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Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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### Transportation Problem

**Problem Statement:**
Consider the transportation problem having the following parameter table:

| | Destination 1 | Destination 2 | Destination 3 | Destination 4 | Supply |
|-------|---------------|---------------|---------------|---------------|--------|
| **Source 1** | 500 | 750 | 300 | 450 | 12 |
| **Source 2** | 650 | 800 | 400 | 600 | 17 |
| **Source 3** | 400 | 700 | 500 | 550 | 11 |
| **Demand** | 10 | 10 | 10 | 10 | |

**Initial Basic Feasible Solution:**
Assume we have obtained an initial BF solution from the northwest corner method:

- \( x_{11} = 10 \)
- \( x_{12} = 2 \)
- \( x_{22} = 8 \)
- \( x_{23} = 9 \)
- \( x_{33} = 1 \)
- \( x_{34} = 10 \)

So, the initial transportation simplex tableau looks as follows. Boxed values are cost values, circled values are basic variable values.

| | Destination 1 | Destination 2 | Destination 3 | Destination 4 | Supply | \( u_i \) |
|-------|---------------|---------------|---------------|---------------|--------|-----------|
| **Source 1** | \(\boxed{500}\) | \(\boxed{750}\) | \(\boxed{300}\) | 450 | 12 | \( u_1 = 0 \) |
| | \(\circled{10}\) | \(\circled{2}\) | | | | |
| **Source 2** | 650 | \(\boxed{800}\) | \(\boxed{400}\) | 600 | 17 | \( u_2 = \) |
| | | \(\circled{8}\) | \(\circled{9}\) | | | |
| **Source 3** | 400 | 700 | \(\boxed{500}\) | \

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