Modeling vehicle routing with uncertain demands as a stochastic program

Properties of the corresponding solution

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.

Original languageEnglish (US)
Pages (from-to)432-441
Number of pages10
JournalEuropean Journal of Operational Research
Volume64
Issue number3
DOIs
StatePublished - Feb 5 1993
Externally publishedYes

Fingerprint

Vehicle Routing
Vehicle routing
Vehicle Routing Problem
Modeling
Multi-state Model
Hamiltonians
Graph Representation
Hamiltonian circuit
Decision Model
Stochastic models
Markov Model
Stochastic Model
Optimal Solution
Vehicle routing problem
Uncertain demand
Mathematical Model
Mathematical models
decision model
Vertex of a graph

Keywords

  • Routing
  • Stochastic programming

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation
  • Information Systems and Management

Cite this

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title = "Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution",
abstract = "In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.",
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AB - In this paper we address the issue of different mathematical models for the stochastic vehicle routing problem (SVRP). This problem is inherently much more difficult than the generic deterministic vehicle routing problem (VRP) for which optimal procedures can solve only small problems. Presently, we cannot even begin optimal solution procedures for the SVRP for any problem size exceeding 3 nodes. Thus, we need to examine modeling approaches to this problem in order to exploit the structure and solution properties. We present a multistate stochastic model for the SVRP. We prove that this model has an interesting minimal graph representation in which a SVRP solution corresponds to a Hamiltonian cycle. We also present a Markov decision model for the problem, concluding with a discussion of solution prospects and directions.

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