Characterizing Order Processes of (s,S) and (r,nQ) Policies

KU Leuven - Faculty of Economics and Business Working Paper No. KBI_1309

32 Pages Posted: 5 Jun 2013

See all articles by Ann Noblesse

Ann Noblesse

KU Leuven

Robert N. Boute

Vlerick Leuven Gent Management School

Marc Lambrecht

KU Leuven, Research Center for Operations Management, Faculty of Economics and Business

Benny Van Houdt

University of Antwerp

Date Written: April 18, 2013

Abstract

In this paper we provide a novel approach to characterize the order process of an (s,S) and an (r,nQ) inventory policy. These inventory policies are commonly used when a fixed order cost is present. We provide two distinct perspectives. First, we analyze the time between subsequent replenishments, as well as the size of the replenishment orders, and characterize the distribution of both. Second, we look at the number of units ordered over an interval t, and compare it with the demand observed over the same period. Both perspectives are complementary and provide useful information for the upstream supplier observing this order process. We are in particular interested in the impact of the batching parameter (Q or S - s) on the order variance amplification ratio. It is commonly accepted in the supply chain literature that batching of orders creates a bullwhip effect. Our analysis shows that the answer is more subtle. For instance, the squared coefficient of variation (scv) of time between subsequent orders is smaller than or equal to the scv of time between subsequent demand arrivals for both policies. The order quantities can exhibit either variance amplication or dampening, compared to the demand quantities, depending on the distribution of the demand sizes and the value of the batching parameter. The bullwhip ratio, defined as the variance of the number of units ordered compared to the variance of the number of units demanded, strongly depends on the time window in which these numbers are observed. Our methodology is based on the properties of the batch-Markovian arrival process.

Keywords: Inventory policy, Batching, Bullwhip effect, Stochastic processes

Suggested Citation

Noblesse, Ann and Boute, Robert N. and Lambrecht, Marc and Van Houdt, Benny, Characterizing Order Processes of (s,S) and (r,nQ) Policies (April 18, 2013). KU Leuven - Faculty of Economics and Business Working Paper No. KBI_1309. Available at SSRN: https://ssrn.com/abstract=2273532 or http://dx.doi.org/10.2139/ssrn.2273532

Ann Noblesse (Contact Author)

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

Robert N. Boute

Vlerick Leuven Gent Management School ( email )

Library
REEP 1
Gent, BE-9000
Belgium

Marc Lambrecht

KU Leuven, Research Center for Operations Management, Faculty of Economics and Business ( email )

Leuven, B-3000
Belgium

Benny Van Houdt

University of Antwerp ( email )

Prinsstraat 13
Antwerp, Antwerp 2000
Belgium

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