A small company with six vans has a contract with a number of airlines to pick up lost or delayed baggage, belonging to customers in the London area, from Heathrow airport at 6 p.m. each evening.[28] The contract stipulates that each customer must have [his or her] baggage delivered by 8 p.m. The company requires a model, which they can solve quickly each evening, to advise them what is the minimum number of vans they need to use and to which customers each van should deliver and in what order. There is no practical capacity limitation on each van. All baggage that needs to be delivered in a two-hour period can be accommodated in a van. Having ascertained the minimum number of vans needed, a solution is then sought, which minimises the maximum time taken by any van.
On a particular evening, the places where deliveries need to be made and the times to travel between them (in minutes) are given in Table 27.1. No allowance is made for drop off times. For convenience, Heathrow will be regarded as the first location.
Formulate optimisation models that will minimise the number of vans that need to be used, and within this minimum, minimise the time taken for the longest time delivery.
Table 27.1:
|
Heathrow |
20 |
25 |
35 |
65 |
90 |
85 |
80 |
86 |
25 |
35 |
20 |
44 |
35 |
82 |
|
Harrow |
15 |
35 |
60 |
55 |
57 |
85 |
90 |
25 |
35 |
30 |
37 |
20 |
40 |
|
|
Ealing |
30 |
50 |
70 |
55 |
50 |
65 |
10 |
25 |
15 |
24 |
20 |
90 |
||
|
Holborn |
45 |
60 |
53 |
55 |
47 |
12 |
22 |
20 |
12 |
10 |
21 |
|||
|
Sutton |
46 |
15 |
45 |
75 |
25 |
11 |
19 |
15 |
25 |
25 |
||||
|
Dartford |
15 |
15 |
25 |
45 |
65 |
53 |
43 |
63 |
70 |
|||||
|
Bromley |
17 |
25 |
41 |
25 |
33 |
27 |
45 |
30 |
||||||
|
Greenwich |
25 |
40 |
34 |
32 |
20 |
30 |
10 |
|||||||
|
Barking |
65 |
70 |
72 |
61 |
45 |
13 |
||||||||
|
Hammersmith |
20 |
8 |
7 |
15 |
25 |
|||||||||
|
Kingston |
5 |
12 |
45 |
65 |
||||||||||
|
Richmond |
14 |
34 |
56 |
|||||||||||
|
Battersea |
30 |
40 |
||||||||||||
|
Islington |
27 |
|||||||||||||
|
Woolwich |