# Advertising and forecasting investments of a newsvendor

- 69 Downloads

## Abstract

We consider a newsvendor that can increase the mean demand with advertising and reduce the variability in the demand by forecasting or market research. We analyze the problem under uniform and normal demand distributions. We also study the distribution-free case by using a lower bound on the newsvendor profit function. We show that when the budget is unlimited, the forecasting expenditure increases with the production cost until the cost of holding an inventory is equal to the cost of a lost sales. Although both expenditures increase with the product price, it turns out that the advertising expenditure is more important for the newsvendor: it allocates more to the advertising for products with higher prices if the budget is limited. It turns out that a newsvendor can benefit more from advertising (forecasting) if the market size (variability) is larger. Moreover, it is more profitable to allocate the expenditures into a single large market rather than allocating it to small segmented markets. The numerical studies show that the ability of forecasting makes a newsvendor more robust to the variance, i.e., the variability level is reduced significantly with the forecasting expenditure.

## Keywords

Advertising Forecasting Newsvendor Inventory## Mathematics Subject Classification

90B05## Notes

### Acknowledgements

The authors wish to thank two anonymous referees for their very helpful comments and suggestions which improved the content and presentation of the paper.

## References

- Alfares HK, Elmorra HH (2005) The distribution-free newsboy problem: extensions to the shortage penalty case. Int J Prod Econ 93–94(1):465–477CrossRefGoogle Scholar
- Campbell RC (2008) Estimating demand for new products using a discrete price variable. J Target Meas Anal Mark 16(2):115–121CrossRefGoogle Scholar
- Fildes R, Nikolopoulos K, Crone SF, Syntetos A (2008) Forecasting and operational research: a review. J Oper Res Soc 59(9):1150–1172CrossRefGoogle Scholar
- Gallego G, Moon I (1993) The distribution-free newsboy problem: review and extensions. J Oper Res Soc 44(8):825–834CrossRefGoogle Scholar
- Gerchak Y, Parlar M (1987) A single period inventory problem with partially controllable demand. Comput Oper Res 14(1):1–9CrossRefGoogle Scholar
- Gerchak Y, Parlar M (1990) Yield randomness, cost tradeoffs, and diversification in the EOQ model. Nav Res Logist 37(3):341–354CrossRefGoogle Scholar
- Güler MG (2014) A note on: the effect of optimal advertising on the distribution-free newsboy problem. Int J Prod Econ 148(1):90–92CrossRefGoogle Scholar
- Glock CH, Ries JM (2012) Channel coordination and variance reduction in a newsvendor setting. Int J Serv Oper Manag 12(3):269–288Google Scholar
- Grasman S, Sari Z, Sari T (2007) Newsvendor solutions with general random yield distributions. RAIRO Oper Res 41(04):455–464CrossRefGoogle Scholar
- Guiffrida A, Jaber M (2008) Managerial and economic impact of reducing delivery variance in the supply chain. Appl Math Model 32(10):2149–2161CrossRefGoogle Scholar
- Güllü R (1996) On the value of information in dynamic production/inventory problems under forecast evolution. Nav Res Logist (NRL) 43(2):289–303CrossRefGoogle Scholar
- Güllü R (1997) A two-echelon allocation model and the value of information under correlated forecasts and demands. Eur J Oper Res 99(2):386–400CrossRefGoogle Scholar
- Hanssens DM, Parsons LJ (1993) Econometric and time-series market response models. In: Eliashberg J, Lilien GL (eds) Handbooks in operations research & marketing science, vol 5. Elsevier Science Publisher, Amsterdam, The Netherlands, pp 409–464Google Scholar
- Hill A, Doran D, Stratton R (2012) How should you stabilise your supply chains? Int J Prod Econ 135(2):870–881CrossRefGoogle Scholar
- Hrabec D, Haugen KK, Popela P (2017) The newsvendor problem with advertising: an overview with extensions. Rev Manag Sci 11(4):767–787CrossRefGoogle Scholar
- Inderfurth K (2004) Analytical solution for a single-period production-inventory problem with uniformly distributed yield and demand. Cent Eur J Oper Res 12(1):117–127Google Scholar
- Jones JP (1995) When ads work-new proof the advertising triggers sales. Lexington Books, New YorkGoogle Scholar
- Khouja M (1999) The single period (news-vendor) problem: literature review and suggestions for future research. Manag Sci 27(1):537–553Google Scholar
- Khouja M, Robbins SS (2003) Linking advertising and quantity decisions in the single-period inventory model. Int J Prod Econ 86(1):93–105CrossRefGoogle Scholar
- Klein R, Shearman R (1997) Estimating new product demand from biased survey data. J Econom 76(1/2):53–76CrossRefGoogle Scholar
- Kunnumkal S, Topalog̃lu H (2008) Price discounts in exchange for reduced customer demand variability and applications to advance demand information acquisition. Int J Prod Econ 111(2):543–561CrossRefGoogle Scholar
- Lee C-M, Hsu S-L (2011) The effect of advertising on the distribution-free newsboy problem. Int J Prod Econ 129:217–224CrossRefGoogle Scholar
- Porteus EL (2002) Foundations of stochastic inventory theory. Stanford University Press, CaliforniaGoogle Scholar
- Qin Y, Wang R, Vakharia AJ, Chen Y, Seref MMH (2011) The newsvendor problem: review and directions for future research. Eur J Oper Res 213(2):361–374CrossRefGoogle Scholar
- Rekik Y, Sahin E, Delivery Y (2007) A comprehensive analysis of the newsvendor model with unreliable supply. OR Spectr 29(2):207–233CrossRefGoogle Scholar
- Scarf H (1958) A min-max solution of an inventory problem. In: Arrow K, Karlin S, Scarf H (eds) Studies in the mathematical theory of inventory and production. Stanford University Press, California, pp 201–209Google Scholar
- Syntetos AA, Boylan JE, Disney SM (2009) Forecasting for inventory planning: a 50-year review. J Oper Res Soc 60(1):S149–S160CrossRefGoogle Scholar