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F03_LP_Excel - Fyrirlestur 3 Lnuleg bestun me tflureikni...

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www.hr.is Sigrún B. Gunnhildardóttir Tækni- og verkfræðideild | T-403 Aðgerðagreining Fyrirlestur 3: Línuleg bestun með töflureikni
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www.hr.is T-403 2 Ákvörðunarbreytur (e. decision variables) Þær breytur sem skal ákvarða Geyma lausn vandamálsins Markfall (e. objective function) Fall af ákvörðunarbreytum og markmiðið er ýmist að hámarka gildi þess (Max) eða að lágmarka (Min) Skorður (e. constraints) Þau skilyrði sem þarf að uppfylla. Geta bæði verið jöfnur og ójöfnur og lýsa sambandi ákvörðunarbreyta Gerð línulegra bestunarlíkana (LP)
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www.hr.is T-403 3 Staðlað form línulegra bestunarlíkana Hámörkum Z = c1x1 + c2x2 + ... + cnxn m.t.t. a11x1 + a12x2 + ... + a1nxn b1 a21x1 + a22x2 + ... + a2nxn b2 am1x1 + am2x2 + ... + amnxn bm x1 0, x2 0, ... xn 0
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www.hr.is T-403 Lausnaraðferðir Myndrænt Myndræn aðferð sem nota má til að fá lausn við vandamáli með tveimur (2d) breytum Simplex Öflug handvirk aðferð Solver Tölvuforrit með tilbúnum reikniaðferðum til að leysa mismunandi bestunarverkefni Aðrar aðferðir Heuristics – margar mismunandi tegundir Metaheuristics – margar mismunandi tegundir
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www.hr.is T-403 Myndræn lausnaraðferð Myndræn lausnaraðferð Höfum markfall og skorður Skorður afmarka lausnarsvæðið Markfallið segir okkur hvar við viljum vera innan lausnarsvæðisins
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www.hr.is Ein (unique) besta lausn B 0 20 40 60 80 100 120 0 10 20 30 40 50 A Max Q P Q 60 Z = $3600 Z = $4664 Optimal solution = (16.36, 81.82)
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www.hr.is Margar bestu lausnir 1 0 0 1 x 1 x 2 2 3 4 2 3 4 z 1 z 2 z 3 Maximize z = 3 x 1 x 2 subject to 15 x 1 – 5 x 2 30 10 x 1 + 30 x 2 120 x 1 0, x 2 0
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www.hr.is Ógjaldgeng lausn (infeasible) 1 0 0 1 x 1 x 2 2 3 4 2 3 4 Maximize z = x 1 + x 2 subject to 3 x 1 + x 2 6 3 x 1 + x 2 3 x 1 0, x 2 0 Ósamræmi milli skorða
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www.hr.is “ótakmörkuð” (unbounded) lausn
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