Online convoy movement problem with k blocked edges

In this paper, we propose a novel online variant of the convoy movement problem, termed the online convoy movement problem with k blocked edges. This problem includes up to k unrecoverable blocked edges, which are unknown in advance and are gradually revealed as convoys encounter them. The goal is to obtain conflict-free paths for convoys under the online scenario to minimize the total flow time for all convoys. The competitive ratio is used to evaluate the performance of online algorithms, which involves comparing their worst-case performance with the optimal offline solutions. We prove a lower bound of 2k|C|+1 for the competitive ratio of all deterministic online algorithms for the proposed problem, where |C| denotes the cardinality of the set of convoys C. Additionally, we develop five online algorithms: backtrack, simple backtrack, iterative local search, modified iterative local search, and iterative disjoint path. We prove that the competitive ratios of the backtrack and simple backtrack algorithms are 2k+1 and |C|·(4k+2), respectively. However, the internal logic of these two algorithms may render them impractical in real-world situations. Therefore, we utilize the three other algorithms to find practically feasible conflict-free paths. Computational experiments are conducted to evaluate these five online algorithms on real-world instances.