Package express companies routinely operate multiple equipment types in their service networks. Nevertheless, the weekly schedule of movements used to transport packages through the network leads to changes in equipment inventory at the facility level, which will hinder their normal operations if it is not carefully taken care of. Traditional rebalancing seeks to move the equipment empty in the most cost efficient way. In contrast, we investigate a substitution-based equipment balancing which has been rarely considered. More specifically, we try to reduce this change, i.e., the equipment imbalance associated with the schedule of movements, by substituting the equipment types initially assigned to movements. Consequently, substantial unnecessary empty repositioning needed to restore balance can be avoided at the end. We conduct complexity analysis of the underlying optimization problems, i.e., finding the minimum imbalance of the network and minimizing the number of substitutions required to achieve the minimum network imbalance. In addition, we develop integer programming (IP) models and propose an efficient two-phase decomposition heuristic for solution. Furthermore, we perform a computational study using real-world instances to analyze the performance of the IP solution approach and assess the benefits of substitution-based equipment balancing.

包裹快递公司通常在其服务网络中运营多种设备类型。然而，用于通过网络运输包裹的每周移动时间表会导致设施级别的设备库存发生变化，如果不小心处理，这将阻碍其正常运营。传统的再平衡旨在以最具成本效益的方式将设备空置。相比之下，我们研究了一种很少考虑的基于替代的设备平衡。更具体地说，我们试图通过替换最初分配给运动的设备类型来减少这种变化，即与运动时间表相关的设备不平衡。因此，最终可以避免恢复平衡所需的大量不必要的空重定位。我们对底层优化问题进行复杂性分析，即找到网络的最小不平衡并最小化实现最小网络不平衡所需的替换次数。此外，我们开发了整数规划 (IP) 模型，并提出了一种有效的两阶段分解启发式解决方案。此外，我们使用真实世界的实例进行计算研究，以分析 IP 解决方案方法的性能并评估基于替代的设备平衡的好处。