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Troop Movement
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.        

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