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Price-directed replenishment of subsets: Methodology and its application to inventory routing

By Daniel Adelman

Abstract

The idea of price-directed control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of industrial gases, so as to minimize long-run time average replenishment costs.Given a marginal value for each product/location, whenever there is a stockout the dispatcher compares the total value of each feasible replenishment with its cost, and chooses one that maximizes the surplus.We derive this operating policy using a linear functional approximation to the optimal value function of a semi-Markov decision process on continuous spaces.This approximation also leads to a math program whose optimal dual prices yield values and whose optimal objective value gives a lower bound on system performance.We use duality theory to show that optimal prices satisfy several structural properties and can be interpreted as estimates of lowest achievable marginal costs.On real-world instances, the price-directed policy achieves superior, near optimal performance as compared with other approaches

Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.2585
Provided by: CiteSeerX
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