@TECHREPORT{DrexlIrnich2012_1,
author = {Michael Drexl and Stefan Irnich},
title = {Solving Elementary Shortest-Path Problems as Mixed-Integer Programs},
institution = {Chair of Logistics Management, Gutenberg School of Management and Economics,
Johannes Gutenberg University Mainz},
address = {Mainz, Germany},
year = {2012},
number = {LM-2012-01},
abstract = {Ibrahim, Maculan, and Minoux (International Transactions in Operational Research,
vol. 16, 2009, pp. 361--369) 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
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 commodity flow
formulation.},
keyword = {Elementary shortest-path problem, Negative cycles, Mixed-integer programming},
}