Approximating Weighted Completion Time for Order Scheduling with Setup Times

Abstract

Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing of operations of different families. A job is completed when its latest operation completes and the goal is to minimize the total weighted completion time of all jobs.We study this problem from the perspective of approximability and provide constant factor approximations as well as an inapproximability result. Prior to this work, only the NP-hardness of the unweighted case and the polynomial solvability of a certain special case were known.

Optimization of cargo delivery volumes by road carries in the system of providing transport services

“…There is also time spent on simple vehicle at the points of departure and destination of cargo a s i.j, which arise as a result of non-coordination of operations during the execution of the transport process. Time delays a s i.j arise because the allowed time limits of orders i,j may not coincide and due to the irregularity of the process [5][6][7][8].…”

“…Limitation (6) means that the number of outgoing trucks flows from the formal start of the ITP does not exceed the predetermined value Rz. The same number of vehicles flows should be included in the formal completion of the ITP, which is evidenced by constraint (7).…”

“…Interaction of enterprises operating in the market of transport services with different methods of interaction is considered by scientists as horizontal cooperation, if it involves the cooperation of subjects in the same supply chains [4][5][6][7][8]. The term "logistics cooperation" suggests considering mechanisms of joint decision-making, in which a group of participants jointly makes decisions that are optimal from the point of view of the entire group [9].…”