Jimbo's Java & Jerk has a portfolio of 9 proposed projects over a 5 year planning horizon. Unfortunately, the total requested funding (all amounts specified in millions) is $2102 and Jimbo's has only $1301 available for funding projects during the next 5 years.

In order to maximize the value of Jimbo's project portfolio, Caitlin Elizabeth, a project office analyst responsible for the project selection and funding process, wants to determine the funding that will maximize the ECV of the company's proposed projects. The table below (all monetary values shown in $ millions) shows the funding requests for 9 projects. Additionally, the table includes the ECV for every project and the available funds for each of the 5 years in the planning horizon. When selecting and awarding funding to projects, the available funds must not be exceeded in any year. Additionally, the company has has decided to cap IT project funding; IT projects may not exceed 50% of total funds awarded (i.e. allocated projects) over the entire planning horizon. The following are classified as IT projects: 2, 3, 5, 6, 8.

Caitlin has confirmed that projects may be partially funded and that the ECV realized for partially funded projects will be proportional to the project's allocated funding relative to its requested funding. Help her out by formulating a mathematical program to select an optimal funded project portfolio. Let Z1, Z2, ..., Z9 be the percentage of the funding request awarded (i.e. funded) for projects 1, 2, ..., 9 respectively. Because decision variable values represent percentages, all decision variable values must be in the range [0, 1]. However, these domain constraints are simple enough that Caitlin can handle defining them (you do not need to specify these "domain" constraints in your formulation, although you would have to include them in your MP setup if you wish to actually find the optimal funding for the proposed projects). Caitlin only needs you to formulate the following:

1. Objective function 2. Annual budget constraints (i.e. available funds constraints) 3. IT funding constraint.

Note: when specifying the mathematical expressions, you must explicitly specify multiplication (e.g. specify 20Z1 as 20 * Z1).

Objective Function: ?

max/min?

Subject To

Budget year 1: ________ = __________

Budget year 2: ________ = __________

Budget year 3: ________ = __________

Budget year 4: ________ = __________

Budget year 5: ________ = __________

IT Funding: ________ = __________

Project 1 2 3 4 5 6 7 8 9 Available Year 1 0 106 0 45 0 36 0 0 0 106 Year 2 0 47 0 104 0 19 0 65 0 157 Year 3 35 92 91 54 26 98 125 92 0 385 Year 4 111 0 43 101 110 46 93 52 0 343 Year 5 93 0 0 57 49 74 12 114 112 310 ECV 0.368 0.082 0.89 0.743 0.701 0.746 0.485 0.249 0.867 Project 1 2 3 4 5 6 7 8 9 Available Year 1 0 106 0 45 0 36 0 0 0 106 Year 2 0 47 0 104 0 19 0 65 0 157 Year 3 35 92 91 54 26 98 125 92 0 385 Year 4 111 0 43 101 110 46 93 52 0 343 Year 5 93 0 0 57 49 74 12 114 112 310 ECV 0.368 0.082 0.89 0.743 0.701 0.746 0.485 0.249 0.867