Abstract This paper studies a generalization of the shortest path tour problem with time windows ( GSPTPTW ). The aim is to find single-origin single-destination path, which has pass through an ordered sequence not necessarily disjoint node-subsets. Each node window for each node-subset it belongs. We investigate theoretical properties and propose dynamic programming approach solve it. Numerica...

In this study we consider the shortest path problem, where arc costs are subject to distributional uncertainty. Basically, decision-maker attempts minimize her worst-case expected loss over an ambiguity set (or a family) of candidate distributions that consistent with decision-maker’s initial information. The is formed by all satisfy prescribed linear first-order moment constraints respect subs...

In real-world optimization problems, effective path planning is important. The Shortest Path Problem (SPP) model a classical operations research that can be applied to determine an efficient from the starting point end in plan. However, real world, uncertainty often encountered and must faced. Significant factors problem of determining shortest are problems difficult predict, therefore new crit...

A theorem of Hardy, Littlewood, and Polya, first time is used to find the variational form of the well known shortest path problem, and as a consequence of that theorem, one can find the shortest path problem via quadratic programming. In this paper, we use measure theory to solve this problem. The shortest path problem can be written as an optimal control problem. Then the resulting distribute...

In this paper it is shown that the core and the bargaining sets of DavisMaschler and Zhou coincide in a class of shortest path games