A Network-Sensitive Reference Policy for Non-Myopic Sequential Network Design and Timing Problems

Availability of real time “Big data” in recent years has driven an increasing interest in dynamic/real-time/online/sequential network design models. Despite a growing number of studies in stochastic dynamic network optimization, the field remains less well defined and unified than other areas of network optimization. Due to the need for approximation methods like approximate dynamic programming, one of the most significant problems yet to be solved is the lack of adequate benchmarks. Common benchmark policies are inadequate; the value of the perfect information policy does not include random effects while the static and myopic policies are not sensitive to value of anticipation due to network structure. The authors propose a new class of network-sensitive reference policies using extreme value distributions to estimate theoretically consistent real option values based on sampled sequences. The reference policy is shown to fit known sequence policies well (particularly Weibull), and has sampling consistency for more than 200 samples. It is applied to sequential versions of the discrete network design and timing problem on the Sioux Falls network, the facility location and timing problem on the Simchi-Levi and Berman (1988) network, and Hyytia et al.’s (2012) dial-a-ride problem.