A Price-Directed Approach to Stochastic Inventory/Routing

We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value func...

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Bibliographic Details
Published in:Operations research Vol. 52; no. 4; pp. 499 - 514
Main Author: Adelman, Daniel
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.07.2004
Institute for Operations Research and the Management Sciences
Subjects:
Approximation
Cost allocation
Cost efficiency
discounted infinite-horizon
Dynamic programming
dynamic programming/optimal control
Gases industry
Influence
Inventories
Inventory control
inventory routing
inventory/production
Linear programming
Manufacturing
Markov processes
Methods
Minimization of cost
multi-item
Optimization
Prices
Pruning
separable functional approximations
stochastic
Stochastic models
Studies
Supply chains
Technology application
transportation
Transportation costs
Vehicles
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value function with the sum of single-customer inventory value functions. The resulting approximation yields statewise lower bounds on optimal infinite-horizon discounted costs. We present a linear program that takes into account inventory dynamics and economics in allocating transportation costs for stochastic inventory routing. On test instances we find that these allocations do not introduce any error in the value function approximations relative to the best approximations that can be achieved without them. Also, unlike other approaches, we do not restrict the set of allowable vehicle itineraries in any way. Instead, we develop an efficient algorithm to both generate and eliminate itineraries during solution of the linear programs and control policy. In simulation experiments, the price-directed policy outperforms other policies from the literature.
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1040.0114