In this paper, a coordinated production scheduling and vehicle routing problem aiming at minimizing the sum of order delivery times is considered, where there are a single machine for production and limited number of homogenous capacitated vehicles for transportation. Given the complexity of the studied problem, a variable neighborhood search (VNS) algorithm is proposed to address this problem. To construct initial solution, vehicle routing is determined with nearest insertion first, whereby the order batch production sequence is determined based on three propositions. Moreover, ten neighborhood structures are designed and a local search algorithm based on tabu search algorithm is proposed for intensification. The effectiveness of the proposed VNS algorithm is validated by comparing it with CPLEX and two heuristic algorithms in the existing literature. The computational results show that the proposed VNS algorithm can obtain optimal or near optimal solutions of the problem and is superior to the two heuristic algorithms proposed in the existing literature.

中文翻译：

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最小化订单交付时间总和的协调生产和运输计划问题

在本文中，考虑了旨在使订单交货时间总和最小化的协调生产调度和车辆路径问题，其中只有一台用于生产的机器和数量有限的用于运输的均质能力车辆。鉴于所研究问题的复杂性，提出了一种可变邻域搜索（VNS）算法来解决该问题。要构建初始解决方案，首先确定车辆路线并最接近插入，然后基于三个命题确定订单批生产顺序。此外，设计了十个邻域结构，并提出了基于禁忌搜索算法的局部搜索算法进行强化。通过将其与CPLEX和现有文献中的两种启发式算法进行比较，验证了所提出的VNS算法的有效性。计算结果表明，所提出的VNS算法能够获得问题的最优解或接近最优解，并且优于现有文献中提出的两种启发式算法。