Optimizing Humanitarian Relief Networks
As a manager in a humanitarian organization, your objective is to reach out to citizens across a
vast geographical region. You need to reach out to people in 6 different camps, each with their
own transportation requirements, and needs. The demand for packages of basic needs in each
camp is given below:
Camp 1 Camp 2 Camp 3 Camp 4 Camp 5 Camp 6
Dry
Food
6,000 4,500 6,700 4,700 4,300 6,000
Fuel 3,000 2,500 3,000 3,000 2,700 3,800
Medical
Supply
800 560 650 700 560 600
Camps 1 and 2 are in region A, camps 3 and 4 are in region B, and camps 5 and 6 are in region C.
Each region has a processing center that would fill its capacity with 30,000 units of dry food,
15,000 units of fuel, or 6,000 units of medical supply. To ensure that all camps are treated equally,
camps in each region must have at least 20% of the dry food, 20% of the fuel and 20% of the
medical supply supplied from your organization. In addition, each camp must have at least 10%
of the total amount of supply packages provided from your organization. Your organization can
purchase dry food, fuel and medical supply for unit price of 40$, 25$, and 120$, respectively. The
shipment costs from your organization’s headquarters to each processing center and camp is
given below:
Headquarter Processing Center,
Region A
Processing Center,
Region B
Processing Center,
Region C
Processing Center,
Region A
$10/unit
Processing Center,
Region B
$16/unit
Processing Center,
Region C
$14/unit
Camp 1 $16/unit $4
Camp 2 $13/unit $2
Camp 3 $28/unit $11
Camp 4 $24/unit $5
Camp 5 $18/unit $6
Camp 6 $20/unit $5
Any supply that is not shipped from your organization can be acquired locally around the camps,
but they would cost 100% more, i.e. dry food, fuel and medical supply would cost 80$/unit,
50$/unit, and 240$/unit, respectively. Find the routing that would minimize the total cost.
Your report should include the following:
• Mathematical formulation
o Define decision variables.
o Formulate objective function and constraints.
• Computer solution: Solve the problem using Xpress. The mosel file should be named
according to the following convention: <accessID1>_<Case1 >.mos
• Conclusion (a paragraph)