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 couple of 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 affect 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 center (DC) that controls all distribution. All incoming shipments will be transported from the airport directly to the center 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.
The weekly demand at each shelter has been estimated as follows:
The capacity of the DC will be limited to 150,000 kits per week. It costs $100,000 per week to set up and run a DC.
Trucks that can operate on the roads after the hurricane are in short supply, so you want to choose the location of the DC to minimize the transport work (tonkm, or the total kit-miles travelled) in the temporary network. Note that transport work per kit is proportional to distance.
Which of the five locations should the NGO choose to minimize the transport work in the temporary network?
Due to road conditions, the shelters furthest away from the center may suffer from late and unreliable deliveries. As a result you are thinking about opening more than one DC.
To trade-off the fixed costs with the variable costs, you estimate that each transported mile costs $2 per kit.
Assuming the military is ok with delivering your supplies to more than one DC, what is the optimal number of DCs?
You realize that the actual cost of setting up and operating a DC is not perfectly known. What is the optimal number of DCs if the fixed costs are instead $300,000 per week per DC? Assume the same transportation costs as in Part 2.
When you see the optimal solution from Part 3, 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?
The optimal number of DCs increases
It is optimal to open DC 2 and DC 5
The optimal number of shipments to Shelter 7 increases