Measuring and avoiding the bullwhip effect: A control theoretic approach. (English) Zbl 1026.90030

Summary: An important contributory factor to the bullwhip effect (i.e. the variance amplification of order quantities observed in supply chains) is the replenishment rule used by supply chain members. First the bullwhip effect induced by the use of different forecasting methods in order-up-to replenishment policies is analysed. Variance amplification is quantified and we prove that the bullwhip effect is guaranteed in the order-up-to model irrespective of the forecasting method used. Thus, when production is inflexible and significant costs are incurred by frequently switching production quantities up and down, order-up-to policies may no longer be desirable or even achievable. In the second part of the paper a general decision rule is introduced that avoids variance amplification and succeeds in generating smooth ordering patterns, even when demand has to be forecasted. The methodology is based on control systems engineering and allows important insights to be gained about the dynamic behaviour of replenishment rules.


90B30 Production models


Full Text: DOI


[1] Adelson, R. M., The dynamic behaviour of linear forecasting and scheduling rules, Operational Research Quarterly, 17, 4, 447-462 (1966)
[2] Aseltine, J. A., Transform methods in linear system analysis (1958), The Maple Press Company: The Maple Press Company New York · Zbl 0057.19406
[3] Baganha, M. P.; Cohen, M. A., The stabilising effect of inventory in supply chains, Operations Research, 46, 3, 572-583 (1998)
[4] Bertrand, J. W.M., Balancing production level variations in complex production systems, International Journal of Production Research, 24, 5, 1059-1074 (1986)
[5] Bonney, M. C.; Popplewell, K., Design of production control systems: Choice of systems structure and systems implementation sequence, Engineering Costs and Production Economics, 15, 173-189 (1988)
[6] Bonney, M. C.; Popplewell, K.; Matoug, M., Effect of errors and delays in inventory reporting on production system performance, International Journal of Production Research, 35, 93-105 (1994)
[7] Chatfield, C., The Analysis of Time Series: An Introduction Texts in Statistical Sciences, ((1996), Chapman & Hall: Chapman & Hall London), 283 · Zbl 0870.62068
[8] Chen, F.; Drezner, Z.; Ryan, J.; Simchi-Levi, D., Quantifying the bullwhip effect in a simple supply chain: The impact of forecasting, lead times, and information, Management Science, 46, 3, 436-443 (2000) · Zbl 1231.90019
[9] Chen, F.; Ryan, J.; Simchi-Levi, D., The impact of exponential smoothing forecasts on the bullwhip effect, Naval Research Logistics, 47, 4, 271-286 (2000) · Zbl 0968.90006
[10] Cochran, W. T.; Cooley, J. W.; Favin, D. L.; Helms, H. D.; Kaenel, R. A.; Lang, W. W.; Maling, G. C.; Nelson, D. E.; Rader, C. M.; Welch, P. D., What is the fast Fourier transform?, IEEE Transactions on Audio Electro-acoustics AU, 15, 2, 45-55 (1967)
[12] Deziel, D. P.; Eilon, S., A linear production-inventory control rule, The Production Engineer, 43, 93-104 (1967)
[14] Elmaghraby, S. E., The Design of Production Systems (1966), Reinhold Publishing Corporation: Reinhold Publishing Corporation New York · Zbl 0203.52502
[16] Forrester, J., Industrial Dynamics (1961), MIT Press: MIT Press Cambridge, MA
[17] Garnell, P.; East, D. J., Guided Weapons Control Systems (1977), Pergamon Press: Pergamon Press Oxford
[19] Houpis, C. H.; Lamont, G. B., Digital Control Systems (1985), McGraw-Hill: McGraw-Hill New York
[20] John, S.; Naim, M. M.; Towill, D. R., Dynamic analysis of a WIP compensated decision support system, International Journal Manufacturing System Design, 1, 4, 283-297 (1994)
[21] Jury, E. I., Theory and application of the \(z\)-transform method (1964), Robert E. Krieger Publishing Company: Robert E. Krieger Publishing Company New York
[22] Kaminsky, P.; Simchi-Levi, D., A new computerized beer game: A tool for teaching the value of integrated supply chain management, POMS Series in Technology and Operations Management, 1, 216-225 (1998)
[24] Karlin, S., One stage inventory models with uncertainty, (Karlin, S.; Scarf, H., Studies in the Mathematical Theory of Inventory and Production (1958), Stanford University Press), 109-134
[25] Lambrecht, M.; Dejonckheere, J., Extending the beer game to include real-life supply chain characteristics, (Bartezzaghi, E.; Filippini, R.; Spina, G.; Vinelli, A., Managing Operations Networks (1999), Servizi Grafici Editoriale: Servizi Grafici Editoriale Padova), 237-243
[26] Lee, H. L.; Padmanabhan, V.; Whang, S., The Bullwhip effect in supply chains, Sloan Management Review, Spring, 93-102 (1997)
[27] Lee, H. L.; Padmanabhan, V.; Whang, S., Information distortion in a supply chain: The bullwhip effect, Management Science, 43, 4, 546-558 (1997) · Zbl 0888.90047
[28] Lee, H. L.; So, K. C.; Tang, C. S., The value of information sharing in a two level supply chain, Management Science, 46, 5, 628-643 (2000) · Zbl 1231.90044
[29] Makridakis, S.; Wheelwright, S. C.; McGee, V. E., Forecasting: Methods and Applications (1978), John Wiley & Sons: John Wiley & Sons New York
[30] Nise, N. S., Control Systems Engineering (1995), The Benjamin/Cummings Publishing Company Inc: The Benjamin/Cummings Publishing Company Inc California
[32] Simon, H. A., On the application of servomechanism theory in the study of production control, Econometrica, 20, 247-268 (1952) · Zbl 0046.37804
[33] Sterman, J., Modelling managerial behaviour: Misperceptions of feedback in a dynamic decision making experiment, Management Science, 35, 3, 321-339 (1989)
[34] Sterman, J., Business Dynamics, Systems Thinking and Modelling for a Complex World, ((2000), Irwin McGraw-Hill: Irwin McGraw-Hill New York), 982
[35] Towill, D. R., Transfer Function Techniques for Control Engineers (1970), Iliffe Books: Iliffe Books London
[36] Towill, D. R., Dynamic analysis of an inventory and order based production control system, International Journal of Production Research, 20, 369-383 (1982)
[38] Towill, D. R.; del Vecchio, A. L., Application of filter theory to the study of supply chain dynamics, Production Planning and Control, 5, 1, 82-96 (1995)
[39] Towill, D. R.; Yoon, S. S., Some features common to inventory system and process controller design, Engineering Costs and Production Economics, 6, 225-236 (1982)
[40] Vassian, H. J., Application of discrete variable servo theory to inventory control, Operations Research, 3, 272-282 (1955) · Zbl 1414.90054
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