Planungsrechnung und Entscheidungstechnik: Operations by WERNER ZIMMERMANN

By WERNER ZIMMERMANN

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22 1. Lineare Optimierung - Optimale Prograrnmgestaltung Bei Anwendung der oben angeflihrten Rechenoperation ergeben sich die rechten Seiten der Restriktionen wie folgt: n ajO i };aijuj aiO - L aijUj j=l (- 500) + (- 800) 3 = - 2900 0 24 24 0 1 2 3 5 + 1 + 6 + 36 = = = 2·3 5·3 6·3 11 16 24 2900 13 8 12 Damit ergibt sich folgende Ausgangsliisung: t t Xz Xl t = 2900 -500 Yl = 13 5 2 yz = 8 1 6 5 Y3 = 12 -800 6 Nach der Optimierung werden die gefundenen Liisungswerte x~ = 0,5 und x~ = 1,5 wieder in den urspriinglichen Koordinaten angegeben Xl = 1,5 und X2 = 4,5.

Auftragsmengen Kapazitiiten: z = 1/2x1 + 1/4x2 + 1/3x3 + ... + 1/3x11 + 1/5x12 1/2x 1 1/3x4 1/5x, 1/4xlO + + + + 1/4x2 1/5xs 1/5xs 1/3x11 + + + + 1/3x3 1/4x6 1/6x9 1/5x12 ~ Max = 100 SO = 80 60. Xl +X4 +X, +xlO =:;;400 X2 + Xs + Xs + X11 =:;; 400 X3 + x6 + x9 + Xu =:;;400. Daraus ergibt sich die erste Simplex-Tabelle; aus der Basis sind zuniichst die gesperrten Variablen zu entfernen. (vgl. 3). 34 1. Lineare Optimierung - Optimale Programmgestaltung 1. Tabelle z=O YI(g) Y2(g) Y3(g) Y4(g) = = = = 100 50 80 60 Xl X2 X3 X4 Xs X6 X7 Xs X9 XIO Xu Xl2 -1/2 -1/4 -1/3 -1/3 -1/5 -1/4 -1/5 -1/5 -1/6 -1/4 -1/3 -1/5 @ 1/4 1/3 1/3 1/5 1/4 1/5 1/5 1/6 1/4 1/3 1/5 Ys = 400 Y6 = 400 Y7 = 400 1 2.

Vgl. Littger, zur Steege [1972]). 12), optimale Dimensionierung des Rohmaterials (vgl. Stahlknecht [1970], S. ). Jedes Verschnittproblem wird in zwei Stufen gelast: a) b) Systematische Ermittlung aller realisierbaren Schnittkombinationen, Ermittlung der optimalen Schnittkombination (mit der Simplex-Methode). 4. 12,' Eine Firma stellt Leichtmetall-Fenster in jeder vom Kunden gewiinsehten Abmessung her. ig untersehiedliehe Stabe benotigt. Als Rohmaterial stehen nur Stangen von 6 Meter Lange zur Verfligung.

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