# A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process

Christian Larsen () and Anders Thorstenson ()
Christian Larsen: Department of Business Studies, Postal: The Aarhus School of Business, Fuglesangs Allé 4, 8210 Aarhus V, Denmark, http://www.asb.dk/staff/bs/chl.aspx?page=%7B803EFF10-69F7-4C0F-AEE3-F7F410E4B6F2%7D
Anders Thorstenson: Department of Business Studies, Postal: The Aarhus School of Business, Fuglesangs Allé 4, 8210 Aarhus V, Denmark, http://www.asb.dk/staff/bs/ath.aspx?page=%7B803EFF10-69F7-4C0F-AEE3-F7F410E4B6F2%7D

Abstract: The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.

Keywords: Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels (search for similar items in EconPapers)
Pages: 16 pages
Date: 2006-04-25
Note: Published as: Larsen, C and Thorstenson A, A Comparison between the Order and the Volume Fill Rate for a Base-stock Inventory Control System under a Compound Renewal Demand Process, Journal of the Operational Research Society, Vol 59, No 6, June 2008, pp 798-804 Published as: Thorstenson, A and Larsen, C, The Order and Volume Fill Rates in Inventory Control Systems, International Journal of Production Economics, http://dx.doi.org/10.1016/j.ijpe.2012.07.021, 2012
Citations: View citations in EconPapers (1)

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