Estimating the benefits of considering travel time variability in urban distribution

Abstract

Urban distribution systems typically require carriers to deliver goods to receivers within specified time windows. This paper presents procedures that allow the variable nature of travel times to be incorporated within optimization methods for the vehicle routing problem with time windows. Expressions are presented for determining the penalty costs associated with truck arrivals at customer locations with time windows when the travel times between customers are normally distributed. Formulations of this problem using stochastic programming and robust optimization (RO) are presented. Stochastic programming procedures require numerical integration techniques to be used and thus are computation..