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
	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
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. You are considering opening only one DC. Which of the five DC’s should you open to minimize total transportation cost?    Due to road conditions, the shelters furthest away from the centre may suffer from late and unreliable deliveries. As a result you are thinking about opening more than one DC. Assuming the military is ok with delivering your supplies to more than one DC, what is the optimal number of DCs?    Suppose it costs $300,000 per week to set up and run a DC. What is the optimal number of DCs? Assume the same transportation costs as in the previous parts of this question.    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?