Coffa is a Sicilian distributor of canned tuna. It is interested in opening a new warehouse in the province of Siracusa. Avola and Buccheri are the two potential locations of the warehouse, shown by a preliminary analysis.
If the warehouse is located in Avola, the annual total facility cost is € 127 500, whereas if it is located in Buccheri, this cost is € 123 000. The goal is to supply, four days a week, all dealers located in the following cities: Syracuse, Augusta, Avola, Buccheri, Ferla, Lentini, Melilli, Noto, Pachino and Priolo. Due to the limited capacity of the vehicles, transport is carried out with a single trip from the warehouse to each of the cities listed above (door-to-door transport). The distances (in km) between the cities are listed in given Table.
Formulate and solve the location problem by assuming 200 working days in a year and a transport cost per km equal to € 0.95.
Furthermore, assume that it is possible to determine the warehouse location in an alternative way, by using the centre of gravity. To this end, use the Cartesian coordinates reported in the last two columns of given Table.
Table: Distances (in km) between the 10 cities and Avola and Bucchcri, respectively, as well as their Cartesian coordinate in the Coffa problem.
|
|
|
Avola
|
Buccheri
|
Abscissa
|
Ordinate
|
|
Siracusa
|
25
|
55
|
7.8
|
7.7
|
|
Augusta
|
56
|
54
|
6.6
|
11.4
|
|
Avola
|
0
|
57
|
5.2
|
4.3
|
|
Buccheri
|
57
|
0
|
0.0
|
9.0
|
|
Ferla
|
52
|
12
|
1.7
|
8.9
|
|
Lentini
|
67
|
35
|
2.8
|
12.6
|
|
Melitti
|
45
|
36
|
5.0
|
10.2
|
|
Noto
|
9
|
45
|
4.0
|
3.9
|
|
Pachino
|
26
|
69
|
4.3
|
0.0
|
|
Priolo
|
38
|
59
|
6.1
|
9.6
|
According to this approach, the optimal warehouse location is that with the minimum Euclidean distance from the centre of gravity among the 10 cities (one can restrict the selection to the best three candidate cities by visually inspecting Figure).
