Integer Programming/Investment Problem/Network Flow Models

All problems to be submitted for assessment (10%)
All assignments should be typed and submitted through Blackboard. For each question you should:

Define your decision variables.
Provide your complete formulation for the problem (objective function, 
constraints and conditions on the decision variables).
Provide the optimal solution obtained using Solver. You are required to 
state the optimal value of the decision variables and, in simple English, the optimal solution with reference to the context (For example, X1=2 and therefore, the company should build 2 5-star hotels…).
Provide a screen shot of your Excel model with the optimal solution.

Question 1:

You are in charge of loading Cargo ships in Newcastle port. An agricultural commodities dealer wants to transport the following products aboard a ship:

You can select to load any and/or all of the available commodities. However, the ship has three cargo holds with the following capacity restrictions:

Only one type of commodity can be placed in any cargo hold. However, because of balance considerations, the weight in the forward cargo hold must be within 15% of the weight in the rear cargo hold. In addition, the center cargo hold must be between 40% and 60% of the total weight on board.

Formulate an ILP model for the problem and solve it using a spreadsheet.

Question 2:

You are given the option to invest 1 million dollars in 5 different investments. The returns, risk factors and maturity in years are given in the following table:

You would like to maximize the return while minimizing the risk and years to maturity. Higher risk factors mean higher risk.
1. Formulate an MOLP model for this optimization problem. Determine the best outcome for each objective and set appropriate goals.
2. What is the optimal investment strategy if you would like to minimize the sum of percentage deviations from all 3 goals?
3. What is the optimal investment policy if maximizing returns is twice as important as minimizing risk and maturity? Use the minmax function to obtain this policy.

Question 3:

You have been put in charge of training new employees (trainees) at a commercial bank. In order to fill the role of an investment consultant each trainee must successfully complete a sub-set of 6 available courses (A, B, C, D, E, F). There are four different sequences of courses that can be taken in order to achieve the required skill level. These sequences are A-E, B, C-F, and A-D-F. The table below provides information on the six courses.

There are 100 new trainees available for training and a demand for 100 skilled investment consultants. Assume all employees (trainees) pass each course they are allocated to and that you are trying to assign trainees to classes in order to minimize the total cost of training. Assume each course will be held.

In addition to the formulation, solution and Excel output you should provide the network flow diagram describing the problem and address the following questions:

What is the expected student load for each course?
Should any course be expanded?
Should any course or sequence be considered for elimination?

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