Safety stock determination of uncertain demand and mutually dependent variables

Sharfuddin Lisan


Safety stock is that point, where the user finds a comfort zone between overstock and understock situation.  It is is defined as the buffer inventory have to be kept to deal with differences between supply and demand. There are different variables to be considered while determining safety stock. In this writing there is an effort to establish a model that include direct and indirect cost related to inventory. The inclusion of Ordering cost, holding cost, Product price, Time, Demand, Demand Variation, Lead time, Mean lead time, Errors in Forecasting, Deviation of lead time etc. are used in this model. This model works economic order quantity, regression, and forecasting error calculation to estimate safety stock while reducing human judgment error in the calculation.

Full Text:



o Astrid Schneider, D. M. (2010). Linear Regression Analysis. Dtsch Arztebl Int, 107(44): 776–782. doi:10.3238/arztebl.2010.0776

o Axsäter, S. (2006). Inventory control (2nd). New York: Springer-Verlag.

o Azoury, K. S. (1985). Bayes solution to dynamic inventory models under unknown demand distribution. Management Science, 31(9), 1150–1160.

o Ahn, H. S., and Olsen, T. L. 2007. “Inventory Competition with Subscriptions.” Working paper, University of Michigan.

o Alfredsson, P., and J. Verrijdt. 1999. “Modeling Emergency Supply Flexibility in a Two-echelon Inventory System.” Management Science 45 (10): 1416–1431.

o Avinadav, T., and T.Arponen. 2009. “An EOQ Model for Items with a Fixed Shelf-life and Declining Demand Rate Based on Time-to-expiry Technical Note.” Asia Pacific Journal of Operational Research 26 (6): 759–767.

o Avinadav, T., A. Herbon, and U. Spiegel. 2013. “Optimal Inventory Policy for a Perishable Item with Demand Function Sensitive to Price and Time.” International Journal of Production Economics 144 (2): 497–506.

o Avsar, S. M., and M. B. Gursoy. 2002. “Inventory Control under Substitutable Demand: A Stochastic Game Application.” Naval Research Logistics Quarterly 49 (4): 359–375.

o Ballou, R. H. (2004). Business logistics management: planning, organizing, and controlling the supply chain. Upper Saddle River, N.J.: Prentice-Hall.

o Beutel, A. L., & Minner, S. (2012). Safety stock planning under causal demand fore- casting. International Journal of Production Economics, 140(2), 637–645.

o Baker, R. C., and T. L. Urban. 1988. “A Deterministic Inventory System with an Inventory-level-dependent Demand Rate.” Journal of The Operational Research Society 39 (9): 823–831.

o Blumenfeld, D. E., R. W. Hall, and W. C. Jordan. 1985. “Trade-off between Freight Expediting and Safety Stock Inventory Costs.” Journal of Business Logistics 6 (1): 79–100.

o Chatfield, D. C., J. G. Kim, T. P. Harrison, J. C. Hayya. 2004. The bullwhip effect—impact of stochastic lead time, information quality, and information sharing. Prod. Oper. Manag. 13(4): 340–353.

o Chopra, S., G. Reinhardt, M. Dada. 2004. The effect of leadtime uncertainty on safety stocks. Dec. Sci. 35(1): 1–24.

o Chopra, S., P. Meindl. 2007. Supply Chain Management: Strategy, Planning and Operation. 3rd edn. Pearson Prentice Hall, New Jersey

o Chai, T. and Draxler, R. R (2014) : Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature, Geosci. Model Dev., 7, 1247-1250,, 2014.

o Chen, L. (2010). Bounds and heuristics for optimal Bayesian inventory control with unobserved lost sales. Operations Research, 58(2), 396–413.

o Chartniyom, S., Lee, M. K., Luong, L., and Marian, R. 2007. “Multi-location Inventory System with Lateral Transshipments and Emergency Orders.” IEEE International Conference on Industrial Engineering and Engineering Management, 1594–1598, edited by IEEE Xplore Press, Singapore, 2006 December 24.

o Chiang, C., and G. J. Gutierrez. 1996. “APeriodic Review Inventory System with Two Supply Modes.” The European Journal of Operational Research 94 (3): 527–547.

