Consider again the Ohio Trust
Consider again the Ohio Trust bank location problem discussed inSection 7.3. The file OhioTrustFull contains data for all of Ohio’s88 counties. The file contains an 88 X 88 matrix with the rows andcolumns each being the 88 counties. The entries in the matrix arezeros and ones and indicate if the county of the row shares aborder with the county of the column (1 = yes and 0 = no).
a. Create a model to find the location of required principalplaces of business (PPBs) to minimize the number of PPBs needed toopen all counties to branches.
b. Solve the model constructed in part (a). What is the minimumnumber PPBs needed to open up the entire state to Ohio Trustbranches?
Answer:
(a) LP Model is following:
Let Xi = 1, if a PPB is located in county i, otherwise Xi =0
Minimize 
s.t.
X2+X12+X16>=1
X1+X3+X12>=1
X2+X4+X9+X10+X12+X13>=1
X3+X5+X7+X9>=1
X4+X6+X7>=1
X5+X7+X17>=1
X4+X5+X6+X8+X9+X17+X18>=1
X7+X9+X10+X11+X18>=1
X3+X4+X7+X8+X10>=1
X3+X8+X9+X11+X12+X13>=1
X8+X10+X13+X14+X15+X18+X19+X20>=1
X1+X2+X3+X10+X13+X16>=1
X3+X10+X11+X12+X15+X16>=1
X11+X15+X20>=1
X11+X13+X14+X16>=1
X1+X12+X13+X15>=1
X6+X7+X18>=1
X7+X8+X11+X17+X19>=1
X11+X18+X20>=1
X11+X14+X19>=1
Xi = {0,1} or binary
(b) Solution using Solver is following:
FORMULAS:
V3 =SUMPRODUCT(B3:U3,$B$26:$U$26) copy to V5:V24
Solution:
X1, X7, X8, X11, X12 = 1,
Therefore, PPBs should be located in counties 1, 7,8,11,12
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
