Question

 4. The following data are monthly sales of jeans at a local department store. The buyer would like to forecast sales of jeans for the next month, July.

 (a) Forecast sales of jeans for March through June using the naive method, a two-period moving average, and exponential smoothing with an a = 0.2. (Hint: Use naive to start the exponential smoothing process.)

 (b) Compare the forecasts using MAD and decide which is best.

 (c) Using your method of choice, make a forecast for the month of July.

 10. Rosa's Italian restaurant wants to develop forecasts of daily demand for the next week. The restaurant is closed on Mondays and experiences a seasonal pattern for the other six days of the week. Mario, the manager, has collected information on the number of custom- ers served each day for the past two weeks. If Mario expects total demand for next week to be around 350, what is the forecast for each day of next week?

Answer 1

Q4 : In Naive method, the forecast for a period is simply the actual sales of the previous month

Hence Forecast as per Naive method is as below

Forecast for March = 30
Forecast for April = 40
Forecast for May = 50
Forecast for June = 55

In two period moving average the forecast for a period is simply the average of actual sales of previous 2 periods

Hence forecast as per the two period moving average is as below

Forecast for March = (45+30)/2 = 37.5
Forecast for April = (30+40)/2 = 35
Forecast for May = (40+50)/2 = 45
Forecast for June = (50+55)/2 = 52.5

In exponential smoothing method the forecast for a period is given using below formula

Forecast = Forecast for previous period + Smoothing constant (Actual sales of previous period - Forecast for previous period)

Hence forecast as per the exponential smoothing is as per below. The forecast for month of February is taken to be the forecast as per the Naive method which will be 45.

Forecast for March = 45+0.2*(30-45) = 42
Forecast for April = 42+0.2*(40-42) = 41.6
Forecast for May = 41.6+0.2*(50-41.6) = 43.28
Forecast for June = 43.28+0.2*(55-43.28) = 45.624

The results are tabulated below for all three methods

To calculate MAD, we find the absolute difference between the forecast and the actual sales and find its average. Absolute difference is the difference without considering the positive or negative sign

The MAD for different methods are shown in the below image

We can see that the MAD is lowest for Exponential Smoothing. Hence this is the best method.

For July the forecast as per Exponential Smoothing is as below

Forecast for July= 45.624 + 0.2*(47-45.624) = 45.624+0.2*1.376 = 45.8992

Q10 :

The first step is to find the seasonal index for each day. To do this we first find the average sales on each day

Average customers on Tuesday = (52+48)/2 = 100/2 = 50
Average customers on Wednesday = (36+32)/2 = 68/2 = 34
Average customers on Thursday = (35+30)/2 = 65/2 = 32.5
Average customers on Friday = (89+97)/2 = 186/2 = 93
Average customers on Saturday = (98+99)/2 = 197/2 = 98.5
Average customers on Sunday = (65+69)/2 = 134/2 = 67

Average customers across all days = (50+34+32.5+93+98.5+67)/6 = 375/6 = 62.5

Now we find the seasonal index of each day. Seasonal index is calculated by dividing average customers on a particular day by average customers across all days

Seasonal index for Tuesday = 50/62.5 = 0.8
Seasonal index for Wednesday = 34/62.5 = 0.544
Seasonal index for Thursday = 32.5/62.5 = 0.52
Seasonal index for Friday = 93/62.5 = 1.488
Seasonal index for Saturday = 98.5/62.5 = 1.576
Seasonal index for Sunday = 67/62.5 = 1.072

Now we can find the forecast for customers on each day of the next week using the formula below

Forecast for the day = Total Demand Expected/6*Seasonal Index for the day

Forecast for Tuesday = 350/6*0.8 = 46.67 47
Forecast for Wednesday = 350/6*0.544 = 31.73 32
Forecast for Thursday = 350/6*0.52 = 30.33 30
Forecast for Friday = 350/6*1.488 = 86.8 87
Forecast for Saturday = 350/6*1.576 = 91.93 92
Forecast for Sunday = 350/6*1.072 = 62.53 63