ON THE k-TRUCK SCHEDULING PROBLEM
Abstract
In this paper, some results concerning the k-truck problem are produced. Firstly, the algorithms and their complexity concerning the off-line k-truck problem are discussed. Following that, a lower bound of competitive ratio (1+θ)·k/(θ·k+2) for the on-line k-truck problem is given, where θ is the ratio of cost of the loaded truck and the empty truck on the same distance, and a relevant lower bound for the on-line k-taxi problem followed naturally. Thirdly, based on the Position Maintaining Strategy (PMS), some new results which are slightly better than those of [11] for general cases are obtained. For example, a c-competitive or (c/θ+1/θ+1)-competitive algorithm for the on-line k-truck problem depending on the value of θ, where c is the competitive ratio of some algorithm to a relevant k-server problem, is developed. The Partial-Greedy Algorithm (PG) is used as well to solve this problem on a line with n nodes and is proved to be a (1+(n-k)/θ)-competitive algorithm for this case. Finally, the concepts of the on-line k-truck problem are extended to obtain a new variant: Deeper On-line k-Truck Problem (DTP). We claim that results of PMS for the STP (Standard Truck Problem) hold for the DTP.
The authors would like to acknowledge the support of Central Research Grant GV-975 of the Hong Kong Polytechnic University and Research Grant from NSF of China. No.19731001.
