*1. ABC is an LTL (less-than-truckload) trucking company that delivers loads on a daily basis
to five customers. The following list provides the customers associated with each route:
Customers served on the route
Route
1
2
3
4
5
6
3,2,4
5,3,4
2,5,1,3
2,3,5
1,4,2
1,3,5
The segments of each route are dictated by the capacity of the truck delivering the
loads. For example, on route 1, the capacity of the truck is sufficient to deliver the loads
to customers 3, 2, and 4 only. The following table lists distances (in miles) among the
truck terminal (ABC) and the customers.
Miles from $i$ to $j$
j
ABC
1
2
3
4
5
i
ABC
0
10
12
16
9
8
1
10
0
32
8
17
10
2
12
32
0
14
21
20
3
16
8
14
0
15
18
4
9
17
21
15
0
11
5
8
10
20
18
11
0
The objective is to determine the least distance needed to make the daily deliveries
to all five customers. Though the solution may result in a customer being served by more
than one route, the implementation phase will use only one such route. Formulate the
problem as an ILP, and find the optimum solution.
