When a natural disaster strikes, normal supply chains are disrupted and many vital supplies cannot reach those affected through the normal routes. To handle the first few days after the disaster, many specialized Non-Governmental Organizations (NGOs) work hard to secure vital supplies such as food, blankets, and medicines, and deliver these to people in the affected areas. To do so, they set up temporary supply networks, which only operate as long as needed.
Suppose you are working with one such NGO to set up a temporary network to distribute disaster-kits in the aftermath of a hurricane. You have secured kits from your central supply facility that will be flown in regularly. The kits need to be delivered once per week (as long as needed) to eight (8) temporary shelters, which are located a few hours’ drive from the airport.
To simplify the operations, you aim to set up a logistics and distribution centre (DC) to control all distribution. All incoming shipments will be transported from the airport directly to the centre by the military, and from the DC you will plan how the kits are delivered to the shelters.
You are choosing between five (5) locations for the DC. The distances between the five (5) potential locations and the eight (8) shelters are shown in the table below. Assume the outbound transportation cost to be $1/mile/unit.
|
Distances in miles |
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|
Shelter 1 |
Shelter 2 |
Shelter 3 |
Shelter 4 |
Shelter 5 |
Shelter 6 |
Shelter 7 |
Shelter 8 |
|
|
DC 1 |
0.61 |
3.32 |
9.5 |
6.52 |
7.77 |
1.92 |
8.52 |
9.75 |
|
DC 2 |
6.04 |
0.51 |
1.34 |
6.06 |
0.22 |
6.33 |
4.61 |
3.28 |
|
DC 3 |
4.99 |
2.41 |
2.33 |
3.95 |
8.84 |
7.94 |
7.87 |
0.94 |
|
DC 4 |
5.58 |
8.8 |
6.32 |
8.54 |
5.15 |
6.06 |
9.42 |
2.16 |
|
DC 5 |
7.87 |
9.64 |
0.7 |
5.92 |
2.7 |
0.26 |
0.5 |
3.4 |
The weekly demand at each shelter has been estimated as follows:
|
Demand |
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|
Shelter 1 |
Shelter 2 |
Shelter 3 |
Shelter 4 |
Shelter 5 |
Shelter 6 |
Shelter 7 |
Shelter 8 |
|
|
14000 |
8000 |
25000 |
22000 |
20000 |
17000 |
18500 |
23000 |
|
|
The capacity of the DC will be limited to 150,000 kits per week.
When you see the optimal solution from part c (above), you realize that under that solution, much of the demand is more than 2 miles away from a DC. How does the optimal solution change if we require that at least 60% of demand should be less than 2 miles from a DC? |
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