Linear Programming –Strategic Allocation of Linear Programming –Strategic Allocation of ResourcesResources

Decision Making with Excel SimulationDecision Making with Excel Simulation

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HomeworkHomework LP Chapter, #2 (omit money constraint) LP Chapter, #4 LP Supp A, LP Supp B

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Applications IncludeApplications Include Strategic Product or Service Mix

Planning Financial Portfolios Choosing the Right Mix (ingredients,

diet) Transportation Problems Staff Scheduling Routing Optimize an Objective Function

◦ Minimize Costs◦ Maximize Profits◦ Constraints

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The Maximization ProblemThe Maximization ProblemBags Tents Resource

AvailabilityCutting 2 1 14

Sewing 5 5 40

Waterproofing 1 3 18

Profit $50 $30

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The Maximization ProblemThe Maximization Problem

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The Maximization ProblemThe Maximization Problem

P R TotalChanging Cells 6.00 2.00 Min Cost/Max Profit $50.00 $30.00 $360.00

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 2 1 14.00 <= 14 0.00Constraint2 5 5 40.00 <= 40 0.00Constraint3 1 3 12.00 <= 18 6.00

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The Minimization ProblemThe Minimization ProblemGrain 1 Grain 2 Resource

RequirementCarbos 24 4 128

Proteins 14 7 168

Fructose 8 32 120

Cost $7 $2

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The Minimization ProblemThe Minimization Problem

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The Minimization ProblemThe Minimization ProblemG1 G2 Total

Changing Cells 2.00 20.00 Min Cost/Max Profit $7.00 $2.00 $54.00

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 24 4 128.00 >= 128 0.00Constraint2 14 7 168.00 >= 168 0.00Constraint3 8 32 656.00 >= 120 536.00

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Example-Transportation Example-Transportation ProblemProblem

Delorian motors has 2 distribution centers (DCs) for their 3 dealerships. Delorian automobiles are shipped from the centers to the dealerships. The shipping cost per auto, monthly dealership requirements, and distribution center levels are shown below. How many automobiles should be shipped per month from each DC to each dealership to minimize shipping costs and satisfy dealership demand?

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DealershipA B C Capacity

DC1 $5.00 $6.00 $3.00 2500DC2 $2.00 $8.00 $6.50 2500Rqmt 1000 2000 1500

ExampleExample

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ExampleExample A local brewery produces three types of beer: premium, regular, and

light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 3.6 pounds of barley and 1.2 pounds of hops, a gallon of regular requires 2.9 pounds of barley and .8 pounds of hops, and a gallon of light requires 2.6 pounds of barley and .6 pounds of hops. The brewery is able to acquire only 55,000 pounds of barley and 20,000 pounds of hops next month. The brewery’s largest seller is regular beer, so it wants to produce at least twice as much regular beer as it does light beer. It also wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 4000 gallons each of light beer and premium beer, but not more than 12,000 gallons of these two beers combined. The brewery makes a profit of $3.00 per gallon on premium beer, $2.70 per gallon on regular beer, and $2.80 per gallon on light beer. The brewery manager wants to know how much of each type of beer to produce next month in order to maximize profit.

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ExampleExampleLP Formulation:

STcapacitybarleyhops2:1 ratiominimum P requirementminimum L requirementmaximum requirement

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ExampleExampleP R L Variable4 Variable5 Variable6 Variable7 Variable8 Total

Changing Cells 4000.00 9761.90 4880.95 Min Cost/Max Profit $3.00 $2.70 $2.80 $52,023.81

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 1 1 1 18642.86 27000 8357.14Constraint2 3.5 2.9 2.6 55000.00 55000 0.00Constraint3 1.1 0.8 0.6 15138.10 20000 4861.90Constraint4 0 1 -2 0.00 0 0.00Constraint5 1 0 0 4000.00 4000 0.00Constraint6 0 1 0 9761.90 4000 5761.90Constraint7 1 0 1 8880.95 12000 3119.05Constraint8 0 0 0

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LP Supp ALP Supp A

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LP Supp BLP Supp B

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