Constrained shortest path with uncertain transit times

Abstract

This paper is concerned with the constrained shortest path (CSP) problem, where in addition to the arc cost, a transit time is associated to each arc. The presence of uncertainty in transit times is a critical issue in a wide variety of world applications, such as telecommunication, traffic, and transportation. To capture this issue, we present tractable approaches for solving the CSP problem with uncertain transit times from the viewpoint of robust and stochastic optimization. To study robust CSP problem, two different uncertainty sets, $${\varGamma }$$Γ-scenario and ellipsoidal, are considered. We show that the robust counterpart of the CSP problem under both uncertainty sets, can be efficiently solved. We further consider the CSP problem with random transit times and show that the problem can be solved by solving robust constrained shortest path problem under ellipsoidal uncertainty set. We present extensive computational results on a set of randomly generated networks. Our results demonstrate that with a reasonable extra cost, the robust optimal path preserves feasibility, in almost all scenarios under $${\varGamma }$$Γ-scenario uncertainty set. The results also show that, in the most cases, the robust CSP problem under ellipsoidal uncertainty set is feasible.