1964/10/01 by Paul C. Gilmore, Ralph E. Gomory · 2 citations
Engineering · Computer Science · Mathematics · #Scheduling and Optimization Algorithms #Optimization and Search Problems #Computability, Logic, AI Algorithms #Travelling salesman problem #Bottleneck #Bottleneck traveling salesman problem #Mathematical optimization #2-opt #State (computer science) #Computer science #Hamiltonian path #Sequence (biology) #Variable (mathematics) #Mathematics #State variable #Traveling purchaser problem #Combinatorics #Algorithm #Graph
paper · doi:10.1287/opre.12.5.655
openalex publication_date 1964/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
We consider a machine with a single real variable x that describes its state. Jobs J 1 , …, J N are to be sequenced on the machine. Each job requires a starting state A, and leaves a final state B i . This means that J i can be started only when x = A i and, at the completion of the job, x = B i . There is a cost, which may represent time or money, etc., for changing the machine state x so that the next job may start. The problem is to find the minimal cost sequence for the N jobs. This problem is a special case of the traveling salesman problem. We give a solution requiring only 0(N 2 ) simple steps. A solution is also provided for the bottleneck form of this traveling salesman problem under special cost assumptions. This solution permits a characterization of those directed graphs of a special class which possess Hamiltonian circuits.