Substitution-based equipment balancing in service networks with multiple equipment types

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.