2017/11/28 by Alper Atamtürk, Atamturk, Alper, Oktay Günlük +1
Business, Management and Accounting · Engineering · Social Sciences · #Advanced Optical Network Technologies #FOS: Mathematics #Facility Location and Emergency Management #Optimization and Control (math.OC) #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1711.10147
openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In network design problems capacity constraints are modeled in three different ways depending on the application and the underlying technology for installing capacity: directed, bidirected, and undirected. In the literature, polyhedral investigations for strengthening mixed-integer formulations are done separately for each model. In this paper, we examine the relationship between these models to provide a unifying approach and show that one can indeed translate valid inequalities from one to the others. In particular, we show that the projections of the undirected and bidirected models onto the capacity variables are the same. We demonstrate that valid inequalities previously given for the undirected and bidirected models can be derived as a consequence of the relationship between these models and the directed model.