The long-range planning department for the Ohio Trust Company is considering expanding its operation into a 88-county region in northeastern Ohio. Currently, Ohio Trust does not have a principal place of business in any of the 88 counties. According to the banking laws in Ohio, if a bank establishes a principal place of business (PPB) in any county, branch banks can be established in that county and in any adjacent county. However, to establish a new principal place of business, Ohio Trust must either obtain approval for a new bank from the state's superintendent of banks or purchase an existing bank.

The following table lists the 88 counties in the region and adjacent counties. For example, County 1 is adjacent to 2, 18, and 19 counties; County 18 is adjacent to 1, 19, 20, 21, 22, 17, 3 and 2 counties; and so on.

Counties Under Consideration	Adjacent Counties (by Number)
1	2, 18, 19
2	1, 3, 17, 18
3	2, 4, 16, 17
4	3, 5, 15, 16, 17
5	4, 6, 15
6	5, 7, 12, 13, 14, 15
7	6, 8, 12
8	7, 9, 11, 12
9	8, 10, 11
10	9, 11, 28, 29
11	8, 9, 10, 12, 27, 28, 29
12	6, 7, 8, 11, 13, 27
13	6, 12, 14, 25, 26
14	6, 13, 15, 24, 25
15	4, 5, 6, 14, 16, 23, 24
16	4, 15, 17, 22, 23
17	2, 3, 4, 16, 18, 21, 22
18	1, 2, 17, 19, 20, 21, 22
19	1, 18, 20
20	18, 19, 21, 39
21	17, 18, 20, 22, 37, 38, 39
22	16, 17, 18, 21, 23, 36, 37
23	15, 16, 22, 24, 34, 35, 36
24	14, 15, 23, 25, 34
25	13, 14, 24, 26, 33, 34
26	12, 13, 25, 27, 33
27	11, 12, 26, 28, 32, 33
28	10, 11, 27, 29, 31, 32
29	10, 11, 28, 30, 31
30	29, 31, 48, 49
31	28, 29, 30, 32, 47, 48
32	27, 28, 31, 33, 46, 47
33	25, 26, 27, 32, 34, 45, 46
34	23, 24, 25, 33, 35, 44, 45
35	23, 34, 36, 42, 43, 44
36	22, 23, 35, 37, 42
37	21, 22, 36, 38, 41, 42
38	21, 37, 39, 40, 41
39	20, 21, 38, 40
40	38, 39, 41, 58
41	37, 38, 40, 42, 57, 58, 59
42	35, 36, 37, 41, 43, 57
43	35, 42, 44, 56, 57
44	34, 35, 43, 45, 55, 56
45	33, 34, 44, 46, 54, 55
46	32, 33, 45, 47, 53, 54
47	31, 32, 46, 48, 51, 52, 53
48	30, 31, 47, 49, 51
49	30, 48, 50, 51
50	49, 51, 70
51	47, 48, 49, 50, 52, 70
52	47, 51, 53, 68, 69, 70
53	46, 47, 52, 54, 66, 68
54	45, 46, 53, 55, 66
55	44, 45, 54, 56, 64, 65, 66
56	43, 44, 55, 57, 59, 63, 64
57	41, 42, 43, 56, 59
58	40, 41, 59, 60, 61
59	41, 56, 57, 58, 61, 62, 63
60	58, 61, 76, 77, 78, 79
61	58, 59, 60, 62, 76
62	59, 61, 63, 74, 75, 76
63	56, 59, 62, 64, 74, 75
64	55, 56, 63, 65, 73, 74
65	55, 64, 66, 67, 72, 73
66	53, 54, 55, 65, 67, 68
67	65, 66, 68, 71, 72
68	52, 53, 66, 67, 69, 71
69	52, 68, 70
70	50, 51, 52, 69
71	67, 68, 72, 88
72	65, 67, 71, 73, 87, 88
73	64, 65, 72, 74, 85, 87, 88
74	63, 64, 73, 75, 84, 85
75	62, 63, 74, 76, 77, 82, 83, 84
76	60, 61, 62, 75, 77, 78
77	75, 76, 78, 81, 82
78	60, 76, 77, 79, 80, 81
79	60, 78, 80
80	78, 79, 81
81	77, 78, 80, 82
82	75, 77, 81, 83
83	75, 82, 84, 86
84	74, 75, 83, 85, 86
85	73, 74, 84, 86, 87
86	83, 84, 85, 87
87	72, 73, 85, 86, 88
88	71, 72, 87

Consider the 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.

Let x_j = 1 if place a PBB in county j, 0 if not; j = 1, 2,...,88

Min	x1 + x2 + x3 + ... + x88
s.t.
	x1 + x2 + x18 + x19	≥	1	County 1
	x1 + x2 + x3 + x17 + x18	≥	1	County 2
	x71 + x72 + x87 + x88	≥	1	County 88

 

Transcribed Image Text:

Consider again the Ohio Trust bank location problem discussed in Section 7.3. The fle CnietrustFull contains data for all of Ohio's 8 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 berder with the county of the column (1 = yes and 0= ne), Use a software package LINGO. a. Create a model to find the location of requred principal places of business (PPB6) to minimize the number of PPBS needed to open all counties to branches. Let x=1if place a PBB In county .o if not: /= 1. 2.68 Man st. 2 1 County 1 X 17 X 162 1 County 2 X 72+ X 87 21 County 88 xj- 0,1 1-1, 2, ., 88 b. Solve the model constructed in part (a). What is the minimum number PPBS needed to open up the entire state to Chio Trust branches? Minimum number of counties is Consider again the Ohio Trust bank location problem discussed in Section 7.3. The fle CnietrustFull contains data for all of Ohio's 8 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 berder with the county of the column (1 = yes and 0= ne), Use a software package LINGO. a. Create a model to find the location of requred principal places of business (PPB6) to minimize the number of PPBS needed to open all counties to branches. Let x=1if place a PBB In county .o if not: /= 1. 2.68 Man st. 2 1 County 1 X 17 X 162 1 County 2 X 72+ X 87 21 County 88 xj- 0,1 1-1, 2, ., 88 b. Solve the model constructed in part (a). What is the minimum number PPBS needed to open up the entire state to Chio Trust branches? Minimum number of counties is

Answer rating: 100% (QA)

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