Capacity balancing in service network design problems

We study the service network design problem for consolidation-based freight carriers in a multi-period setting. The common assumption in the literature states that the current capacity of freight carriers' assets is capable of handling all of the forecasted demand, however, we assume that there are certain times in which peak demand strictly exceeds the capacity. Thus, it is assumed that the carriers have three options: adding additional assets, dispersing demand through early or late delivery with a penalty, or outsourcing. We propose a modeling approach that jointly incorporates asset management and sizing, outsourcing (3PLs), and earliness/tardiness. Given a set of commodities to be delivered from origin terminals to destination terminals on a network over multiple periods, the objective is to minimize the overall operational costs by optimally selecting and scheduling the home fleet, selecting services from third parties, and routing the commodities on the designed service network. We propose an arc-based formulation for this problem and test its performance on randomly generated instances. We investigate the impact of flow patterns and bidirectional demand disparities on the interplay across fleet sizing, outsourcing, and early/tardy deliveries under optimal policies.