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We address a novel ride-sharing model aiming to improve the quality of carpool services, by means of incorporation of passengers' efforts. In densely populated areas, locating and picking up passengers are often time costly. These phenomena, which are rarely considered in literature, will hurdle the service efficiency of ride-sharing businesses by a significant amount, and contribute to the performance gap between theoretical estimation and practical performance. We notice that major platforms, such as DiDi, Uber, and Lyft are all starting innovative ways to encourage passengers to take efforts to walk to the assigned stations. We present a static optimization model for the planning stage of the service and establish an estimation of the carpooling rate for each station together with robustness consideration. In addition, we provide simple and efficient optimization algorithms with theoretical performance guarantee. At the same time, we conduct simulation studies based on both random generated data and open accessible data from DiDi. By applying our model and algorithm to the data of DiDi, we can achieve carpooling rates of 90% while passengers are located within an average radius of 250 m spending an extra waiting time of less than 3 min for their shared rides during rush hour.

In this paper, we consider scheduling of deteriorating jobs on a single machine with slack (SLK) due date assignment, resource allocation, and a rate‐modifying activity. The rate‐modifying activity can change jobs’ processing rates such that the actual processing time of a job depends on whether the job is processed before or after the rate‐modifying activity. In addition, the actual processing time of a job also depends on its position in a processing sequence (i.e., the aging effect) and the amount of resource allocated to it. The objective is to determine the optimal sequence, optimal common flow allowance, optimal resource allocation, and optimal location of the rate‐modifying activity to minimize a total penalty function comprising the earliness, tardiness, common flow allowance, and resource allocation costs. We consider two variants of the problem associated with two different processing time functions and provide a polynomial‐time algorithm to solve each variant.

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