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A 1.5Approximation for SingleVehicle Scheduling Problem on a Line with Release and Handling Times
 In JapanU.S.A. Symposium on Flexible Automation
, 1998
"... In this paper we consider a singlevehicle scheduling problem on a straight line. Let L = (V; E) be a line, where V = fv 1 ; v 2 ; . . . ; v n g is a set of n vertices and E = ffv i ; v i+1 g j i = 1; 2; . . . ; n 1g is a set of edges. The travel times d(u; v) and d(v; u) are associated with each e ..."
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In this paper we consider a singlevehicle scheduling problem on a straight line. Let L = (V; E) be a line, where V = fv 1 ; v 2 ; . . . ; v n g is a set of n vertices and E = ffv i ; v i+1 g j i = 1; 2; . . . ; n 1g is a set of edges. The travel times d(u; v) and d(v; u) are associated with each edge fu; vg 2 E, and a job, which is also denoted as v, is located at each vertex v 2 V . Each job v has release time r(v) and handling time h(v). There is a single vehicle, which is initially situated at one of the end vertices, without loss of generality say v 1 2 V , and visits all the jobs on L to process them before it returns back to v 1 . The processing of a job v cannot be started before its release time r(v) (hence the vehicle has to wait if it arrives at v before time r(v) for processing) and requires h(v) time units once it has been started (no preemption is allowed). It is known that the problem of minimizing the completion time is NPhard, and that there exists an approximate al...