Forecasting Sales: Models, Managers (Experts) and their Interactions

Transcription

1 Forecasing Sales: Models, Managers (Expers) and heir Ineracions Philip Hans Franses Erasmus School of Economics ISF 203, Seoul

2 Ouline Key issues Durable producs SKU sales Opimal behavior Observed behavior Are exper-adjused forecass beer? How can forecass be improved? Furher work 2

3 Colofon Thanks o co-auhors Rianne Legersee, Richard Paap and Ber de Bruijn, Henk Kranendonk, Debby Lanser Various resuls have been or will be published in for example IJF, JofF, Inerfaces, JORS, and a review appears as a book wih Cambridge UP in 204 3

4 Key issues Area: Forecasing sales (in unis or money) of durable goods (compuers, cars, books) or of fas moving consumer goods (a he SKU level in supermarkes). Claim: Sales forecasing usually amouns o a combinaion of saisical modeling and an exper s ouch (for durable producs i is necessary, for SKU sales i can be useful) 4

5 Key issues - 2 Typically, he saring poin is a saisical model, bu in he end a manager or exper gives he forecas a final wis. Is ha a good idea? Ideally, how should such an exper ouch look like? Do exper-adjused forecass come close o his ideal siuaion? How can forecass (model, exper, combined?) be improved? 5

6 Durable producs.8 UK Towards mauriy.7.6 Inflecion poin Take off

7 Durable producs One usually needs o have some impression of he expeced oal sales (o be achieved perhaps many years in he fuure) and his canno be prediced on he basis of acual sales daa a he beginning of he curve The guessimae is usually given by he produc manager. Over ime i ges modified. The model (see below) ha is ofen used for forecasing durables sales can only esimae oal sales (wih some degree of accuracy) when sales are very close o oal sales, ha is, by he ime is forecas is no longer of ineres. 7

8 SKU level sales 56,000 52,000 48,000 44,000 40,000 36,000 IV I II III IV I II III IV ACTUAL MODEL EXPERT 8

9 SKU level sales Forecass are usually creaed by exrapolaion mehods (packaged in specialized sofware so ha quick updaes can be made). Managers (expers) usually know his, and hey manipulae he forecass owards heir own expecaions, bu hey may also ignore he model forecass alogeher. This is usually unknown. 9

10 Durable producs The Bass model or in OLS forma 0 ) ( ) ( ) ( qf p F f N N N m q N p q pm N m N m q N m p X ) ( ) ( ) (

11 Muli-sep-ahead forecass from he Bass model Key issue: Bass model is NON-linear, and i usually holds ha E(F(x)) F(E(x)) One sep: Xˆ ˆ ˆ ˆ n 2Nn 3 Two seps done linearly gives upward biased forecass: 2 n2 ) 3 N E( X ˆ n X 2 2 n

12 Forecass from Bass model So, for wo seps, resor o simulaion mehods Xˆ n 2, i g( Z n, X n, i; ) ˆ ˆ e i 2

13 Illusraion Y

14 Illusraion - 2 CY 7,000 6,000 5,000 4,000 3,000 2,000,

15 Some resuls Sample ends in Esimae of m sandard error

16 Guessimaing Suppose now ha he sample would have ended before he inflecion poin, hen one would need o fix he value of he mauriy level m in order o ge proper esimaes of he shape of he funcion. Suppose he sample ends in November 2005, which is one monh before he srong seasonal peak in December If an exper wih domain knowledge would have he m a 700 (imes 000 unis), hen one ges esimaes for p and q ha are consisen wih he full sample esimaes. This suggess ha he shape of he curve, which is characerized by he p and he q parameers, can reasonably be prediced using a firs guess of m. 6

17 SKU-level sales SKU-level sales daa have oher properies. Usually, here are many of hem. A regular reail sore carries housands of SKUs and may wan o make forecass on a weekly basis. Daa are available a high frequency. Managers wan deailed forecass so mos SKU series are no aggregaed. SKU-level daa ofen have irregular paerns due o a variey of reasons, like holidays, ou-of-sock condiions, price cus, promoions and so on. Hence, SKU-level daa are no easy o forecas. 7

18 Forecasing models Regression-based models if here is ime o creae hem. Exrapolaion echniques (Hol-Winers, ARIMA, BSM) if only lagged sales are inpu (usually pu in a Forecas Suppor Sysem, FSS). 8

19 An ineresing paradox M compeiions (Makridakis e al) usually show ha simple exrapolaion echniques are bes. Sill, people feel he need (almos always!) o adjus model forecass when he very same echniques are used. 9

20 Empirical evidence Various sudies in he lieraure and also daa from Organon (daa for 40+ counries, 000+ producs, forecas horizons o 24 monhs) KLM (passengers, 5 areas, monhly) CPB (3 key macroeconomic variables, years) Bayer (similar and more han Organon) 20

21 Wha would be ideal? Suppose: Model forecas is Forecas error is 2 ), ( ~ 2 S N S M S S ˆ ˆ ˆ M S S ˆ ˆ ˆ

22 Wha would an exper do, ideally? Turn fuure forecas error ino: An exper forecas hus becomes 22 ˆ v W ˆ ˆ ˆ E W S S

23 Ideally: Modeling poin of view (heory): Expers have (parial) knowledge abou fuure forecas errors Forecasing poin of view (heory): EF = MF + v, wih v ( Inuiion ) orhogonal o MF and unpredicable, hen SPE can become smaller Pracical poin of view: Models may miss relevan variables and updaed values of predicors may need correcion 23

24 Wha is ofen observed? EF is almos always differen from MF EF is more ofen > MF han < MF EF-MF is ofen predicable (double couning) Expers oo ofen fully ignore MF (cerainly in case of SKU sales) EF-MF for older expers and EF-MF for more experienced expers 24

25 Are exper-adjused forecass beer? Sales daa: If exper forecass are more accurae, hen only a lile more accurae. If heir forecass are worse hey are very inaccurae (for longer horizons differences ge smaller) Macroeconomic daa: In general more accuracy, especially for price series. 25

26 How can forecass be improved? Mach loss funcion wih model s loss funcion (disconnec forecas from acion) In fac: alernaive loss funcions imply very complicaed expressions for forecass (involving muliple inegrals). Hence, very unlikely ha individuals can solve hose. Give various forms of feedback ( do you know wha you do and which resuls i gives? ): i does help! Take averages of exper-adjused forecass and model forecass Include pas inuiion in FSS 26

27 Conclusion Model forecass are hard o bea bu someimes need help of an exper Exper adjusmen, preferably: infrequen and boh signs Subsanial room for improvemen More work o do: How o properly consruc forecas inervals for exper-adjused forecass? How o compare ses of expers forecass? 27