This study focuses on the robust partitioned distribution problem with courier learning and demand uncertainty. The research is divided into tactical (customer point zoning) and operational (courier route planning within zones) stages, for which mathematical models are established. Nonlinear learning curves are linearized via piecewise methods, and the robust partitioned distribution model for demand uncertainty is converted into a robust linear model. An improved adaptive large neighborhood search algorithm is designed; on 13 standard capacitated vehicle routing problem (CVRP) benchmarks, it achieves a 1.72% average gap to the best-known solutions and the best or tied-best gap on 12 of them, outperforming the genetic algorithm, tabu search, and general adaptive large neighborhood search (ALNS) comparators. Its effectiveness is further verified through extensive numerical experiments. First, considering couriers' learning effects reduces the total costs and concentrates route coverage. Second, the benefit of robust solutions is instance-dependent: They reduce overload costs under demand fluctuations in some cases, while excessively large uncertainty parameters lead to conservative, cost-increasing outcomes. Experimental results on real enterprise data clearly validate the superiority of the proposed model and algorithm over existing approaches.
Citation: Chi Zhang, Xue Bai, Guojun Sheng, Zhili Zhou. The robust partitioned distribution problem with courier learning and demand uncertainty[J]. Journal of Industrial and Management Optimization, 2026, 22(11): 5961-6002. doi: 10.3934/jimo.2026201
This study focuses on the robust partitioned distribution problem with courier learning and demand uncertainty. The research is divided into tactical (customer point zoning) and operational (courier route planning within zones) stages, for which mathematical models are established. Nonlinear learning curves are linearized via piecewise methods, and the robust partitioned distribution model for demand uncertainty is converted into a robust linear model. An improved adaptive large neighborhood search algorithm is designed; on 13 standard capacitated vehicle routing problem (CVRP) benchmarks, it achieves a 1.72% average gap to the best-known solutions and the best or tied-best gap on 12 of them, outperforming the genetic algorithm, tabu search, and general adaptive large neighborhood search (ALNS) comparators. Its effectiveness is further verified through extensive numerical experiments. First, considering couriers' learning effects reduces the total costs and concentrates route coverage. Second, the benefit of robust solutions is instance-dependent: They reduce overload costs under demand fluctuations in some cases, while excessively large uncertainty parameters lead to conservative, cost-increasing outcomes. Experimental results on real enterprise data clearly validate the superiority of the proposed model and algorithm over existing approaches.
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Chi Zhang, Xue Bai, Guojun Sheng, Zhili Zhou. The robust partitioned distribution problem with courier learning and demand uncertainty[J]. Journal of Industrial and Management Optimization, 2026, 22(11): 5961-6002. doi: 10.3934/jimo.2026201
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