The optimization-based model was used to produce several scenarios. For each scenario, only the information that would have been available to managers ai the time they wouid have run the mode! was used. The objective was to be able to recreate what management would have done throughout the life cycle of the LTO. First, the time-line of a LTO is reviewed, Second, the forecasting and forecast updating processes used to generate the input to the mode! are explained. Third, the modeling scenarios that were developed are described.
Time-line of a LTO
The first event in a LTO that matters to this research is the franchisor’s formal communication to all managers involved, containing planning information. Informal communications occurred as needed both before initiating the LTO and throughout the life cycle of the promotion. Even before the formal communication, through informal contacts, the other supply chain members learned about the LTO.
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The first formal communication happened 10 weeks before the LTO was intiated. At this time, the marketing depariment at the franchisor published the forecast of the LTO mix. The LTO mix was the expected fraction of fotal sales in the form of promotional meals. Other elements of the formal communication were relevant dates such as the first and the last dates of availability of ingredients to the restaurant, wnen the advertising starts and ends, and the earliest and lates? date for disengagement. The formal communication also included information not direcily related to this research, such as description of meals, portioning of ingredients, costs, and key contacts.
Table 4.8 is an example of the typical time-line for a LTO; this particular one Is for LTO-1 P which was analyzed in this research. The column labeled Fhase Description shows the chases for which there was advertisement. Table 4.8 includes the disguised forecast of the LTO mix. Restaurant managers use the column labeled Forecast Mix with their own forecast of total sales to determine the forecast in unis for the LTO at their own restaurants. Therefore, the firsi necessary step in modeling dynamic time- based postponement in this setting was to produce a forecast for LTO-11.
Forecasting the LTO
The first step in planning for the LTO was fo produce a forecast. Producing a forecast for a LTO implies that the expected average sales and the expected variability of demand are produced for each restaurant included in the model.
Determining Expected Average LTO Sales. The poini-forecast, the expected average LTO sales, was determined by multiplying the expert's forecast of the mix by each restaurant's forecast of total sales. This forecast was produced during the planning ohase which happened 10 weeks before the LTO is initiated (see the column labeled Week Number in Table 4.8). Note that the forecast was for the entire LTO;
therefore, the same total sales figure by restaurant had to be used for ali phases of 179
Planning Planning Training Before Initiation
í Initiation 1st week pre-media 9.37% 133
2 |\Growth Half week media 11.47% 318
K) 4 5 6
7 Decline 1st full week post media 10.37% 221
+... | Termination 2nd full week post media 9.37% 133
Disengagement |After Termination
Table 4.8
Typical Timeline for a Limited-Time Offer
the LTO. The total sales figure multiplied by the expected LTO Mix for each phase of the LTO produced the expected LTO Sales, which varied by phase.
The forecast of total sales used for planning purposes, and included in the initial formal communication described earlier, was based on the system-wide average and developed in the Marketing function at the franchisor’s headquarters.
However, restaurant managers forecast total sales for their own restaurants every week. Restaurant managers were instructed to forecast using the modified moving average method described earlier in this chapter.
Determining a Measure of Demand Variability. A measure of variability of demand for each demand stage was needed for modeling. To determine the COVd's, the variability of forecast errors of six past LTOs were used. Forecast errors were computed as follows:
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1. Forecast the number of meals to be sold by restaurant by phase (week).
2. Determine the actual number of meals sold by restaurant by week.
3. Calculate the percentage forecast errors by restaurant for each phase as:
PFE, = (Actual, ằ, - Forecast, ằ, ) Actual, py,
where:PFE , ,,: Percent Forecast Error for restaurant R and phase Ph R: Restaurant
Ph: Phase
4. Calculate the standard deviation of the percentage forecast errors for each phase across allrestaurants.
The standard deviation of the weekly percentage forecast errors was calculated for each of the phases of the LTOs. Using this measure for the expected variability of demand has two benefits. First, safety stock requirements are lower when using the standard deviation of forecast errors rather than the standard deviation of demand [7]. Second, using a measure of variability of the forecast errors allows one to assume that the correlation of demand over time is zero [8];
ignoring the effect of autocorrelation of demand would make the number of stockouts larger than expected [9].
Figure 4.15 shows the standard deviation of the weekly percentage forecast errors for seven past LTOs. Based on these data, the expected variability of demand for LTO-11 was estimated. Figure 4.15 indicates with an arrow for each phase the expected COVd used as the initial inout for modeling LTO-11. Table 4.9 shows the coefficients of variation of demand used as input to the optimization model. To confirm that this approach gave meaningful estimates, the actual standard deviation of the percentage forecast errors for LTO-11 were calculated and shown in Figure 4.15.
18]
Standard Deviation of Forecast Errors co
0
4 2 3 4 5 6 7 8
LTO Phase
—e—LTO-00 —#--LTO-01 --A--LTO-02 —ằx—LTO-03 —X--LTO-04 —e--LTO-10 ——LTO-11
Note: The arrows indicate the expected variability of demand for which inventory deployment would be planned.
Figure 4.15
Determining the Expected Variability of Demand
3.00 1.50 0.70 0.40 0.50 0.70 1.20 2.00 1
2
4 3 5 6 Ÿ 8
Table 4.9
Initial Coefficients of Variation of Demand Used for Modeling 182