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<p>The last-mile delivery problem is often related to the capacitated vehicle routing problem (CVRP) in literature. It is found in practice that experienced drivers usually find better routes than those relying solely on the in-house computerized tools. This study aims to incorporate drivers’ experience into the decision process by applying data mining techniques from historical data. Thus, the decision-making process can be kept uniform for drivers with different levels of experience. A bi-objective integer programming model is formulated to simultaneously minimize the cost and maximize the reuse of drivers’ experience. A branch-and-price (B&amp;P) algorithm with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> </InlineEquation>-constraint is proposed to solve the bi-objective model. Thus, a set of Pareto solutions with different tendencies is obtained. Experimental study demonstrates that solutions obtained from the B&amp;P algorithm achieve a good trade-off between the two objectives. Sensitivity analyses provide valuable insights for decision makers.</p>

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A branch-and-price algorithm for the last-mile delivery problem considering drivers’ experience

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Zhe Li,
  • Lu Chen,
  • Xiaoni Li

摘要

The last-mile delivery problem is often related to the capacitated vehicle routing problem (CVRP) in literature. It is found in practice that experienced drivers usually find better routes than those relying solely on the in-house computerized tools. This study aims to incorporate drivers’ experience into the decision process by applying data mining techniques from historical data. Thus, the decision-making process can be kept uniform for drivers with different levels of experience. A bi-objective integer programming model is formulated to simultaneously minimize the cost and maximize the reuse of drivers’ experience. A branch-and-price (B&P) algorithm with \(\varepsilon \) -constraint is proposed to solve the bi-objective model. Thus, a set of Pareto solutions with different tendencies is obtained. Experimental study demonstrates that solutions obtained from the B&P algorithm achieve a good trade-off between the two objectives. Sensitivity analyses provide valuable insights for decision makers.