Speed-Aware Network Design: A Parametric Optimization Approach

TL;DR

This paper introduces a parametric optimization method for network design that balances routing costs and delivery speed, using a novel speed-coverage concept to improve efficiency in transportation and communication networks.

Contribution

It develops a mixed-integer linear programming model for speed-coverage optimization and proposes a sampling strategy to handle complex inventory coverage evaluations.

Findings

Outperforms baseline by 8.36% on average in numerical tests.

Effectively balances routing costs and delivery speed.

Provides a scalable approach for complex network design problems.

Abstract

Network design problems have been studied from the 1950s, as they can be used in a wide range of real-world applications, e.g., design of communication and transportation networks. In classical network design problems, the objective is to minimize the cost of routing the demand flow through a graph. In this paper, we introduce a generalized version of such a problem, where the objective is to tradeoff routing costs and delivery speed; we introduce the concept of speed-coverage, which is defined as the number of unique items that can be sent to destinations in less than 1-day. Speed-coverage is a function of both the network design and the inventory stored at origin nodes, e.g., an item can be delivered in 1-day if it is in-stock at an origin that can reach a destination within 24 hours. Modeling inventory is inherently complex, since inventory coverage is described by an integer function with a large number of points (exponential to the number of origin sites), each one to be evaluated using historical data. To bypass this complexity, we first leverage a parametric optimization approach, which converts the non-linear joint routing and speed-coverage optimization problem into an equivalent mixed-integer linear program. Then, we propose a sampling strategy to avoid evaluating all the points of the speed-coverage function. The proposed method is evaluated on a series of numerical tests with representative scenarios and network sizes. We show that when considering the routing costs and monetary gains resulting from speed-coverage, our approach outperforms the baseline by 8.36% on average.