Vehicle Routing Problem (VRP) is a classic combinatorial optimization problem. In urban last-mile delivery scenarios, this paper investigates the Multi-Trip Vehicle Routing Problem with Soft Time Windows and Delay Penalty (MTVRPSTW). Here, each vehicle can make multiple trips to serve customers before the depot closes. In practical logistics, companies often use overtime compensation to address delivery delays. Therefore, in this problem, if a customer receives service after the time window ends, a delay cost is incurred. MTVRPSTW aims to minimize vehicle usage costs, travel distance costs, and delay penalty costs. An Adaptive Large Neighborhood Search (ALNS) algorithm based on sequential insertion is designed. The effectiveness of the model and algorithm is verified through comparative analysis of solution results.
With the aim of mitigating workload imbalance among workers, this paper optimizes multi-skilled worker and task assignments with the consideration of lot-splitting. A mixed-integer nonlinear programming model is proposed to minimize the maximum workload of workers. To verify the effectiveness of the proposed model, the model without lot-splitting is used for comparison. These models can be linearized and solved by optimization solver CPLEX. Computational experiments show that our fairness-oriented model has better performance on mitigating the workload imbalance while maintaining high production efficiency.
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