The Vehicle Routing Problem with Stochastic Demand and Duration Constraints

Authors:
Alan L. Erera;Juan C. Morales;Martin Savelsbergh
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;BNSF Railway, Fort Worth, Texas 76131;CSIRO Mathematics, Informatics, and Statistics, North Ryde, NSW 1670 Australia
Venue:
Transportation Science
Year:
2010

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Abstract

Time considerations have been largely ignored in the study of vehicle routing problems with stochastic demands, even though they are crucial in practice. We show that tour duration limits can effectively and efficiently be incorporated in solution approaches that build fixed, or a priori, tours for such problems. We do so by assuming that each tour must be duration feasible for all demand realizations, and determine the maximum duration of a given delivery tour by solving the optimization problem of an adversary. A computational study demonstrates the approach, and shows that enforcing tour duration limits impacts the structure of nearly-best solutions and may create the need for additional tours. However, for the instances considered, the price paid for robustness is small as the increase in total expected tour duration is modest.