Simple assembly line balancing problem type 1 is the most studied assembly line problem and many procedures have been proposed to solve it. Ho and Emrouznejad proposed to add a novel set of constrains into a binary integer‐programming model that is useful for breaking symmetries between equivalent solutions. The purpose of this paper is to compare this way of breaking symmetries with the usual ones existing in the literature (by means of the objective function and by means of additional constraints) and propose two novel ways of breaking symmetries which improve the existing ones.
For the comparison, the authors solve the well‐known benchmark instances.
It was found that the most efficient model is one of the new models which has not been proposed in the literature to date. Moreover, the authors noticed that Ho and Emrouznejad attribute a mathematical model to Patterson and Albracht that is different from the original model proposed by Patterson and Albracht.
There is not, in the literature, a comparison between classical and new mathematical models. The authors give an empirical comparison between them, together with two new ones that the authors propose. Moreover, the authors point out the mistake about the attribution model in Ho and Emrouznejad's, work attributing a mathematical model to Patterson and Albracht, with the aim of preventing its possible propagation in future researches.
Pastor, R., García‐Villoria, A. and Corominas, A. (2011), "Comparing ways of breaking symmetries in mathematical models for SALBP‐1", Assembly Automation, Vol. 31 No. 4, pp. 385-387. https://doi.org/10.1108/01445151111172970
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