An Auction Bidding Approach to Balance Performance Bonuses in Vehicle Routing Problems with Time Windows

Abstract

In the field of operations research, the vehicle routing problem with time windows (VRPTW) has been widely studied because it is extensively used in practical applications. Real-life situations discussed in the relevant research include time windows and vehicle capabilities. Among the constraints in a VRPTW, the practical consideration of the fairness of drivers’ performance bonuses has seldom been discussed in the literature. However, the shortest routes and balanced performance bonuses for all sales drivers are usually in conflict. To balance the bonuses awarded to all drivers, an auction bidding approach was developed to address this practical consideration. The fairness of performance bonuses was considered in the proposed mathematical model. The nearest urgent candidate heuristic used in the auction bidding approach determined the auction price of the sales drivers. The proposed algorithm both achieved a performance bonus balance and planned the shortest route for each driver. To evaluate the performance of the auction bidding approach, several test instances were generated based on VRPTW benchmark data instances. This study also involved sensitivity and scenario analyses to assess the effect of the algorithm’s parameters on the solutions. The results show that the proposed approach efficiently obtained the optimal routes and satisfied the practical concerns in the VRPTW.

Data-Driven Bus Route Optimization Algorithm Under Sudden Interruption of Public Transport

“…G. Srivastava [16] proposed a Genetic Algorithm II based on Non-dominant Sorting (NSGA-II), which designs crossover and mutation operators by using the characteristics of the problem and the attributes of each target. C. Chen Yang [17] proposed an auction bidding method to balance the performance bonus awarded to all drivers, which not only achieved the balance of performance bonus, but also planned the shortest route for each driver, making the strategy more reasonable. W. Jiahai [18] proposed a hybrid multi-objective Memetic Algorithm for solving multi-objective where a two-stage strategy is designed to improve the comprehensive performance of convergence and diversity, providing another idea for heuristic solution.…”

“…Objective function: Equation ( 7) defines the minimization objective, which is composed of bus operation cost and passenger traffic cost; Equation (8) represents the operating cost of public transport, including departure cost, running time cost and running distance cost; Equation ( 9) represents passenger traffic cost, including passenger travel cost and passenger waiting time. Constraints: Equation (10) indicates that the site can be accessed only once; Equation (11) indicates that the vehicle departs from the station and returns; Equation ( 12) specifies the minimum passenger capacity of each vehicle; Equation ( 13) assigns constraints to passengers; Equation ( 14) is the vehicle capacity constraint; Equation (15) ensures that the time of vehicle departure from the station is feasible; Equation ( 16) is expressed as a time window constraint; Equation (17) indicates that the vehicle departure time is the sum of the vehicle arrival time and the service time.…”