Concept 3.5 Concept 3.5 The Delphi method relies on experts' knowledge to forecast, and it is designed to control social interaction in such a way that the signal about
3.12.3 The early sales model
Once the product is on the market, we can observe sales and judge the market potential for the product through its early sales. In the specific case of seasonal products (and more generally for products with a preset life cycle) such as fashion apparel, one could try to estimate demand up to season-end through the early sales. For example, one could try to forecast the season demand for a sandal based on sales in the month of March.
To do so, one has to estimate the relationship between the demand in the month of March and the demand for the total season. One can study the relationship between these two variables in the past to check whether actually demand in March is a good predictor of total season sales and, if this is the case, estimate the relationship. Notice that the underlying assumption is that the distribution of sales within the season next year will behave like it has behaved in past years. Thus, this process acknowledges that different products succeed t o different degrees. Yet, it still somehow assumes that the future resembles the past. In particular it assumes that pattern of sales of any item within the season (in a product category) is the same year after year.32 Concept 3.7 W h e n season after season sales keep the same pattern over time, early sales are a good predictor of total season's sales.
To judge the merits of this approach, one can draw the so-called "percent- age done" curves. In other words. we can use demand data from past seasons and measure the percentage of total season sales accumulated by a given point in time in the season.
More formally, let Y,,t be the demand for item i a t time t within the season, T the duration of the selling season, C,,t the cumulative demand for item z a t time t, and P,.t the percentage of total season's sales of item i occurred by
3 2 N ~ t i c e t h a t this concept is closely related t o t h e seasonality model presented in section 3.8. However, there are two differences. First and foremost. in this case the product has less t h a n one year or season of history, thus we cannot use t h e past demand t o estimate t h e fluctuations of future demand. Therefore. we basically resort t o related products t o estimate how demand varies within t h e season. Also, in this case we do not look a t sales in each time bucket (say one week), b u t rather at t h e sales up t o a given point in time t.
FORECASTlNG DEMAND FOR NEW PRODUCTS 173
Table 3.22 Demand d a t a for a set of seasonal products
Time Product 1 Product 2 Product 3 Product 4
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 20 19 21 22 23 24 25 26 27 29 30 32 31 33 34 35
a
28
206 127
291 193
565 296
826 469
590 273
514 242
514 269
482 194
452 194
529 186
483 190
46 1 214
466 228
568 210
427 191
394 154
400 189
347 134
314 122
294 109
304 112
286 97
233 85
199 101
216 105
229 112
221 102
176 96
143 73
146 64
127 73
137 81
117 76
841 482
465 187
4aa 674 1017 925
607 541 497 610 427 46 1 472 532 528 464 526
444 357 354 347 327 287 262 235 263 259 200 202 212 203 216 212 a61
482
408 328
192 334 394 370 238 224 214 156 157 160 173 166 192 206 141 166 163 131 121 101 119 103 91 108 84
91 93 86 70 65 76 72 289
iaa
a4
Demand in the season 12963 6030 15228 5618
Table 3.23 Percentage done of season demand curves
Time Product 1 Product 2 Product 3 Product 4 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
2%
4%
8%
15%
21%
26%
30%
34%
37%
41%
45%
49%
52%
56%
59%
64%
67%
70%
73%
76%
78%
80%
83%
85%
87%
88%
90%
92%
93%
95%
96%
97%
98%
99%
100%
2%
5%
10%
18%
26%
31%
35%
39%
42%
45%
49%
52%
55%
58%
62%
66%
69%
71%
74%
77%
79%
80%
82%
84%
85%
87%
89%
91%
92%
94%
95%
96%
97%
99%
100%
3%
8%
14%
20%
26%
30%
34%
38%
41%
44%
47%
50%
53%
56%
60%
63%
66%
69%
72 % 74%
77%
79%
81%
83%
85%
87%
88%
90%
92%
93%
94%
96%
97%
99%
100%
3%
9%
15%
22%
28%
32%
36%
40%
43%
46%
49%
52%
55%
58%
61%
65%
68%
70%
73%
76%
78%
80%
82%
84%
85%
87%
88%
90%
92%
93%
95%
96%
97%
99%
100%
FORECASTlNG DEMAND FOR NEW PRODUCTS 175
percentage done of season sales
0 5 10 15 20 25 30 35 40
time
Fig. 3.29 Predicting season’s sales with t h e early sales: percentage done curves.
time t:
t
(3.45) (3.46) In this case. time t is the time elapsed since the beginning of the selling season.
