A power plant has three boilers. If a given boiler is operated, it can be used to produce a quantity of steam (in tons) between the minimum and maximum as shown below. The cost of producing a ton of steam on each boiler is also given. Steam from the boilers is used to produce power on three turbines. If operated, each turbine can process an amount of steam (in tons) between the minimum and maximum shown below. Also shown is the cost of processing a ton of steam and the power produced by each turbine. Formulate an IP that can be used to minimize the cost of producing 8,000 kwh of power. Turbine Number Kwh per Ton of Steam Processing Cost per Ton ($) Boiler Number Minimum Steam Maximum Steam Cost/Ton ($) Minimum Maximum 1 500 1,000 10 1 300 600 4 300 900 8 500 800 5 3 3 400 800 6. 3 600 900 6. 4

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
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Chapter2: Introduction To Spreadsheet Modeling
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This is not a writing assignment, just formulating an IP

### Power Plant Optimization Problem

A power plant operates with three boilers, each of which can produce steam in quantities ranging from a specified minimum to a maximum, as detailed in the table below. The cost of producing one ton of steam on each boiler is provided.

Steam generated by these boilers is used to create power through three turbines. Each turbine can process a certain range of steam tonnage and has associated costs and power output per ton of steam. The tables illustrate these specifications.

The objective is to formulate an integer programming (IP) model aimed at minimizing the total cost of producing 8,000 kWh of power.

#### Boiler Specifications

| **Boiler Number** | **Minimum Steam (tons)** | **Maximum Steam (tons)** | **Cost/Ton ($)** |
|-------------------|--------------------------|--------------------------|------------------|
| 1                 | 500                      | 1,000                    | 10               |
| 2                 | 300                      | 900                      | 8                |
| 3                 | 400                      | 800                      | 6                |

#### Turbine Specifications

| **Turbine Number** | **Minimum (tons)** | **Maximum (tons)** | **kWh per Ton of Steam** | **Processing Cost per Ton ($)** |
|--------------------|--------------------|--------------------|--------------------------|---------------------------------|
| 1                  | 300                | 600                | 4                        | 2                               |
| 2                  | 500                | 800                | 5                        | 3                               |
| 3                  | 600                | 900                | 6                        | 4                               |

Through this layout, you can analyze how to efficiently allocate steam production and processing to minimize costs while meeting the power output requirement.
Transcribed Image Text:### Power Plant Optimization Problem A power plant operates with three boilers, each of which can produce steam in quantities ranging from a specified minimum to a maximum, as detailed in the table below. The cost of producing one ton of steam on each boiler is provided. Steam generated by these boilers is used to create power through three turbines. Each turbine can process a certain range of steam tonnage and has associated costs and power output per ton of steam. The tables illustrate these specifications. The objective is to formulate an integer programming (IP) model aimed at minimizing the total cost of producing 8,000 kWh of power. #### Boiler Specifications | **Boiler Number** | **Minimum Steam (tons)** | **Maximum Steam (tons)** | **Cost/Ton ($)** | |-------------------|--------------------------|--------------------------|------------------| | 1 | 500 | 1,000 | 10 | | 2 | 300 | 900 | 8 | | 3 | 400 | 800 | 6 | #### Turbine Specifications | **Turbine Number** | **Minimum (tons)** | **Maximum (tons)** | **kWh per Ton of Steam** | **Processing Cost per Ton ($)** | |--------------------|--------------------|--------------------|--------------------------|---------------------------------| | 1 | 300 | 600 | 4 | 2 | | 2 | 500 | 800 | 5 | 3 | | 3 | 600 | 900 | 6 | 4 | Through this layout, you can analyze how to efficiently allocate steam production and processing to minimize costs while meeting the power output requirement.
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