o Decroix, G. A. 2006. “Optimal Policy for a Multiechelon Inventory System with Remanufacturing.” Operations Research 54 (3): 532–543.

o Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1952). The inventory problem: Ii. case of unknown distributions of demand. Econometrica, 20(3), 450–466.

o Eppen, G. D., & Martin, R. K. (1988). Determining Safety Stock in the Presence of Stochastic Lead Time and Demand. Management Science, 34(11), 1380-1390. doi:10.1287/mnsc.34.11.1380

o Feller, W. 1957. An Introduction to Probability Theory and Its Applications. 2nd edn. John Wiley & Sons, New York.

o Hyndman, R. J., & Athanasopoulos, G. (2016). Forecasting: principles and practice. Heathmont: OTexts

o Harris, F. W. (1913), "How many parts to make at once", Factory: The Magazine of Management, No. 10, pp. 135-6.

o Haddley, S. C. (September 2004 I). SAFETY INVENTORY ANALYSIS why and how. STRATEGIC FINANCE, 27-33.

o Hon KKB (2005) Performance and evaluation of manufacturing systems. CIRP Annals – Manufacturing Technology 54(2):139–154.

o Iglehart, D. L. (1964). The dynamic inventory problem with unknown demand dis- tribution. Management Science, 10(3), 429–440.

o Janssen, E., Strijbosch, L., & Brekelmans, R. (2009). Assessing the effects of using demand parameters estimates in inventory control and improving the perfor- mance using a correction function. International Journal of Production Economics, 118(1), 34–42.

o Karlin, S. (1960). Dynamic inventory policy with varying stochastic demands. Man- agement Science, 6(3), 231–258.

o Kulkarni, and J. Swaminathan. 2007. “Coordinated Inventory Planning for New and Old Products under Warranty.”Probability in the Engineering and Informational Sciences 21 (2): 261–287.

o Kalpakam, S., and G. Arivarignan. 1988. “A Continuous Review Perishable Inventory Model.” Statistics 19 (3): 389–398.

o Kelle, P., and E. A. Silver. 1989. “Forecasting the Returns of Reusable Containers.” Journal of Operations Management 8 (1): 17–35. Khmelnitsky, E., and Y. Gerchak. 2002. “Optimal Control Approach to Production Systems with Inventory Level-dependent Demand.”IEEE Transactions on Automatic Control 47 (2): 289–292.

o Kanet JJ, Gorman MF, Sto ßlein M (2010) Dynamic planned safety stocks in supply networks. International Journal of Production Research 48(22):6859–6880.

o Lariviere, M. A., & Porteus, E. L. (1999). Stalking information: Bayesian inventory management with unobserved lost sales. Management Science, 45(3), 346–363.

o Lippman, S. A., and K. F. McCardle. 1997. “The Competitive Newsboy.” Operations Research 45 (1): 54–65.

o Mark Lunt(2015) Introduction to statistical modelling: linear regression, Rheumatology, Volume 54, Issue 7, 1 July 2015, Pages 1137–1140,

o Muckstadt, J. A., & Sapra, A. (2010). Principles of inventory management (1st). New York: Springer.

o Neale, J. J., B. T. Tomlin, S. P. Willems. 2003. The role of inventory in superior supply chain performance. Harrison, T. B., H. L. Lee, J. J. Neale eds. The Practice of Supply Chain Management: Where Theory & Application Converge. Springer Inc., New York, 31–59.

o Nahmias, S., D. Perry, and W. Stadje. 2004. “Perishable Inventory Systems with Variable Input and Demand Rates.” Mathematical Methods of Operational Research 60 (1): 155–162.

o Netessine, S., and N. Rudi. 2003. “Centralized and Competitive Inventory Models with Demand Substitution.” Operations Research 51 (2): 329–335.

o Neuts, F. 1964. “An Inventory Model with an Optimal Time Lag.” SIAM Journal on Applied Mathematics 12 (1): 179–185.

o Prak, D., Teunter, R., & Syntetos, A. (2017). On the calculation of safety stocks when demand is forecasted. European Journal of Operational Research, 256(2), 454-461. doi:10.1016/j.ejor.2016.06.035

o Prak, D., Teunter, R., & Syntetos, A. (2017). On the calculation of safety stocks when demand is forecasted. European Journal of Operational Research, 256(2), 454-461. doi:10.1016/j.ejor.2016.06.035

o Parlar, M. 1988. “Game Theoretic Analysis of the Substitute Product Inventory Problem with Random Demand.” Naval Research Logistics Quarterly 35 (3): 397–409.

