The Online Transportation Problem: Competitive Scheduling of Elevators
Norbert Ascheuer, Sven Oliver Krumke, Jörg Rambau · 1998
In this paper we consider the following online transportation problem (OLTP): Objects are to be transported between the vertices of a given graph. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and target vertex. These requests are to be handled by a server which commences its work at a designated origin vertex and which picks up and drops objects at their starts and destinations. After the end of its service the server returns to its start. The goal of OLTP is to come up with a transportation schedule for the server which finishes as early as possible. We first show a lower bound of 5/3 for the competitive ratio of any deterministic algorithm. We then analyze two simple and natural strategies which we call Replan and Ignore. Replan completely discards its schedule and recomputes a new one when a new request arrives. Ignore always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, Replan and Ignore, are 5/2-competitive. We also present a somewhat less natural strategy Sleep which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. We also establish a competitive ratio of 5/2 for the algorithm Sleep. Our results are extended to the case of “open schedules ” where the server is not required to return to its start position at the end of its service.