In the daily dispatching of urban deliveries, a delivery manager has to consider workload balance among the couriers to maintain workforce morale. We consider two types of workload: incentive workload, which relates to the delivery quantity and affects a courier’s income, and effort workload, which relates to the delivery time and affects a courier's health. Incentive workload has to be balanced over a long period of time (e.g., a week or a month) whereas effort workload has to be balanced over a short period of time (e.g., a shift or a day). We formulate a multi-period workload balancing problem under stochastic demand and dynamic daily dispatching as a Markov Decision Process. We propose a balanced penalty policy based on Cost Function Approximation and use a hybrid algorithm combining the modified nested partitions method and the KN++ procedure to search for the optimal policy parameters. A comprehensive numerical study demonstrates that the proposed balanced penalty policy outperforms four benchmark policies and establishes the impact of demand variation and manager preferences on workload balance.
Department of Industrial Engineering, Tsinghua University & H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. Current version: January 2021