The vehicle routing problem
Traveling Salesman Problems with Profits
Transportation Science
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
Mathematical Programming: Series A and B
The Shortest-Path Problem with Resource Constraints and k-Cycle Elimination for k ≥ 3
INFORMS Journal on Computing
Models for Evaluating and Planning City Logistics Systems
Transportation Science
Accelerated label setting algorithms for the elementary resource constrained shortest path problem
Operations Research Letters
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Ibrahim et al. (Int Trans Oper Res 16:361---369, 2009) presented and analyzed two integer programming formulations for the elementary shortest-path problem (ESPP), which is known to be NP-hard if the underlying digraph contains negative cycles. In fact, the authors showed that a formulation based on multi-commodity flows possesses a significantly stronger LP relaxation than a formulation based on arc flow variables. Since the ESPP is essentially an integer problem, the contribution of our paper lies in extending this research by comparing the formulations with regard to the computation time and memory requirements required for their integer solution. Moreover, we assess the quality of the lower bounds provided by an integer relaxation of the multi-commodity flow formulation.