o Ray, W. D. 1981. Computation of reorder levels when the demands are correlated and the lead time random. J. Oper. Res. Soc. 32(1): 27–34. Atkinson, C. 2005. Safety Stock. Inventory Management Review, June 10, 2005.

o Roach, B. (2005). Origin of the economic order quantity formula; transcription or transformation? Management Decision, 43(9), 1262-1268. Retrieved from

o Rajashree Kamath, K., & Pakkala, T. P. M. (2002). A Bayesian approach to a dynamic inventory model under a unknown demand distribution. Computers and Opera- tions Research, 29(4), 317–422.

o Rosenshine, M., and D. Obee. 1976. “Analysis of a Standing Order Inventory System with Emergency Orders.” Operations Research 24 (6): 1143–1155.

o Ruiz-Torres AJ, Mahmoodi F (2010) Safety stock determination based on parametric lead time and demand information. International Journal of Production Research 48(10):2841–2857.

o Silver, E. A., D. F. Pyke, R. Peterson. 1998. Inventory Management and Production Planning and Scheduling. 3rd ed. John Wiley & Sons, New York.

o Schneider, A., Hommel, G., & Blettner, M. (2010). Linear Regression Analysis: Part 14 of a Series on Evaluation of Scientific Publications. Deutsches Ärzteblatt International, 107(44), 776–782.

o Schwarz, L. (2007). The EOQ Model. Kluwer Academic Publishing,

o Swift, L., & Piff, S. (2014). Quantitative methods for business, management & finance. Basingstoke: Palgrave Macmillan.

o scheidler, J. w. (FALL 2009). safety stock: everybody wants. THE JOURNAL OF BUSINESS FORECASTING, 4-12

o Scarf, H. (1959). Bayes solutions of the statistical inventory problem. Annals of Math- ematical Statistics, 30(2), 490–508.

o Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3rd). New York: John Wiley & Sons.

o Strijbosch, L. W. G., & Moors, J. J. A. (2005). The impact of unknown demand pa- rameters on (r,s)-inventory control performance. European Journal of Operational Research, 162(3), 805–815.

o Teunter, R., and D. Vlachos. 2001. “An Inventory System with Periodic Regular Review and Flexible Emergency Review.” IIE Transactions 33 (8): 625–635.

o Wang, P., Zinn, W., & Croxton, K. L. (2009). Sizing Inventory When Lead Time and Demand are correlated. Production and Operations Management, 19(4), 480-484. doi:10.1111/j.1937-5956.2009.01109.x

o Wilson, R. 2009. 20th Annual State of Logistics Report. Council of Supply Chain Management Professionals, http://www.cscmp. org (accessed date May 17, 2009).

o Weiss, H. 1980. “Optimal Ordering Policies for Continuous Review Perishable Inventory Models.” Operations Research 28 (2): 365–374. Whittemore, A. S., and S. Saunders. 1977. “Optimal Inventory under Stochastic Demand with Two Supply Options.” SIAM Journal on Applied Mathematics 32 (2): 293–305.

o Yamazaki, T., Shida, K., & Kanazawa, T. (2015). An approach to establishing a method for calculating inventory. International Journal of Production Research, 54(8), 2320-2331. doi:10.1080/00207543.2015.1076179

o Yuan, X. M., and K. L. Cheung. 1998. “Modeling Returns of Merchandise in an Inventory System.” Operations Research Spektrum 20 (3): 147–154.



  • There are currently no refbacks.

Comments on this article

View all comments

Copyright (c) 2018 Sharfuddin Lisan


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


If you find difficulties in submitting manuscript please forward your doc file to Our support team will assist you in submission process and other technical matters.

In order to get notifications on inbox please add  this domain in your email safe list.

International journal of business and social research (Print)
ISSN 2164-2540

International journal of business and social research (Online)
ISSN 2164-2559

[International Journal of Business and Social Research (IJBSR) previously published by MIR Center for Socio-Economic Research, MD, USA. From February 2018 this journal is published by the LAR Center Press, OR, USA]