76
3. A Procedure for Solving the Optimal Expansion
Problem
To
12
3
4
From
1 oo
25
64
93
Matrix 1: C -
2 25
oo 50 100
3 64
50
oo
140
4 93 100 140
oo
Fig. 3.3 The relative locations of cities 1, 2, 3, 4. Intercity distances are shown in
miles; e.g., c 8 4
β
140 mi.
(c)
FIRST BRANCHING SEQUENCE
In matrix 2 there are six elements (whose values of Cij are equal to zero)
that could be considered as the first arc of the branching sequence. Table
3.1 gives the values of θα for the arcs corresponding to each of these eleTable 3.1
Calculation of 0 t; for the Zero Elements of Matrix 2
Element
of matrix 2
α»
ft
(1, 2)
0
0
0
(1, 4)
0
7
7
(2, 1)
0
0
0
(2, 3)
0
14
14
(3, 2)
14
0
14
(4, 1)
7
0
7