MTH309 - Transport and Network Models - Integer Programming Problem - Mathematics Assignment Help

Assignment Task

Question 1
A company sells computers to universities around Australia and ships them from three distribution warehouses. The company is able to supply the following numbers of computers by the beginning of the academic year:
Warehouse Supply
1 Sydney        420
2 Brisbane     610
3 Melbourne  340
Total 1370

Four universities have ordered computers:

University Demand
A Griffith 520
B Federation 250
C Charles Sturt 400
D Canberra 380
Total 1550

a. Show how you would start to solve the problem using the transportation simplex method (Section 2.1, Section 2.2.1) by constructing the initial tableau and using the minimum cell cost method to find an initial feasible solution. You do not need to solve the full problem using this method.
 

b. Formulate this as an integer programming problem (Section 2.3) and hence find the solution using a linear programming tool such as LPSolve. In your answer you must:
Introduce appropriate variables and briefly describe what they mean. It is fine to describe a collection of indexed variables generically rather than making an exhaustive list. Define the objective function and briefly describe it.

• Introduce constraints and briefly explain them.
• Solve the problem with a software tool. You must show the input and output from the tool.
• Provide a brief concluding statement summarising your findings.

Question 2 
Each day a fishing company makes deliveries to four restaurants it supplies in the metropolitan Sydney. The service uses one truck that starts at the warehouse, makes a
delivery to each restaurant, and then returns to the warehouse. The distance (km) between the warehouse (Location 1) and each of the restaurants (Locations 2, 3, 4, and 5) is shown in the following table:

The aim is to determine the route the truck should take to start at the warehouse, visit each restaurant once, and return to the warehouse while minimising the total
distance traveled.

a. Draw a graph illustrating the situation. You must label all nodes and include the appropriate weight on each arc connecting them. Since the weights (distances) are
the same in both directions you do not need to include arrows.

b. Formulate this as an integer programming problem. In your answer you must
Introduce appropriate variables and briefly describe what they mean. It is fine to describe a collection of indexed variables generically rather than making an exhaustive list.

• Define the objective function and briefly describe it.
• Introduce constraints and briefly explain them.

c. Solve the problem using an integer simplex method to find the route and and the minimum total distance. You will need to use a linear programming tool such as
LPSolve. All working, computer input and computer output must be shown and you must provide a brief concluding statement to summarise your findings.

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