5. Consider the transportation problem having the following parameter table: Destination 1 Destination 2 Destination 3 Source 1 Source 2 Demand The initial BF solution given by Source 1 Source 2 Demand 3 2.9 3 X11 = 3, X12 = 2, X22=2, X23 = 2. Interactively apply the transportation simplex method to obtain an optimal solution. The initial transportation simplex tableau is Destination 1 Destination 2 2.7 Vj 3 2.9 3 3 2.7 2.8 4 2.8 4 2 2 Destination 3 0 0 0 2 0 2 2 supply 5 4 supply 5 4 U₁ For each iteration tableau, clearly mark: U₁, V, values, C₁j+ or negative values, the loop, the entering BV, the leaving BV. At the end of each iteration, also write out clearly what the new BF solution, and the new objection value.
5. Consider the transportation problem having the following parameter table: Destination 1 Destination 2 Destination 3 Source 1 Source 2 Demand The initial BF solution given by Source 1 Source 2 Demand 3 2.9 3 X11 = 3, X12 = 2, X22=2, X23 = 2. Interactively apply the transportation simplex method to obtain an optimal solution. The initial transportation simplex tableau is Destination 1 Destination 2 2.7 Vj 3 2.9 3 3 2.7 2.8 4 2.8 4 2 2 Destination 3 0 0 0 2 0 2 2 supply 5 4 supply 5 4 U₁ For each iteration tableau, clearly mark: U₁, V, values, C₁j+ or negative values, the loop, the entering BV, the leaving BV. At the end of each iteration, also write out clearly what the new BF solution, and the new objection value.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
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Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:**Transportation Problem: Initial Simplex Tableau Example**
**Problem Statement:**
Consider the transportation problem with the following parameters:
| | Destination 1 | Destination 2 | Destination 3 | Supply |
|--------------|---------------|---------------|---------------|--------|
| Source 1 | 3 | 2.7 | 0 | 5 |
| Source 2 | 2.9 | 2.8 | 0 | 4 |
| **Demand** | **3** | **4** | **2** | |
The initial basic feasible (BF) solution is given by:
- \( x_{11} = 3 \)
- \( x_{12} = 2 \)
- \( x_{22} = 2 \)
- \( x_{23} = 2 \)
**Objective:**
Interactively apply the transportation simplex method to obtain an optimal solution.
**Initial Transportation Simplex Tableau:**
| | Destination 1 | Destination 2 | Destination 3 | Supply | \( u_i \) |
|--------------|---------------|---------------|---------------|--------|-----------|
| Source 1 | 3 | 2.7 | 0 | 5 | |
| | (3) | (2) | | | |
| Source 2 | 2.9 | 2.8 | 0 | 4 | |
| | | (2) | (2) | | |
| **Demand** | **3** | **4** | **2** | | |
| \( v_j \) | | | | | |
**Instructions for Iteration:**
1. For each iteration tableau, clearly mark:
- \( u_i \), \( v_j \) values
- \(\bar{c}_{ij}\) + or - values
- The loop
- The entering basic variable (BV)
- The leaving BV
2. At the end of each iteration:
- Write out the new BF solution
- State the new objective value
This setup provides a structured approach for solving transportation problems using the transportation simplex method, facilitating an efficient search for the optimal solution.
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