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Mathematical Optimization

In: Business and Management

Submitted By rasp11ab
Words 5806
Pages 24
Mathematical Optimization: Models, Methods and Applications
Final Assignment
06-11-2015
Rasmus pages / 13.137 characters (including spaces) |

Part 1
General about part 1
The purpose with this part is to analyze a Single-Sourcing Problem (SSP). A Single-Sourcing Problem of course both has benefits and risks, but I will discuss that furthermore through the assignment. During the assignment I will try to discuss and comment on everything that I do. My code and the answers I receive from www.neos-server.org can be seen in my appendices.
(i)
In the first question in part 1, I am asked to solve the SSP using the data in Figure 1. We have 4 facilities and 30 customers. In Figure 1 the demand of each customer is also given, and of course I will have to satisfy this. Therefore this will become one of my constraints. It is also known that each facility has a capacity, and of course this will become a constraint as well. Because it is a SSP problem, we are also given the information that each customer has to be served by exactly one facility. When a facility delivers one unit to a customer it faces a cost. The purpose with the first question is to minimize the cost that the facility faces delivering the units. I will now show what the problem looks like:
Minimizexi=1mj=1nai,j dj xi,j subject to j=1ndj xi,j≤ci , i=1,…,m i=1m xi,j=1 , j=1,…,n x∈0,1, i=1,…,m , j=1,…, n
Now I have formulated the problem, and I will now use a Mixed Integer Linear Programming solver from www.neos-server.org. As I mentioned earlier my code and the whole answer from the website will be in my appendices.
With the constraints from the first question I get a minimum cost of: 18951. 37
(ii)
In the second question a new constraint has been given. It says that each facility must satisfy at least umin=20 % of the customers. Therefore our problem will now like this:…...

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