mD) (21)
Supplier profit of the second sales period is
= × (cD – mD) (22)
Supplier profit of the entire sales period is
= + (23)
Buyer profit of the first sales period is
= min ( , ) × pD – × cD (24) Buyer profit of the second sales period is
= min ( , ) × pD – × cD – × sD (25) Buyer profit of the entire sales period is
= + (26)
Total supply chain profit is
= + (27)
4.3 Experimental Design
In order to analyze the effect of DOC with the improved demand forecast, we experiment on scenarios which take account of the different standard deviation of the second order , which are given by different k fraction of . The smaller the k means the forecast is more accurate. And each scenario would simulate in terms of different SL. Besides, we assume that
(1) The supplier allows the buyer break up the purchase of the entire sales period into two orders. The first order covers the earlier half sales period, whereas the second order covers the latter half sales period. Thus,
= = (28)
= (29)
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(2) Since we assume the market information will improve the forecast, the standard deviation of quantity demanded of the second half sales period of DOC will be less than that of the first half sales period.
= k × , k 1 (30)
(3) In order to analyze the impact of DOC, we assume that the cost parameters of both SOC and DOC are the same.
= , = , = , = (31)
(4) In order to compare the effect of DOC, we assume that the market demand of both SOC and DOC are the same. Thus,
= + (32)
and are independent.
Table 6 indicates the parameters used in SOC and DOC simulation models, Table 7 summarizes the different scenarios we test in simulation analysis in terms of different values of service level and forecast capability index.
Table 5 Parameters Setting of SOC and DOC Simulation Model
p 150
c 90
m 40
s 30
3,000 1,000
Table 6 Simulation Scenarios of SOC and DOC
34 4.4 Simulation Modeling (Excel)
In our study, we use Microsoft Excel to design and implement our simulation analysis. Through this simulation model, we generate 500 samples for both contracts to discuss the buyer’s profit, the supplier’s profit and total supply chain profit of each contract respectively to understand the effect of DOC.
Here we briefly summarize the simulation steps by using Excel.
Step 1: Set up the simulation parameters in the Excel spreadsheet based on Table IV-2.
Step 2: Generating random numbers of market demand using Excel. We use the Excel function NORMINV(RAND(), μ, σ) to generate 1,000 samples of the random demand as defined in 2.4.2. Both μ and σ are based on the assumption of variables in
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section 4.3. Note that the first 500 sample points were not adopted to avoid the initial warm-up bias of the random number generator.
Step 3: Set up the formulas of supplier’s profit, buyer’s profit, total supply chain profit, buyer’s overstock and understock corresponding to the 500 samples of demand for each scenario based on the formulas in section 4.1 and 4.2.
Step 4: Evaluate the average of the simulation results of 500 samples.
Step 5: Analysis of different scenarios. Using the Excel tool “Data Tables”, we generate different simulation results in SL as shown in Table 7 and then we use the Excel tool “Scenario Manager” to generate different simulation results in terms of k described in Table 7.
(4a) Different SL for a given k.
(4b) For different values of k.
4.5 Simulation Results
From the simulation results, we have found that
1. Figure 10 shows the buyer’s profit on SOC and DOC with various k. The buyer’s profit is increasing while the SL is higher. Under the same SL, the buyer’s profit with DOC is higher than that of SOC. The buyer’s profit with DOC is higher while k is smaller. Also, in this case, the optimal SL of DOC is larger than that of SOC. Furthermore, the margin of DOC profit and SOC profit increases with the increased SL.
2. Figure 11 shows the supplier’s profit on SOC and DOC with various k. The supplier suffers loss from DOC obviously. The margin of DOC loss and SOC loss increases with the increased SL. And it seems that the k doesn’t affect the profit.
3. Figure 12 shows total supply chain profit on SOC and DOC with various k.
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The total supply chain profit is getting higher while the SL is higher. The total supply chain profit with DOC is better than that of SOC while SL is over 0.8.
Furthermore, the impact from k decreases when SL is getting larger.
4. Thus, DOC favors the buyer and hurts the supplier. It makes total supply chain efficiently when SL is over 0.8. It seems that the better the buyer’s forecast capability doesn’t affect too much. Furthermore, applying DOC makes the buyer achieve higher SL and better satisfy customer’s needs.
Figure 10 Buyer’s Profit
80 90 100 110 120 130 140 150 160 170
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
Profit(,000)
Service Level SOC
k=1/3 k=1/4 k=1/5
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Figure 11 Supplier’s Profit
Figure 12 Total Supply Chain Profit
110
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
Profit(,000)
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
Profit(,000)
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4.6 Sensitivity Analysis and Discussion
Same with QFC, as mentioned above, we can find that DOC has a positive effect on the buyer, whereas the supplier suffers a loss from DOC. In the case of section 4.5, we know that buyer’s overstock cost is equal to the buyer’s understock cost, Cu/Co=1, i.e. the product margin is equal to the leftover cost. What is the impact on the ordering quantity and the supply chain members if the product margin is higher or lower?
To analyze this, we simulate different scenarios which have different ratio of Cu/Co introducing in Table 8.
Table 7 Simulation Scenarios of DOC Sensitivity Analysis Scenarios
Variables Cu/Co=2 Cu/Co=1 Cu/Co=0.5
cF 70 90 110
For simplifying, we only take SOC and DOC with k = 1/4 as a example to introduce our finding as follows. The detailed simulation results are diagramed in Appendix B.
1. Figure 13 indicates the effect of DOC on the buyer’s profit under various ratio of Cu/Co. For the buyer, no matter the ratio of Cu/Co is higher or lower, the buyer benefits from DOC. However, the buyer benefits more when the ratio of Cu/Co is lower.
2. Figure 14 indicates the effect of DOC on the supplier’s profit under various ratio of Cu/Co. For the supplier, no matter the the ratio of Cu/Co is high or low, the supplier lose from DOC. In addition, the supplier loses more from DOC while the ratio of Cu/Co is smaller.
3. Figure 15 indicates the effect of DOC on total supply chain profit under various ratio of Cu/Co. It seems that the k doesn’t affect the total supply cahin
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profit. And the total supply chain profit with DOC is better than that of SOC while SL is over 0.8. The profit increases approximate to 3% when SL is very high.
4. Thus, the DOC benefits the buyer, whereas the supplier suffers a loss from DOC. As to the total supply chain, DOC is effective only when the SL is high.
Figure 13 Effect of Buyer’s Profit (k=1/4)
-40
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Figure 14 Effect of Supplier’s Profit (k=1/4)
Figure 15 Effect of Total Supply Chain Profit (k=1/4)
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