The order and volume fill rates in inventory control systems

This paper differentiates between an order (line) fill rate and a volume fill rate and specifies their performance for different inventory control systems. When the focus is on filling complete customer orders rather than total demanded quantity the order fill rate would be the preferred service level measure. The main result shows how the order and volume fill rates are related in magnitude. Earlier results derived for a single-item, single-stage, continuous review inventory system with backordering and constant lead times controlled by a base-stock policy are extended in different directions. Demand is initially assumed to be generated by a compound renewal process. An important generalization then concerns the class of customer order-size distributions, i.e. compounding distributions, with increasing failure rate for which the volume fill rate always exceeds the order fill rate. Other extensions consider more general inventory control review policies with backordering, as well as some relations between service measures. A particularly important result in the paper concerns an alternative service measure, the customer order fill rate, and shows how this measure always exceeds the other two more well-known service measures, viz. the order fill rate and the volume fill rate.

[1]  Hau L. Lee,et al.  Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies , 1998, Eur. J. Oper. Res..

[2]  Dmitry Krass,et al.  Inventory models with minimal service level constraints , 2001, Eur. J. Oper. Res..

[3]  Warren H. Hausman.  Minimizing Customer Line Items Backordered in Inventory Control , 1969 .

[4]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[5]  Stephen A. Smith,et al.  Estimating negative binomial demand for retail inventory management with unobservable lost sales , 1996 .

[6]  Christian Larsen,et al.  Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand , 2011 .

[7]  John E. Boylan,et al.  An examination of the size of orders from customers, their characterisation and the implications for inventory control of slow moving items , 2003, J. Oper. Res. Soc..

[8]  Kaj Rosling,et al.  Inventory Cost Rate Functions with Nonlinear Shortage Costs , 2002, Oper. Res..

[9]  Jing-Sheng Song.  On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System , 1998, Oper. Res..

[10]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[11]  Sven Axsäter,et al.  Approximating general multi-echelon inventory systems by Poisson models , 1994 .

[12]  Dennis K. J. Lin,et al.  On the single item fill rate for a finite horizon , 2003, Oper. Res. Lett..

[13]  D. Simchi-Levi.  Designing And Managing The Supply Chain , 2007 .

[14]  C Larsen,et al.  A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process , 2008, J. Oper. Res. Soc..

[15]  Jagdish K. Patel,et al.  A catalog of failure distributions , 1973 .

[16]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[17]  Anders Thorstenson,et al.  An inventory control project in a major Danish company using compound renewal demand models , 2008 .

[18]  Douglas J. Thomas,et al.  Measuring Item Fill-Rate Performance in a Finite Horizon , 2005, Manuf. Serv. Oper. Manag..

[19]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[20]  Helmut Schneider,et al.  Effect of service-levels on order-points or order-levels in inventory models , 1981 .

[21]  Paul H. Zipkin,et al.  Foundations of Inventory Management , 2000 .

[22]  Ram C. Tripathi,et al.  On the monotonic properties of discrete failure rates , 1997 .