This paper introduces and formulates a covering traveling salesman problem with profit arose in the last mile delivery. In this problem, a set of vertices including a central depot, customers and parcel lockers (PL) are given, and the goal is to construct a Hamiltonian cycle within a pre-defined cost over a subset of customers and/or PLs to collect maximum profits, each unvisited customer is covered by a PL in the cycle or outsourced. To solve the problem, a two-phase heuristic combined with a feasible solution construction procedure and an improvement procedure is proposed. The algorithm is evaluated on two sets of instances, and the computational results indicated its efficiency.

本文介绍并制定了最后一英里交付中产生利润的覆盖旅行商问题。在此问题中，给出了一组包括中央仓库，客户和包裹储物柜（PL）的顶点，目标是在预先定义的成本范围内构建一部分客户和/或PL的汉密尔顿周期，以收集最大的费用。利润，每个未访问的客户在周期中由PL覆盖或外包。为了解决该问题，提出了一种两阶段启发式算法，结合可行的构造方法和改进程序。该算法在两组实例上进行了评估，计算结果表明了该算法的有效性。