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Network Models

Network Models. Lecture 17 (Part v.) Vogel’s Approximation Method. Vogel’s Approximation Starting Procedure. Calculate Row and Column Penalties by taking the absolute value of the two lowest “available” costs in the row or column deducted from one another.

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Network Models

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  1. Network Models Lecture 17 (Part v.) Vogel’s Approximation Method FOMGT 353 Introduction to Management Science

  2. Vogel’s Approximation Starting Procedure • Calculate Row and Column Penalties by taking the absolute value of the two lowest “available” costs in the row or column deducted from one another. • Select the Maximum of the Row and Column Penalties to identify the Row or Column into which flow will go. • In the Row selected find the lowest “available” cost to identify the Column. OR in the Column selected find the lowest “available” cost to identify the Row. We have identified the Xij to be increased! FOMGT 353 Introduction to Management Science

  3. Vogel’s Approximation Starting Procedure cont… • Fill in as much flow for that Decision Variable, Xij, as possible. • Adjust the Border Demands and Supplies to take into account the Flow allocated. • If there is still a positive amount of Border Demand, goto 1, otherwise stop. FOMGT 353 Introduction to Management Science

  4. Vogel’s Approximation 1 2 Lowest Costs in Column 1 are 4 and 5 so Column Penalty is 1 2 Lowest Costs in Column 2 are 10 and 11 so Column Penalty is 1 The Maximum Penalty is 7 [max(1,1,5,7,6)] So Row 2 will get some flow! 2 Lowest Costs in Row 1 are 12 and 6 so Row Penalty is 6 2 Lowest Costs in Row 2 are 11 and 4 so Row Penalty is 7 In Row 2 the Column with the Lowest cost is Column 1, so insert flow into x21 2 Lowest Costs in Row 3 are 10 and 5 so Row Penalty is 5 FOMGT 353 Introduction to Management Science

  5. In x21, insert the min of S2 and D1 Subtract x21 from S2 and from D1. 15,000 0 Vogel’s Approximation 2 FOMGT 353 Introduction to Management Science

  6. Vogel’s Approximation 3 2 Lowest Costs in Column 1 are 5 and 6 so Column Penalty is 1 2 Lowest Costs in Column 2 are 10 and 12 so Column Penalty is 2 The Maximum Penalty is 6 [max(1,2,5,0,6)] So Row 1 will get some flow! Row 1 Penalty unchanged at 6 In Row 1 the Column with the Lowest cost is Column 1, so insert flow into x11 2 Lowest Costs in Row 2 are 11 and 11 so Row Penalty is 0 Row 3 Penalty unchanged at 5 FOMGT 353 Introduction to Management Science

  7. In x11, insert the min of S1 and D1 Subtract x11 from S1 and from D1. 5,000 0 Vogel’s Approximation 4 FOMGT 353 Introduction to Management Science

  8. Note Column 1 has zero Border Demand, so “Green Out” Column 1! Vogel’s Approximation 5 2 Lowest Costs in Column 1 are 5 and 5 so Column Penalty is 0 2 Lowest Costs in Column 2 are 10 and 12 so Column Penalty is 2 2 Lowest Costs in Row 1 are 12 and 12 so Row Penalty is 0 The Maximum Penalty is 2 [max(0,2,0,0,0)] So Col 2 will get some flow! In Column 2 the Row with the Lowest cost is Row 3, so insert flow into x32 2 Lowest Costs in Row 2 are 11 and 11 so Row Penalty is 0 2 Lowest Costs in Row 3 are 10 and 10 so Row Penalty is 0 FOMGT 353 Introduction to Management Science

  9. 5,000 In x32, insert the min of S3 and D2 Subtract x32 from S3 and from D2. 0 Vogel’s Approximation 6 FOMGT 353 Introduction to Management Science

  10. Vogel’s ApproximationInitial Feasible Solution FOMGT 353 Introduction to Management Science

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