Considering that the time of meeting the demands is very important for emergency vehicle and emergency vehicle can’t reject any request, we introduce a more realistic cost form into online traveling salesman problem(OL-TSP). When a new request arrives, if the salesman can’t serve the request immediately, per-unit-time cost will be generated. The goal is to minimize server’s total costs(travel makespan plus the per-unit-time costs). We consider the server is a non-zealous server and show that neither deterministic nor randomized online algorithms can achieve constant competitive ratio for OL-TSP on general metric space. While on truncated line segment and uniform metric space, we prove lower bounds, and present competitive online algorithms. Especially for the case with uniform metric space, we prove an optimal Greedy algorithm.

考虑到满足需求的时间对于紧急车辆非常重要，并且紧急车辆不能拒绝任何请求，因此我们在在线旅行推销员问题（OL-TSP）中引入了一种更现实的成本形式。当一个新的请求到达时，如果推销员不能立即满足该请求，则将产生每单位时间的成本。目的是最大程度地减少服务器的总成本（旅行量和每单位时间成本）。我们认为服务器是非热心服务器，并且表明确定性或随机在线算法都无法在通用度量空间上实现OL-TSP的恒定竞争率。在截断的线段和统一的度量空间上，我们证明了下界，并提出了具有竞争力的在线算法。特别是对于度量空间均匀的情况，我们证明了一种最优的贪婪算法。