Question

Consider again the Ohio Trust bank location problem discussed in Section 7.3. The file OhioTrustFull contains data for all of Ohio’s 88 counties. The file contains an 88 X 88 matrix with the rows and columns each being the 88 counties. The entries in the matrix are zeros and ones and indicate if the county of the row shares a border with the county of the column (1 = yes and 0 = no).

a. Create a model to find the location of required principal places of business (PPBs) to minimize the number of PPBs needed to open all counties to branches.

b. Solve the model constructed in part (a). What is the minimum number PPBs needed to open up the entire state to Ohio Trust branches?

Answer 1

(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