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Network Models with Excel
Simple Structure Intuition into solver Numerous applications Integral data means integral solutions
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PROTRAC Engine Distribution
500 800 700 400 900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 500 800 500 400 700 200 900
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Transportation Costs Minimize
Unit transportation costs from harbors to plants Minimize the transportation costs involved in moving the engines from the harbors to the plants
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A Transportation Model
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Model Components Adjustables or Variables Objective Constraints
By changing cells selection ranges separated by commas Objective Target Cell Min or Max Constraints LHS is a cell reference >=, <=, = (others for later) RHS is a cell reference or number.
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How the Solver works Belgium Netherlands Germany 500 800 700 400 200
900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50
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A Basic Feasible Solution
500 800 700 400 900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50
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Finding an Entering Variable
500 800 700 400 900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 500 800 500 400 700 200 900
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Finding an Entering Variable
500 800 700 400 900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50
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Computing Reduced Cost
500 800 700 400 900 200 * Belgium Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 $122
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Computing Reduced Cost
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 $122 $100
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Computing Reduced Cost
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 $122 $100 $40
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Computing Reduced Cost
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 $122 $100 $40 $90 Costs$122 $ 40 $162 Saves$100 $ 90 $190 Net $28
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Finding a Leaving Variable
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 Red flows decrease. Green flows increase. Leaving variable is first to reach 0
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New Basic Feasible Solution
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50
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New Basic Feasible Solution
500 800 700 400 900 200 * Germany Netherlands The Hague Amsterdam Antwerp Nancy Liege Tilburg Leipzig Miles 100 50 300 600
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Quantity Discounts Minimize Cost Total Cost $3 $4 Shipment Size
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Crossdocks and Warehouses
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Flow Balance At the DCs At the Plants At the Customers
Flow into the DC - Flow out of the DC = 0 At the Plants Flow out of Plant - Flow into the Plant Supply At the Customers Flow into the Cust. - Flow out of the Cust. Demand
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A Solver Model
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Network Flow Models Variables are flows of a single homogenous commodity Constraints are Net flow Supply/Demand Lower Bound Flow on arc Upper Bound Theorem: If the data are integral, any solution solver finds will be integral as well.
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An Important Special Case
One unit available at one plant One unit required at one customer Minimizing the cost of shipping is....
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