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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 1 Kafli 2Tn í Chase … Línuleg bestun (Linear Programming) með Excel Solver Línuleg bestun Hámörkun, dæmi Lágmörkun, dæmi

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 2 Línuleg bestun Notuð við flókin ákvörðunarvandamál þegar aðföng (forðar) eru takmarkaðir og geta verið flöskuhálsar. LP reiknilíkön hafa markfall (objective function) –Hámörkun hagnaðar eða lágmörkun kostnaðar m.t.t. skorða á aðföngum gefur bestu gildi á ákvarðanabreytum. Bæði markfall og skorður verða að vera línuleg föll. Breytur verða að vera samfelldar (ekki heiltölur) og ekki neikvæðar.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 3 Markfall (Objective Function) Max (eða Min) Z = C 1 X 1 + C 2 X 2 +... + C n X n C j eru stuðlar sem lýsa framlegð eða hagnaði eða kostnaði á einingu af X j sem getur t.d. verið framleitt magn af vöru. Z er heildar framlegð eða hagnaður eða kostnaður af öllum vörum.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 4 Skorður (Constraints) A 11 X 1 + A 12 X 2 +... + A 1n X n B 1 A 21 X 1 + A 22 X 2 +... + A 2n X n B 2 : A M1 X 1 + A M2 X 2 +... + A Mn X n = B M A ij er þörf vöru nr. j (ákvarðanabreytu X j ) fyrir aðföng (resource) nr. i. B i lýsir hve mikið er fyrir hendi af aðföngum nr. i. Skorðurnar geta verið , , eða =.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 5 Breytur ekki neikvæðar (Non- Negativity) X 1,X 2, …, X n 0 Öll LP-líkön byggja á því að breyturnar séu ekki neikvæðar. Við teljum þessar kröfur þó ekki með skorðum.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 6 Dæmi um hámörkun LawnGrow Manufacturing Company must determine the mix of its commercial riding mower products to be produced next year. The company produces two product lines, the Max and the Multimax. The average profit is $400 for each Max and $800 for each Multimax. Fabrication and assembly are limited resources. There is a maximum of 5,000 hours of fabrication capacity available per month (Each Max requires 3 hours and each Multimax requires 5 hours). There is a maximum of 3,000 hours of assembly capacity available per month (Each Max requires 1 hour and each Multimax requires 4 hours). Question: How many of each riding mower should be produced each month in order to maximize profit? Now let’s formulate this problem.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 7 Markfall If we define the Max and Multimax products as the two decision variables X 1 and X 2, and since we want to maximize profit, we can state the objective function as follows:

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 8 Skorður Given the resource information below from the problem: We can now state the constraints and non-negativity requirement a: Note that the inequalities are less-than-or-equal since the time resources represent the total available resources for production.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 9 Lausn Produce 715 Max and 571 Multimax per month for a profit of $742,800. Produce 715 Max and 571 Multimax per month for a profit of $742,800.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 10 Dæmi um lágmörkun HiTech Metal Company is developing a plan for buying scrap metal for its operations. HiTech receives scrap metal from two sources, Hasbeen Industries and Gentro Scrap in daily shipments using large trucks. Each truckload of scrap from Hasbeen yields 1.5 tons of zinc and 1 ton of lead at a cost of $15,000. Each truckload of scrap from Gentro yields 1 ton of zinc and 3 tons of lead at a cost of $18,000. HiTech requires at least 6 tons of zinc and at least 10 tons of lead per day. Question: How many truckloads of scrap should be purchased per day from each source in order to minimize scrap metal cost? Now let’s formulate this problem.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 11 Markfall Minimize Z = 15,000 X 1 + 18,000 X 2 Where Z = daily scrap cost X 1 = truckloads from Hasbeen X 2 = truckloads from Gentro Hasbeen Gentro If we define the Hasbeen truckloads and the Gentro truckloads as the two decision variables X 1 and X 2, and since we want to minimize cost, we can state the objective function as follows:

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 12 Skorður 1.5X 1 + X 2 > 6(Zinc/tons) X 1 + 3X 2 > 10(Lead/tons) X 1, X 2 > 0(Non-negativity) Given the demand information below from the problem: We can now state the constraints and non-negativity requirement a: Note that the inequalities are greater-than-or-equal since the demand information represent the minimum necessary for production.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 13 Lausn Order 2.29 truckloads from Hasbeen and 2.57 truckloads from Gentro for daily delivery. The daily cost will be $80,610. Order 2.29 truckloads from Hasbeen and 2.57 truckloads from Gentro for daily delivery. The daily cost will be $80,610.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 14 Túlkun bestu lausnar Gildi á ákvörðunarbreytum og markfalli, t.d. Hve mikið á að framleiða og hvað það gefur í heildar framlegð Slakar = ónotuð aðföng Skuggaverð (stök í markfallsröð undir slakbreytum) = jaðarbreyting markfalls m.v. jaðarbreytingu á aðföngum (hægri hlið), þ.e. hvers virði er viðbótareining aðfanga.

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 15 Dæmi: Pakkningaval í fiskvinnslu

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 16

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Operations Management For Competitive Advantage © The McGraw-Hill Companies, Inc., 2001 C HASE A QUILANO J ACOBS ninth edition 17

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