# Service Network Design Problem with Capacity-Demand Balancing

## TL;DR

This paper develops a comprehensive model for service network design that balances capacity and demand fluctuations, incorporating asset management, outsourcing, and penalties, with efficient solution methods tested on various instances.

## Contribution

It introduces a joint modeling approach for capacity-demand balancing in service networks, including novel valid inequalities and a multi-phase heuristic algorithm.

## Key findings

- Valid inequalities improve solution times by 25%.
- The proposed algorithm effectively handles large instances.
- The model reduces operational costs by optimizing capacity and outsourcing.

## Abstract

This paper addresses developing cost-effective strategies to respond to excessive demand in the service network design problem in a multi-period setting. The common assumption states that the capacity of freight carriers' assets is capable of handling all of the forecasted demand; however, we assume that there are certain periods such as holiday season in which excessive demand is observed. The demand strictly exceeds the carrier's capacity; even though, the average demand can be still fulfilled throughout the year. In this sense, we let the carrier has three options to respond to the demand: Dispersing the demand with a penalty, leasing additional asset(s) temporarily, and outsourcing some capacity. We propose a modeling and solution approach that jointly incorporates asset management and sizing, outsourcing (3PLs), and earliness/tardiness penalties. The objective is to minimize the overall operational costs by optimally selecting and scheduling the home fleet with respect to 'demand shifting' choices, selecting services from third parties, and routing the commodities on the designed network. We propose an arc-based formulation as well as valid inequalities and present a comprehensive computational study on the randomly generated instances. The formulations with valid inequalities (VIs) outperform the regular formulation in obtaining tighter lower bounds. One set of VIs can improve the CPU time elapsed by 25% on medium-instances that can be solved optimally within the time limit. Furthermore, we develop a custom multi-phase dedicate-merge-and-mix algorithm (DMaM) to solve CSSND problem with an emphasis of obtaining solutions as high-quality as possible practically in a short time in the real world. DMaM has a promising potential to obtain solutions especially for very large instances whereas the commercial solver cannot initialize the B&B algorithm due to excessive memory usage.