On the identification of sales forecasting model in the presence of promotions Juan R. Trapero, Nikolaos Kourentzes, Robert Fildes Journal of Operational Research Society, (2014), Forthcoming This work was supported by the SAS/IIF research grant Promotional Support Systems In “Analysis of judgemental adjustments in the presence of promotions” (Trapero et al., 2013) we showed that: • Simple statistical promotional models outperform on average human adjustments • Not all information of human judgment is captured by simple promotional models • There is room for improvement with more advanced promotional modelling Furthermore: • There is an apparent gap in the published work (and software) for promotional support systems for SKU level predictions • Existing brand level promotional models have limitations: 1. Require extensive model inputs → feasibility and cost considera:ons . Comple1 input 0ariable selection is re8uired 9 which are the rele0ant promotions? .. Promotions are often multicollinear 9 di>cult to es:mate their impact and get reliable forecasts 4. These models re8uire past promo:on history 9 promo:onal forecasts for new products? 5. These models do not capture the demand dynamics ade8uately These limitations explain the observed reliance on expert adjustments (Lawrence et al., 2000; Fildes and Goodwin, 2007) Case Study A manufacturing company specialized in household detergent products 9 data a0ailable/ • Shipments • One-step-ahead system forecasts (SF) • One-step-ahead ad,usted or final forecasts (FF) • Promotional information/ 1. Price cuts . Feature ad0ertising .. Shelf display 4. Product category ( categories) 5. Customer ( main customers) A. Days promoted in each week The data contains A0 SK6s (all contain promotions) Data withheld for out-of-sample forecast e0aluation Some products do not contain promotions in the parameterisation (historical) sample Case Study Example time series Periods highlighted in grey ha0e some type of promotion Models Statistical Promotional Model The proposed promotional model contains the following elements/ • Principal component analysis of promotional inputs / The A promotional inputs are combined a new composite inputs that are no longer multicollinearC 9 Only a few new inputs are needed now, simplifying the model. • Pooled regression / Dhen an SK6 does not ha0e promotions in each history, we pool together information from other SK6s (the product category information is a0ailable to the model) to identify an a0erage promotional effect. Dhen enough promotional history for an SK6 is a0ailable we do not pool information from other products • Dynamics of promotions / Carry-o0er effects of promotions, after they are finished, are captured • Dynamics of the time series / Demand dynamics are modelled for both promotional and non-promotional periods. CTwo inputs are called multicollinear when it is impossible to distinguish what is the effect of each indi0idual input on the forecasted demand. For instance, assuming that we run two promotions running in parallel, resulting in a sales uplift of E.00F, it is impossible to identify the indi0idual impact of each promotion. This is 0ery problematic is it is possible that the promotions can also run separately. Models Benchmarks A series of benchmark models are used to assess the performance of the proposed promotional model • System Forecast ( SF )/ The baseline forecast of the case study company • Final Forecast ( FF )/ This is the SF ad,usted by human e1perts in the company • Naïve / A simple benchmark that assumes no structure in the demand data • E1ponential Smoothing ( SES )/ An established benchmark that has been shown to perform well in supply chain forecasting problems. It cannot capture promotions • Last Like promotion ( LL )/ This is a SES forecast ad,usted by the last obser0ed promotion. Dhen a promotion occurs the forecast is ad,usted by the impact of the last obser0ed promotion Note that only FF and LL can capture promotions from our benchmarks Case Study Results Forecast accuracy under promotions DR / Proposed High error Promotional Model 2ow error Number of forecasts Size of ad,ustment Negati0e ad,ustments Positi0e ad,ustments Case Study Results Forecast accuracy under promotions Human ,udgment High error performs inconsistently 22 has o0erall poor accuracy DR is always better 2ow error under promotions DR is more accurate than human e1perts and statistical benchmarks in promotional periods Case Study Results Forecast accuracy in non-promotional periods Human ,udgment performs poorly High error No reason for positi0e ad,ustments? 22 has o0erall poor accuracy 2ow error DR marginally DR is models worse that SF accurately carry- o0er promotional effects DR accurately captures carry-o0er promotional effects. SF is marginally better because the forecasts are based on ad,usted historical demand. DR is modelled in raw data. Case Study Results Overall forecast accuracy High error 2ow error DR pro0ides the most accurate forecasts o0erall The proposed ad0anced statistical promotional model captures most of the human e1pert information, in a systematic way, producing superior forecasts. Case Study Results High error No promotions Promotions Overall 0.9 1.4 0.9 0.I 1. 0.I 0.7 0.7 1 0.A 0.A 0.5 0.I 0.5 0.4 0.A 0.4 0.. 0.. 0.4 0. 0. 0. 0.1 0.607 0.652 0.762 0.629 0.612 0.601 1.069 1.327 1.092 0.904 1.122 0.868 0.1 0.671 0.745 0.808 0.667 0.682 0.638 0 0 0 SF FF Naïve SES LL DR SF FF Naïve SES LL DR SF FF Naïve SES LL DR 2ow error Best Best Best Improvement of DR over FF • Proposed promotional model is consistently the most accurate Overall +14.4% • Substantially outperforms current case study Promotions +34.6% company practice (FF) No promotions +7.8% • Ma,or impro0ements during promotional periods 0.0% 10.0% 20.0% 30.0% 40.0% Conclusions 1. Proposed statistical promotional model significantly outperform human e1perts and statistical benchmarks . Company can benefit from increased automation of the forecasting process and reduced effort of e1perts to maintain forecasts, while accuracy is increased .. Can produce promotional forecasts when there is no or limited promotional history for an SK6 4. O0ercomes limitations of pre0ious promotional models 5. Final model is relati0ely simple Detailed analysis, findings and references in the paper/ http///kourentzes.com/forecasting/ 014/04/19/on-the-identification-of-sales-forecasting- models-in-the-presence-of-promotions/ .