Shortest Route Problems

Abstract

Shortest routes (paths or chains) are of fundamental importance in network and combinatorial optimisation problems, both in their own right and as sub-problems of other optimisation problems. Shortest route problems have obvious relevance when a shortest (or quickest or least cost) route is required between two points of a transportation system. Similar problems arise when it is required to find a maximal flow or least cost flow augmenting chain (chapters 9 and 10) or a maximum reliability or maximum capacity route between two points.(For the latter two problems the objective function is not additive but of the forms given in exercise 2.7 parts (a) and (c) respectively.) Shortest paths between two vertices of a special network are sought in knapsack problems (section 2.4) and in the inspection and assembly line balancing problems discussed below (section 4.1 and exercise 4.2).