Routing and scheduling on a shoreline with release times
Management Science
Twenty years of routing and scheduling
Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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In this paper, we study a problem of finding a vehicle scheduling to process a set of n jobs which are located in an asymmetric metric space. Each job j has a positive handling time h(j), a time window [r(j),d(j)], and a benefit b(j). We consider the following two problems: MAX-VSP asks to find a schedule for a single vehicle to process a subset of jobs with the maximum benefit; and MIN-VSP asks to find a schedule to process all given jobs with the minimum number of vehicles. We first give an O(@rn^3^+^@c) time algorithm that delivers a 2-approximate solution to MAX-VSP, where @r=max"j","j"^"'(d(j)-r(j))/h(j^') and @c is the maximum number of jobs that can be processed by the vehicle after processing a job j and before visiting the processed job j again by deadline d(j). We then present an O(@rn^4^+^@c) time algorithm that delivers a 2H(n)-approximate solution to MIN-VSP, where H(n) is the nth harmonic number.