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Routing Two-Machine Flowshop Problems on Networks with Special Structure

The authors consider a version of the routing two-machine flowshop problem, where n jobs located at different nodes of a transportation network must be executed by two machines traveling between the jobs. Each job must be processed by both machines in the order, machine 1 first, machine 2 second. The goal is to minimize the makespan given that the total distance traveled must be as small as possible. Properties of the problem are discussed, and algorithms with complexity O (n log n) are developed for the problem on trees and cactuses.