An army wants to move troops from 3 training camps to 4 different bases. How should | ||||||

the troops be moved to minimize cost? | ||||||

Moving Cost Per Man | ||||||

Base 1 | Base 2 | Base 3 | Base 4 | |||

Camp 1 | $34 | $26 | $29 | $31 | ||

Camp 2 | $42 | $33 | $28 | $35 | ||

Camp 3 | $36 | $29 | $32 | $38 | ||

Number Of Troops Moved | ||||||

Base 1 | Base 2 | Base 3 | Base 4 | Total | Available | |

Camp 1 | 100 | 100 | 100 | 100 | 400 | 500 |

Camp 2 | 100 | 100 | 100 | 100 | 400 | 400 |

Camp 3 | 100 | 100 | 100 | 100 | 400 | 400 |

Total | 300 | 300 | 300 | 300 | ||

Required | 200 | 250 | 350 | 300 | ||

Cost | $11,200 | $8,800 | $8,900 | $10,400 | $39,300 | |

Problem | ||||||

An army wants to move troops from 3 training camps to 4 different bases. All costs of moving a | ||||||

soldier from any camp to any base are known. How should the army move the troops to | ||||||

minimize cost? | ||||||

Solution | ||||||

1) The variables are the number of soldiers that are moved from each camp to each base. On | ||||||

worksheet Troops these are given the name Troops_moved. | ||||||

2) The constraints are | ||||||

Troops_moved >= 0 via the Assume Non-Negative option | ||||||

Troops_per_camp <= Troops_available | ||||||

Troops_per_base = Troops_required | ||||||

3) The objective is to minimize the total cost. This is defined on the worksheet as Total_cost. | ||||||

Remarks | ||||||

This model is a transportation model, like those shown in the Logistics Examples workbook. You | ||||||

might wonder why there is no constraint to assure that the numbers of troops moved are integers. | ||||||

It is a mathematical property of these types of problems that if the constants in the constraints are | ||||||

integers, the solution values for the variables are always integers. It is beyond the scope of these | ||||||

examples to further explore this. | ||||||