Integer Programming Formulation Problem 1. Integer Programming Formulation. As t

Question

Integer Programming Formulation

Problem 1. Integer Programming Formulation. As the planning engineering, you will chose some new sites to place generators. You must determine the least cost solution of choosing 5 out 10 possible sites. Label the sites S1, S2,..., S1o and the cost associated with each as C1, C2, ..., C1o. There are several regional development restrictions: 1. Choosing S and S will prevent you from choosing S 2. Choosing S3 or S4 will prevent you from choosing S5. 3. Of the group S5, S6, S7, S8, only two sites may be used Formulate an integer program to determine the minimum-cost scheme that satisfy all con- straints.

Explanation / Answer

Let S1,..S10 be binary variables such that if a site is selected its value becomes 1, otherwise it is 0.

Constraints

1) S1S7 + S8=1

If both S1 and S7 are 1 or selected, then S8 must be 0

Similarly,

2) S3+S5=1 , S4+S5=1

3) S5+S6+S7+S8=2

Out of these 4 sites, only 2 can be 1 or selected.

Minimization function

f(x) = S1*C1+S2*C2+.....+S10*C10

The one with sites selected or sites having value 1, costs for them gets added to this function, otherwise the costs corresponding to the sites having value 0 did not come into this term.

Just for example, first 5 sites are selected

f(x) =1*C1+1*C2+1*C3+1*C4+1*C5+0*C6+0*C7+0*C8+0*C9+0*C10

f(x) = C1+...+C5

Hope it helps.... :) :)

  

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