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# Lab 8 - you define your Nodes and Arcs in your formulation...

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Lab 8 – Network Flow Problems 1. A Distribution Problem (Question 6 from the Network Formulation Problems) A distribution company produces its product at two different factories (50 units at F1 and 40 units at F2) to meet a demand for its product at its two warehouses (30 units at W1, and 60 units at W2), sometimes via a distribution center (DC). From F1 it costs 900 \$/unit to ship to W1, 400 \$/unit to ship to DC, and 200 \$/unit (up to 10 units) to ship to F2. From F2 the units can only be shipped to DC at a cost of 300 \$/unit. From DC a maximum of 80 units can be shipped to W2 at a cost of \$100/unit. In addition units can be shipped from W1 to W2 at 300 \$/unit, and from W2 to W1 at \$200/unit. How should the goods be shipped to minimize transportation cost? The associated Network Flow Problem is: 2. Generic AMPL Code for Network Flow Problems A Generic Formulation for Network Problems is available for most Network Flow Problems as long as

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Unformatted text preview: you define your Nodes and Arcs in your formulation appropriately. The .mod file is: set NodeName; set ARC within (NodeName cross NodeName); param lower {ARC}; param upper {ARC}; param value {ARC}; minimize TotalValue; node NODE {k in NodeName}; arc Flow {(i,j) in ARC}, >= lower [i,j], <= upper [i,j], obj TotalValue value [i,j] from NODE [i], to NODE [j]; 3. Data File Network Flow Problems The Data File for the above Network Flow problem is: set NodeName:=Source F1 F2 DC W1 W2 Sink; param:ARC: lower, upper, value:= Source F1 50 50 0 Source F2 40 40 0 F1 W1 0 Infinity 900 F1 DC 0 Infinity 400 F1 F2 0 10 200 F2 DC 0 Infinity 300 DC W2 0 80 100 W1 W2 0 Infinity 300 W2 W1 0 Infinity 200 W1 Sink 30 30 0 W2 Sink 60 60 0 Sink Source 0 Infinity 0;...
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