For this problem, we propose a 0–1 mixed integer programming model, in which we simultaneously consider “forward” and “reverse” flows and their mutual interactions. An algorithm based on Lagrangian heuristics is developed and the model is tested on data adapted from classical test problems. These academic papers are available to purchase through Sciencedirect.com, usually at US$30 each. To do this, it is necessary to register via the weblink given.

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