In this study, we introduce the Traveling Car Renter with Passengers (CaRSP), an extension of the Traveling Car Renter Problem (CaRS). The latter generalizes the Traveling Salesman Problem (TSP) by allowing several cars with different costs to be available for use during the salesman’s tour. In the CaRSP, passengers are allowed in the salesman’s car and share trip expenses with the driver. Passengers have different pick-up and drop-off points and share the costs of the part of the trip in which they are in the vehicle. We present two mixed integer programming formulations for the CaRSP. The first model is based on the Dantzig-Fulkerson-Johnson formulation for the TSP and the second on the Miller–Tucker–Zemlin formulation. The formulations are linearized regarding two different techniques, resulting in four linear models. One of those linearization techniques is proposed in this study. We present the results of an experiment in which 54 instances are submitted to two optimization solvers, concerning the four linear models introduced.

在这项研究中，我们介绍了“带乘客乘车租赁人”（CaRSP），它是“乘车租赁人问题”（CaRS）的扩展。后者通过允许在销售员的旅行期间使用具有不同成本的几辆汽车来推广旅行业务员问题（TSP）。在CaRSP中，允许乘客乘坐推销员的汽车，并与驾驶员分担旅行费用。乘客有不同的接送点，并分担他们在车辆中旅行的那部分费用。我们为CaRSP提出两种混合整数规划公式。第一个模型基于用于TSP的Dantzig-Fulkerson-Johnson公式第二种是关于Miller-Tucker-Zemlin公式的。关于两种不同的技术，对配方进行了线性化，从而得到了四个线性模型。这项研究中提出了一种线性化技术。我们介绍了一个实验的结果，其中将54个实例提交给两个优化求解器，涉及引入的四个线性模型。