Modeling stock-out loss and overstocking loss generated by bullwhip effect

Document Type : Research Note


1 Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

2 Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Department of Industrial Engineering, Istanbul Sehir University, Istanbul, Turkey.; Beedie School of Business, Simon Fraser University, Vancouver, Canada.


Although the literature of the supply chain is teemed with the analysis of the bullwhip effect, few studies regarding the impact of the bullwhip effect or demand distortion on the supply chain profit have been done. Hence, we introduce the concept of Distance to Loss (DL), which is a function of the retailer’s selling price, the manufacturer’s wholesaler price, the end item’s salvage value, the retailer’s expected demand and the retailer’s variance of demand. This concept can perfectly model both stock-out loss and overstocking loss emanated by the bullwhip effect and combines both the newsvendor model and credit risk concepts. Our findings are based on an experimental design and are profoundly in line with previous research. In particular, our model indicates that variations in demand parameters, retailer’s selling price and manufacturer’s wholesaler price impinge on the retailer’s DL, whereas a slight increase in the salvage value negligibly affect the retailer’s DL.


Main Subjects

1. Chopra, S. and Meindel, P., Supply Chains Management, 2nd Ed., Prentice-Hall Co. (2004).
2. Stock, J.R. and Lambert, D.M., Strategic Logistic Management, 4th Ed., McGraw-Hill Co. (2001).
3. Poirier, C.C., Advance Supply Chain Management, 1st Indian Ed., Berret-Koehler Publisher, Inc. (2002).
4. Lee, H., Padmanabhan, V., and Wang, S. "The bullwhip effect in supply chains", Sloan Management Review, 38, pp. 93-102 (1997).
5. Lee, H., Padmanabhan, V., andWang, S. "Information distortion in a supply chains: the bullwhip effect", Management Science, 43, pp. 546-558 (1997).
6. Cambridge, M.A. and Kahn, J.A. "Inventories and the volatily of production", American Economic Review, 174, pp. 667-679 (1987).
7. Chen, Y.F., Drezner, Z., Ryan, J.K., and Simchi- Levi, D. "Quantifying the bullwhip effect in a simple supply chains: The impact of forecasting, lead-times and information", Management Science, 46, pp. 436- 443 (2000).
8. Dejonckheere, J., Disney, S.M., Lambrecht, M.R., and Towill, D.R. "Measuring and avoiding the bullwhip effect: A control theoretic approach", European Journal of Operational Research, 147, pp. 567-590 (2003).
9. Eichenbaum, M.S. "Some empirical evidence of the production level and production cost smoothing models of inventory investment", American Economic Review, 79, pp. 853-864 (1989).
10. Frangoo, J.C. and Wooters, M.J.F. "Measuring the bullwhip effect in the supply chains", Supply Chains Management, 5, pp. 78-89 (2000).
11. Khan, A. and Thomas, J.K. "Inventories and the business cycle: An equilibrium analysis of (S,s) policies", Federal Reserve Bank of Minneapolis, Research Department Staff Report 329 (2003).
12. KMV Corporation, Credit Monitor Overview, San Francisco, CA (1993).
13. Kealhofer, S., Measuring Default Risk in Portfolios of Derivatives, Mimeo KMV Corporation", San Francisco, CA (1996).
14. Crouhy, M., Galai, D., and Mark, R. "A comparative analysis of current credit risk models", Journal of Banking and Finance, 24, pp. 59-117 (2000).
15. Altman, E.I. and Saunders, A. "Credit risk measurement: Developments over the last 20 years", Journal of Banking and Finance, 21, pp. 1721-1742 (1997).
16. Scott, J. "The probability of bankruptcy: A comparison of empirical predictions and theoretical models", Journal of Banking and Finance, 5, pp. 317-344 (1981).
17. Carey, M. and Hrycay, M. "Parameterizing credit risk models with rating data", Journal of Banking and Finance, 25, pp. 197-270 (2001).
18. Li, L., Yang, J., and Zou, X. "A study of credit risk of Chinese listed companies: ZPP versus KMV", Applied Economics, 48, pp. 2697-2710 (2016). 
19. Norliza, M.Y. and Maheran, M.J. "Forecasting the probability of default of PN17 company using KMVMerton model", International Journal of Applied Mathematics & Statistics, 53, pp. 103-108 (2015).
20. Lee, W.C. "Redefinition of the KMV model's optimal default point based on genetic algorithms - Evidence from Taiwan", Expert Systems with Applications, 38, pp. 10107-10113 (2011).
21. Zhang, Y. and Shi, B. "Non-tradable shares pricing and optimal default point based on hybrid KMV models: Evidence from China", Knowledge-Based Systems, 110, pp. 202-209 (2016).
22. Ching-Chiang, Y., Fengyi, L., and Chih-Yu, H. "A hybrid KMV model, random forests and rough set theory approach for credit rating", Knowledge-Based Systems, 33, pp. 166-172 (2012).
23. Machuca, J.A.D. and Barajas, R.P. "The impact of electronic data interchange on reducing bullwhip effect and supply chains inventory costs", Transportation Research Part E: Logistics and Transportation Review, 40, pp. 209-228 (2004).
