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Lecture6a - MBAC6080 Decision Modeling and Applications...

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1 MBAC6080 Thomas Vossen Assistant professor of Operations Management Leeds School of Business University of Colorado Boulder, CO 80309-0419 Decision Modeling and Applications
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Lecture 6,part I, 2-20-2008 2 MBAC6080 Today’s Agenda Network Models Quick Review Integer Programming Introduction Formulating IPs Examples Exam P(review ) Review Material Prepare for Midterm Exam, Sample test questions Answer questions
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Lecture 6,part I, 2-20-2008 3 MBAC6080 Network Models
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Lecture 6,part I, 2-20-2008 4 MBAC6080 Data for Distribution Network   F1 DC F2 W2 W1 80 units produced 70 units  produced 60 units needed 90 units  needed $700/unit $900/unit $300/unit  [50 units max.] $400/unit  [50 units max.] $200/unit  [50 units max.] $400/unit  [50 units max.]
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Lecture 6,part I, 2-20-2008 5 MBAC6080 Constraints for Network Flow Problems: The Balance-of-Flow Rules For Minimum Cost Network Apply This Balance-of-Flow Flow Problems Where: Rule At Each Node: Total Supply > Total Demand Inflow-Outflow >= Supply or Demand Total Supply < Total Demand Inflow-Outflow <=Supply or Demand Total Supply = Total Demand Inflow-Outflow = Supply or Demand
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Lecture 6,part I, 2-20-2008 6 MBAC6080 The American Car Association B'ham Atlanta G'ville Va Bch Charl. L'burg K'ville A'ville G'boro Raliegh Chatt. 1 2 3 4 6 5 7 8 9 10 11 2.5 hrs 3 pts 3.0 hrs 4 pts 1.7 hrs 4 pts 2.5 hrs 3 pts 1.7 hrs 5 pts 2.8 hrs 7 pts 2.0 hrs 8 pts 1.5 hrs 2 pts 2.0 hrs 9 pts 5.0 hrs 9 pts 3.0 hrs 4 pts 4.7 hrs 9 pts 1.5 hrs 3 pts 2.3 hrs 3 pts 1.1 hrs 3 pts 2.0 hrs 4 pts 2.7 hrs 4 pts 3.3 hrs 5 pts -1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0
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Lecture 6,part I, 2-20-2008 7 MBAC6080 The Maximal Flow Problem
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Lecture 6,part I, 2-20-2008 8 MBAC6080 The Maximal Flow Problem In some network problems, the objective is to determine the maximum amount of flow that can occur through a network. The arcs in these problems have upper and lower flow limits. Examples How much water can flow through a network of pipes? How many cars can travel through a network of streets?
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Lecture 6,part I, 2-20-2008 9 MBAC6080 The Northwest Petroleum Company Oil Field Pumping Station 1 Pumping Station 2 Pumping Station 3 Pumping Station 4 Refinery 1 2 3 4 5 6 6 4 3 6 4 5 2 2
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Lecture 6,part I, 2-20-2008 10 MBAC6080 The Northwest Petroleum Company Oil Field Pumping Station 1 Pumping Station 2 Pumping Station 3 Pumping Station 4 Refinery 1 2 3 4 5 6 6 4 3 6 4 5 2 2
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Lecture 6,part I, 2-20-2008 11 MBAC6080 Formulation of the Max Flow Problem MAX: X 61 Subject to: +X 61 - X 12 - X 13 = 0 +X 12 - X 24 - X 25 = 0 +X 13 - X 34 - X 35 = 0 +X 24 + X 34 - X 46 = 0 +X 25 + X 35 - X 56 = 0 +X 46 + X 56 - X 61 = 0 with the following bounds on the decision variables: 0 <= X 12 <= 6 0 <= X 25 <= 2 0 <= X 46 <= 6 0 <= X 13 <= 4 0 <= X 34 <= 2 0 <= X 56 <= 4 0 <= X 24 <= 3 0 <= X 35 <= 5 0 <= X 61 <= inf
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Lecture 6,part I, 2-20-2008 12 MBAC6080 Bottleneck Analysis Oil Field Pumping Station 1 Pumping
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Lecture6a - MBAC6080 Decision Modeling and Applications...

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