To conduct this supply-chain-wide research, it was necessary to determine the fraction of the business of each supply chain member that would be analyzed.
Data from each supply chain member had to be scaled to the portion of the supply chain for which there were data available. Based on data available, summarized in Figure 4.4, the largest portion of the supply chain that could be analyzed was determined by the number of restaurants for which there was data available. Cost and inventory data from each supply chain member were multiplied by the corresponding scaling factor in order to perform calculation of the same magnitude.
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There are two approaches that can be used to determine these scaling factors. One is based on the number of restaurants for which there are data available.
The other is based on the amount of ingredients that these restaurants ordered as a percentage of the total manufactured. If there is no systematic bias on the selection of the restaurants for which there are data available, the results of these two approaches should be equivalent.
Table 4.3 shows the number of restaurants owned by the franchisor owned when LTO-11 was held and the number of restaurants that was available to participate in this research. Table 4.3 should be read as follows: from the 1,777 franchisor-owned restaurants when LTO-11 was held, 1,202 had some point-of-sale data for LTO-11;
689 of these 1,202 were served by one of the nine distribution centers participating in this research; from these 689 restaurants, 387 had good quality point-of-sale data.
The final count of the restaurants included in the analysis was 384 because three restaurants were discarded for other data-quality-related reasons. Table 4.3 also shows that these 384 restaurants represented 6.4% of the number of restaurants system-wide. Table 4.3 is a break-out of Figure 4.4.
Percentage of
System-wide
Description Count Percentage Restaurants
Franchisor-owned Restaurants
Franchisor-owned Restaurants 1,777 100.0% 29.6%
Franchisor-owned Restaurants with Some
9 9
Point-of-Sale Data for LTO-11 1,202 67.6% 20.0%
Franchisor-owned Restaurants with Sales 9 9
served by Selected Distribution Centers 689 38.8% 11.5%
Franchisor-owned Restaurants sorrow 387 21.8% 6.5%
with Point-of-Sale Data
Restaurants Available for the Research
Table 4.3
Number of Restaurants Participating in the Research
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Even though the restaurant count provides a measure of the portion of the supply chain, another meaningful measure is the percentage of product flow. Using the percentage of product flow for scaling the results of the analyses to the whole supply chain helps to avoid any possible selection bias on the sizes of the restaurants.
As mentioned before, all manufacturing runs were included in the data provided. The number of cases manufactured of each of the ingredients was used as a base to scale the rest of the product flow. Table 4.4 shows that from the total product produced by each manufacturer, 45% of Ingredient A and 48% of Ingredient B were shipped to one of the nine distribution centers. Also, Table 4.4 shows that 18% of Ingredient A and 19% of Ingredient B that was manufactured was sold through franchisor-owned restaurants that were replenished from any of the nine distribution centers of the Distributor. Finally, Table 4.4 shows that the 384 restaurants available to participate in this research represent 6.1% and 6.6% of all Ingredient A and Ingredient B manufactured, respectively.
Ingredient A Ingredient B
Product M anufactured 100% 100%
Product Shipped to Included Distribution Centers 45% 48%
Sales as a Percentage of Product Manufactured - 3
all Franchisor-Owned Restaurants 18% 19%
Sales as a Percentage of Product
Manufactured - Available Restaurants 6.1% Wy )
Table 4.4
Percentage of Product Flow for Which There Was Data Available at Each Tier of the Supply Chain
14]
Note that both, the number of restaurants available to participate in the research (384 restaurants} as a percentage of the system-wide count and the amount of product shipped to the same 384 restaurants as a percentage of fotal manufactured product, are similar.
These percentages can be used to estimate the system-wide costs and deiermine The size of the business opportunity. For example, if product lef over in allnine disinloution centers is 100 cases of one of the ingredients; then the estimated product left over system-wide, accounting for all distribution centers, is about 222 cases (100 cases/45%}. lt is assumed that the nine distribution centers are a representative sample and that the rest of the distripution centers will behave in a similar way. It is also assumed that the 384 restaurants are a representative samole of allrestaurants, both franchisor- and franchisee-owned.
These assumptions seem reasonable because both approaches to dejiermining the scaling factors produce similar results. Additionally, the validity of these two assumptions was corroborated with the franchisor’s management. A concer was whether the franchisor-owned restaurants performed better than the average restaurants. However, ifwas confirmed that there was no difference in ihe performance of franchisee-owned versus franchisor-owned restaurants.
The restaurants that were included in the model did not show a systematic bias in ferms of performance. The ulfimate measure of ihe restaurants’ performance is totalsoles. Therefore, weekly totalsoles were standardized for confidentiality reasons and a Student t-test was performed on the restaurants available to participate in the research. From the 384 restaurants only two were outside the confidence inferval at 99% level. Figure 4.5 shows the distribution of the standardized weekly total sales during the weeks of the analyzed LTO. Figure 4.5 shows that selected restaurants were normally distributed, lightly skewed fo the right. This is expected because there are some restaurants that perform better than average. Generally, this is due to the fact that these restaurants are better located.
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For the purpose of modeling, a representative fraction of the supply chain needs to be modeled in order to learn about its dynamics and extend the results.
After consulting with an expert in the use of the optimization software used for this research, it was determined that modeling approximately 150 restaurants would be sufficient to learn about the potential benefits of implementing dynamic time-based postponement in this setting. These 150 restaurants could not be any restaurant, the model had to include a representative number of restaurants for each of the distribution centers in the research. Therefore, the 384 restaurants participating in the research, were grouped by distribution center. The number of restaurants by distribution center was divided by four and rounded to the next integer. The result was the number of restaurants by distribution center to include in the optimization model. Table 4.5 shows the result of this process. The total number of restaurants included was 177 which represent 3.1% of the supply chain both in terms of the number of restaurants and as a fraction of the total product manufactured.
Therefore, 3.1% was determined as the scaling factor for the restaurants.
80
70 + 60 +
50 +
40 +
Frequency 30 +
20 +
-1.4 -0.7 0 0.7 1.4 2.1 2.8
Number of Standard Deviations from the Mean
Figure 4.5
Distribution of Restaurants Based on the Standardized Weekly Total Sales 143
All Restaurants | Percentage of | Restaurants in | Percentage of gs Restaurants with Data Restaurants the Model |All Restaurants
Distribution . . .
Available with Data in Model
Center Available
[A] [B] [BIA] [C] [CIA]
12 3/ 23 62% 10 27%
13 130 72 55% 32 25%
14 147 82 56% 37 25%
15 34 18 53% 9 26%
16 12 11 92% 4 33%
17 108 49 45% 28 26%
18 60 34 57% 16 27%
19 70 43 61% 18 26%
20 91 52 57% 23 25%
Table 4.5
Restaurants Included in the Model