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@inproceedings{45267, author = {Bartl, David}, address = {Karviná}, booktitle = {The 3rd International Conference on Decision Making for Small and Medium-Sized Enterprises}, keywords = {homogeneous linear programming; strong duality theorem; failure mode and effects analysis}, howpublished = {tištěná verze "print"}, language = {eng}, location = {Karviná}, isbn = {978-80-7510-456-4}, pages = {61-70}, publisher = {Silesian University in Opava, School of Business Administration in Karviná}, title = {A Note on Homogeneous Linear Programming}, url = {https://www.researchgate.net/publication/353732455_A_Note_on_Homogeneous_Linear_Programming}, year = {2021} }
TY - JOUR ID - 45267 AU - Bartl, David PY - 2021 TI - A Note on Homogeneous Linear Programming PB - Silesian University in Opava, School of Business Administration in Karviná CY - Karviná SN - 9788075104564 KW - homogeneous linear programming KW - strong duality theorem KW - failure mode and effects analysis UR - https://www.researchgate.net/publication/353732455_A_Note_on_Homogeneous_Linear_Programming N2 - We consider the homogeneous variant of linear programming problems in the setting of a module over a linearly ordered commutative associative ring. We formulate the optimality condition for the primal and for the dual problem; by combining the aforementioned results, we obtain the Strong Duality Theorem for the homogeneous linear programming problems. Albeit the results are based on a general discrete variant of Farkas’ Lemma, which has been published recently, further restrictive assumptions are necessary to prove the results. We also propose a simple application of the results – an extension of the FMEA (Failure Mode and Effects Analysis) method – in business decision making of small and medium-sized enterprises. ER -
BARTL, David. A Note on Homogeneous Linear Programming. In \textit{The 3rd International Conference on Decision Making for Small and Medium-Sized Enterprises}. Karviná: Silesian University in Opava, School of Business Administration in Karviná, 2021, s.~61-70. ISBN~978-80-7510-456-4.
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