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Marcel Turkensteen

A vendor managed inventory model using continuous approximations for route length estimates and Markov chain modeling for cost estimates

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We consider a vendor that supplies a set of geographically dispersed retailers and that can monitor the inventory levels at the retailers. Such an arrangement is often called Vendor Managed Inventory (VMI). The dispatch of a vehicle is made to a fixed group of retailers. Normally, the inventory levels at the vendor’s warehouse and at the retailers are established by modeling the problem as a Joint Replenishment Problem (JRP). This fixed set-up cost ignores the differences in distances, number of retailers visited and vehicle load that may occur, in particular when these retailers are served on joint delivery trips.
This paper develops a more detailed specification of the transport costs than JRP models. In order to ensure that the complexity of the problem does not
become overwhelming, we assume that the retailers are identical and uniformly distributed across an area, which can either be a two-dimensional area or a one-dimensional line structure (corresponding to e.g. a major traffic artery).
The expected travel distances across a given number of retailers can now be estimated analytically, using results from the field of continuous approxim
ation for two-dimensional areas, or using our own approximation for one-dimensional ones. We choose to use a Markov chain approach to minimize transport and inventory model simultaneously. When the routes through the retailers are not fixed, such an approach would require a large number of states if we keep track of all the inventory positions of the retailers. Using our analytic approximations, we are able to obtain more accurate set-up costs than regular JRP approaches, most clearly when demand is infrequent. In addition, the etailed specification of our transport costs means that we can easily derive interesting properties of the resulting distribution set-up, such as the resulting average CO2 emissions.
TidsskriftInternational Journal of Production Economics
Sider (fra-til)120-132
StatusUdgivet - 2014

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