24. Forrester, J.W. "Industrial dynamics - A major breakthrough for decision makers", Harvard Business Review, 36, pp. 37-66 (1958).
25. Forrester, J.W., Industrial Dynamics, MIT Press and John Wiley & Sons, Inc., New York (1961).
26. Towill, D. "Supply chain dynamics", International Journal of Computer Integrated Manufacturing, 4, pp. 197-208 (1991). 
27. Wickner, J., Towill, D.R., and Naim, M. "Smoothing supply chain dynamics", International Journal of Production Economics, 22, pp. 231-248 (1991).
28. Kim, J.G., Chatfield, D., Harrison, T.P., and Hayya, J.C. "Quantifying the bullwhip effect in a supply chain with stochastic lead time", European Journal of Operational Research, 173, pp. 617-636 (2006).
29. Sterman, J.D. "Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiments", Management Science, 35, pp. 321-339 (1989).
30. Croson, R. and Donohue, K. "Behavioral causes of the bullwhip effect and the observed value of inventory information", Management Science, 52, pp. 323-336 (2006).
31. Croson, R. and Donohue, K. "Impact of POS data sharing on supply chain management: An experimental study", Production and Operations Management, 12, pp. 1-11 (2003).
32. Haines, R., Hough, J., and Haines, D. "A metacognitive perspective on decision making in supply chains: Revisiting the behavioral causes of the bullwhip effect", International Journal of Production Economics, 184, pp. 7-20 (2017).
33. Sarkar, S. and Kumar, S. "A behavioral experiment on inventory management with supply chain disruption", International Journal of Production Economics, 169, pp. 169-178 (2015).
34. Zhang, X. "The impact of forecasting methods on the bullwhip effect", International Journal of Production Economics, 88, pp. 15-27 (2004).
35. Sadeghi, A. "Providing a measure for bullwhip effect in a two-product supply chain with exponential smoothing forecasts", International Journal of Production Economics, 169, pp. 44-54 (2015).
36. Khosroshahi, H., Moattar Husseini, S.M., and Marjani, M.R. "The bullwhip effect in a 3-stage supply chain considering multiple retailers using a moving average method for demand forecasting", Applied Mathematical Modelling, 40, pp. 8934-8951 (2016).
37. Sirikasemsuk, K. and Luong, H.T. "Measure of bullwhip effect in supply chains with first-order bivariate vector autoresgression time-series demand model", Computers & Operations Research, 78, pp. 59-79 (2017).
38. Paik, S.K. and Bagchi, P. "Understanding the causes of the bullwhip effect in a supply chain", International Journal of Retail & Distribution Management, 35, pp. 308-324 (2007).
39. Sourirajan, K., Ramachandran, B., and An, L. "Application of control theoretic principles to manage inventory replenishment in a supply chain", International Journal of Production Research, 46, pp. 6163-6188 (2008).
40. Salcedo, C.A.G., Hernandez, A.I., Vilanova, R., and Cuartas, J.H. "Inventory control of supply chains: Mitigating the bullwhip effect by centralized and decentralized internal model control approaches", European Journal of Operational Research, 224, pp. 261-272 (2013).
41. Fu, D.F., Ionescu, C., Aghezzaf, E.H., and Keyser, R.D. "Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy", Computers & Industrial Engineering, 81, pp. 46-57 (2015).
42. Wang, X. and Disney, S.M. "Mitigating variance amplification under stochastic lead-time: The proportional control approach", European Journal of Operational Research, 256, pp. 151-162 (2017).
43. Miragliotta, G. "Layers and mechanisms: A new taxonomy for the bullwhip effect", International Journal of Production Economics, 104, pp. 365-381 (2006).
44. Metters, R. "Quantifying the bullwhip effect in supply chain", Journal of Operation Management, 15, pp. 89- 100 (1997).
45. Chen, F., Ryan, J.K., and Simchi-Levi, D. "The impact of exponential smoothing forecasts on the Bullwhip Effect", Naval Research Logistics, 47, pp. 269-286 (2000).
46. Chen, L. and Lee, H.L. "Information sharing and order variability control under a generalized demand model", Management Science, 55, pp. 781-797 (2009).
47. Isaksson, O.H.D. and Seifert, R.W. "Quantifying the bullwhip effect using two-echelon data: A crossindustry empirical investigation", International Journal of Production Economics, 171, pp. 311-320 (2016).
48. George, J. and Pillai, V.M. "Transfer function models of inventory policies and bullwhip quantification in supply chain", Procedia Technology, 25, pp. 1064-1071 (2016).
49. Sodhi, M.S., Sodhi, N.S., and Tang, C.S. "An EOQ model for MRO customers under stochastic price to quantify bullwhip effect for the manufacturer", International Journal of Production Economics, 155, pp. 132-142 (2014).
50. Ma, J. and Bao, B. "Research on bullwhip effect in energy-efficient air conditioning supply chain", Journal of Cleaner Production, 143, pp. 854-865 (2017).
51. Zipkin, P.H. "Critical number policies for inventory models with periodic data", Management Science, 35, pp. 71-80 (1989).
52. Moody's KMV Company, Modeling Default Risk, Modeling Methodology (2003).