We study a target-oriented, multi-period location–transportation problem where customer demands are uncertain. This problem is to determine the facility locations, production quantities, capacities, and shipment quantities, where the objective is to achieve the desired profit and fill rate to the full extent when it is impossible to reach both. To achieve the goal, we propose a target-oriented framework for the location–transportation problem, where a service-level measure is constructed to guarantee the desired fill rate and a hard constraint on profit is imposed to ensure a decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization approach. To capture the characteristics of a multi-period decision-making process, an affine decision rule is introduced. Our method not only ensures that the transportation decisions of each period can adapt to realized demands wisely, but also prevents the high complexity of the model resulting from uncertainty and adaptation. Specifically, to tackle challenges of problem intractability, we reformulate the robust counterpart of the problem into a conservative approximation in the form of a mixed-integer quadratic program and propose a Benders decomposition approach to produce effective solutions. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.

我们研究了一个以目标为导向的、多周期的位置交通问题，其中客户需求是不确定的。这个问题是确定设施位置、生产数量、产能和装运数量，其中的目标是在不可能达到两者时最大程度地实现所需的利润和填充率。为了实现这一目标，我们为位置-交通问题提出了一个面向目标的框架，其中构建了服务水平度量以保证所需的填充率，并对利润施加硬约束以确保获得可观的利润。该框架摆脱了在多目标优化方法中估计不同目标的权重所产生的问题。为了捕捉多周期决策过程的特征，引入了仿射决策规则。我们的方法不仅确保了每个时期的交通决策能够明智地适应已实现的需求，而且还防止了由于不确定性和适应性而导致模型的高度复杂性。具体来说，为了解决问题难以处理的挑战，我们将问题的稳健对应物重新表述为混合整数二次规划形式的保守近似，并提出了一种 Benders 分解方法来产生有效的解决方案。最后，通过基于真实实例的计算实验评估面向目标框架的性能。为了解决问题难以处理的挑战，我们将问题的稳健对应物重新表述为混合整数二次规划形式的保守近似，并提出了一种 Benders 分解方法来产生有效的解决方案。最后，通过基于真实实例的计算实验评估面向目标框架的性能。为了解决问题难以处理的挑战，我们将问题的稳健对应物重新表述为混合整数二次规划形式的保守近似，并提出了一种 Benders 分解方法来产生有效的解决方案。最后，通过基于真实实例的计算实验评估面向目标框架的性能。