So the second week of the selling season of year ‘05 and ’06 both refer to t = 2 . If the graph of percentage done shows that products in the past had a rather similar behavior as in figure 3.29, then we know how demand behaves within the season. Actually, we are not interested in sales on a specific day or in a specific week. We just notice that by time t we tend to sell a given percentage of the total season sales.33
In this case. a more trivial approach is t o estimate the average distribution of sales as the average of the percentage done curves of all N products sold in past season(s).
N
(3.47)
1 1
c,
tpt
=c
z = 1 P,.t = -~v c
2 = 1 -,ct
T3 3 N ~ t i c e t h a t t h e products we analyze shall be related to the products we want t o forecast during next season. For example. they should belong t o t h e same product category in order t o share the same demand pattern during t h e selling season.
We can then use this percentage done curve to estimate total season sales for the new product j as
(3.48) This procedure is often adopted though it is rather crude, as we assume t ha t E(W) = E ( W / X )
.
E(X), which in general is not true and holds only if the two variables are independent. If this process is followed, we tend t o measure the accuracy of this prediction as the standard deviation of P,,i (i.e..the percentage of total season sales occurred by time t for various products), which again is an oversimplification as the real uncertainty depends on the standard deviation of l/P,.t.
A more appropriate description of the process is t o investigate the rela- tionship between the two variables through a regression. We can use past seasons' d at a to estimate the relationship between the sales up to time t, C, t ,
and total season sales, C, T . In particular. if we assume that the relationship is proportional. we can investigate the following relationship:
Cz,T = a
+
B 'ct
t+
6 .Once we have estimated the parameters Q and ,!3 through a and b. we can use them to estimate total season sales for product J as follows:
Linear regression provides us with more information on the distribution of errors and enables us to estimate errors and thus uncertainty [see equation (3.44)].
If the curves of various products show rather different behaviors over time, we might want t o investigate the drivers of such differences. First. products might have inherently different demand patterns. For example, sandals and shoes that are part of a spring-summer collection might show different behav- iors and we might want t o tell one from the other by drawing two separate percentage done curves for the two clusters of products. Also, the actual selling pattern of products might be influenced by actions and decisions of the company. For example, demand might be influenced by the number of stores carrying the item, the current price and the availability of the product variants. All these variables might distort sales and thus open a gap between the natural demand pattern and the actual sales pattern we observe. For example, two products might have a relatively similar demand pattern over time. but one might take off at a later stage simply because it is delivered to stores at a later stage. Also, one product can take off at a given point in time simply because its price was significantly reduced.34 Finally. sales might dip
34This is a very relevant issue in those countries where retailers can freely reduce price at any point in time. In other more regulated countries, such as Italy, the retailers can reduce prices only during the off-price season (e.g., January 10-February 15).
THE BASS MODEL 177
at a given point in time simply because stores are running out of the product.
This means t h a t either the product actually stocks-out or that inventories are so low that sales are reduced.
Example 3.18 Indeed. for some products the inventory level drives sales.
This theme is widely investigated for fast moving goods such as grocery. In- terestingly. similar findings hold in the case of slow moving goods. In the case of shoes. a US company has estimated that when less than ten pairs of a given shoe (style-color combination) are available. sales start declining.
Indeed. with less than ten units the size distribution is broken and itore man- agers start pulling back the product and even salespersons might riot suggest the product to a consumer simply because he/she does not know whether the right size is available. The salesperson might prefer to suggest another product not to disappoint the consumer and embarrass him/herself.