Summary: 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 (\(1+\theta)\cdot k/(\theta\cdot k+2)\) for the on-line \(k\)-truck problem is given, where \(\theta\) 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 W. Ma, Y. Xu and K. Wang [J. Glob. Optim. 21, 15–25 (2001; Zbl 1067.90048)] for general cases are obtained. For example, a \(c\)-competitive or (\(c/\theta +1/\theta +1\))-competitive algorithm for the on-line \(k\)-truck problem depending on the value of \(\theta\) , 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 (\(1+(n-k)/\theta\))-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.