Taming the bullwhip effect whilst watching customer service in a single supply chain echelon.

*(English)*Zbl 1125.90312Summary: We study a generalised order-up-to policy that has highly desirable properties in terms of order and inventory variance and customer service levels it generates. We quantify exactly the variance amplification in replenishment orders, i.e. the bullwhip effect, and the variance of inventory levels over time, for i.i.d. and the weakly stationary auto regressive (AR), moving average (MA) and auto regressive moving average (ARMA) demand processes. We demonstrate that high customer service as measured by fill-rate, and smooth replenishments need not increase inventory cost substantially. We observe that in some instances of the ARMA demand pattern this comes at the expense of a relatively small increase in safety stock, whilst in other instances inventory levels can actually be reduced.

##### MSC:

90B05 | Inventory, storage, reservoirs |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

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\textit{S. M. Disney} et al., Eur. J. Oper. Res. 173, No. 1, 151--172 (2006; Zbl 1125.90312)

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##### References:

[1] | Axsäter, S., Control theory concepts in production and inventory control, International journal of systems science, 16, 2, 161-169, (1985) · Zbl 0557.90043 |

[2] | Baganha, M.P.; Cohen, M.A., The stabilizing effect of inventory in supply chains, Operations research, 46, 3, 572-583, (1998) |

[3] | Balakrishnan, A.; Geunes, J.; Pangburn, M.S., Coordinating supply chains by controlling upstream variability propagation, Manufacturing & service operations management, 6, 2, 163-183, (2004) |

[4] | Box, G.E.; Jenkins, G.M., Time series analysis forecasting and control, (1970), Holden-Day San Francisco · Zbl 0249.62009 |

[5] | Brown, R.G., Smoothing, forecasting and prediction of discrete time series, (1962), Prentice-Hall Englewood Cliffs, NJ · Zbl 0192.25606 |

[6] | Chen, F.; Drezner, Z.; Ryan, J.K.; Simchi-Levi, D., Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead-times and information, Management science, 46, 436-443, (2000) · Zbl 1231.90019 |

[7] | Dejonckheere, J.; Disney, S.M.; Lambrecht, M.R.; Towill, D.R., Measuring the bullwhip effect: A control theoretic approach to analyse forecasting induced bullwhip in order-up-to policies, European journal of operational research, 147, 3, 567-590, (2003) · Zbl 1026.90030 |

[8] | Dejonckheere, J.; Disney, S.M.; Lambrecht, M.R.; Towill, D.R., The impact of information enrichment on the bullwhip effect in supply chains: A control engineering perspective, European journal of operational research, 153, 727-750, (2004) · Zbl 1099.90503 |

[9] | Deziel, D.P.; Eilon, S., A linear production-inventory control rule, Production engineer, 43, 93-104, (1967) |

[10] | Disney, S.M.; Towill, D.R., A discrete linear control theory model to determine the dynamic stability of vendor managed inventory supply chains, International journal of production research, 40, 179-204, (2002) · Zbl 1175.90138 |

[11] | Disney, S.M.; Towill, D.R., On the bullwhip and inventory variance produced by an ordering policy, OMEGA: the international journal of management science, 313, 157-167, (2003) |

[12] | Forrester, J., Industrial dynamics, a major breakthrough for decision makers, Harvard business review, July-August, 67-96, (1958) |

[13] | Graves, S.C., A single-item inventory model for a non-stationary demand process, Manufacturing and service operations management, 1, 50-61, (1999) |

[14] | Holmström, J., Product range management: A case study of supply chain operations in the European grocery industry, Supply chain management, 2, 3, 107-115, (1997) |

[15] | John, S.; Naim, M.M.; Towill, D.R., Dynamic analysis of a WIP compensated decision support system, International journal of manufacturing systems design, 1, 4, 283-297, (1994) |

[16] | Lee, H.L.; Padmanabhan, P.; Whang, S., Information distortion in a supply chain: the bullwhip effect, Management science, 43, 543-558, (1997) · Zbl 0888.90047 |

[17] | Lee, H.L.; Padmanabhan, P.; Whang, S., The bullwhip effect in supply chains, Sloan management review, 93-102, (1997) |

[18] | Lovejoy, W., Stopped myopic policies in some inventory models with generalized demand processes, Management science, 38, 5, 688-707, (1992) · Zbl 0757.90018 |

[19] | Magee, J.F., Guides to inventory policy—II. problems of uncertainty, Harvard business review, March-April, 103-116, (1956) |

[20] | Makridakis, S.; Andersen, A.; Carbone, R.; Fildes, R.; Hibon, M.; Lewandowski, R.; Newton, J.; Parzen, R.; Winkler, R., The accuracy of extrapolation (time series) methods: results of a forecasting competition, Journal of forecasting, 1, 11-153, (1982) |

[21] | Muth, J.F., Optimal properties of exponentially weighted forecasts, Journal of the American statistical association, 55, 299-306, (1960) · Zbl 0100.14602 |

[22] | Nise, N.S., Control systems engineering, (1995), The Benjamin Cummings Publishing Company San Francisco, CA |

[23] | Rao, U., Properties of the periodic review (R, Q) inventory control policy for stationary stochastic demand, Manufacturing & service operations management, 51, 37-53, (2003) |

[24] | Schmenner, R.W., Looking ahead by looking back: Swift, even flow in the history of manufacturing, Production and operations management, 10, 1, 87-95, (2001) |

[25] | Silver, E.A.; Pyke, D.F.; Peterson, R., Inventory management and production planning and scheduling, (1998), John Wiley & Sons New York |

[26] | Simon, H.A., On the application of servomechanism theory to the study of production control, Econometrica, 20, 247-268, (1952) · Zbl 0046.37804 |

[27] | Sterman, J., Modelling managerial behaviour: misperceptions of feedback in a dynamic decision making experiment, Management science, 35, 3, 321-339, (1989) |

[28] | 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) |

[29] | Treharne, T.; Sox, C., Adaptive inventory control for non-stationary demand and partial information, Management science, 48, 607-624, (2002) · Zbl 1232.90098 |

[30] | Tsypkin, Y.Z., Sampling systems theory and its application, (1964), Pergamon Press Oxford |

[31] | Vassian, H.J., Application of discrete variable servo theory to inventory control, Journal of the operations research society of America, 3, 272-282, (1955) · Zbl 1414.90054 |

[32] | Zipkin, P.H., Foundations of inventory management, (2000), McGraw-Hill New York · Zbl 1370.90005 |

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