An Optimization Approach on 'How to Create a Succesful Consortium for Grant Writing?'

As an academic staff, we do need to attract funding from different resources. This money is going to be used for research, developing human capacity, educational purposes and etc. Some of the funding agencies seek (and encourage) to receive proposals from multi-national consortiums. Now the story begins.

Suppose you are the lead institute (bad cop) to write this proposal. The frist step is to select who might be suitable to join the consortium. Every institute has a unique skillset, reputation and availability. The following graph shows the weight of each entity in the available pool of options (various available partners with different weights (size of each circle) ):

Suppose we need to select 12 members in this pool. One trivial answer is choosing the 12 largest?weights?(reputation + skills) to maximize the chance of winning the grant. However, as you know collaboration is constructive?most of the time but not?Always.

The following graph shows the collaborative impacts of the partners. The graph shows how two partners might improve the quality of the proposal if they both exist in the consortium (green link) or how they deteriorate it (red link).

Here is the photo of the PI in the lead institute who intends to choose the right team and prepare the proposal before the approaching deadline.

The difficulty is to find a solution (or a set of solutions) that not only maximizes the weight of the consortium but also increases the value of collaboration (ease of working, improving the quality, less difficult conversations). So the manager decided to use an optimization approach.

The operation research expert wrote the following set of equations to describe the optimization problem:

• How to maximize the total weight values as well as the collaboration values by selecting the right partners (12 of them).

Where

• w_i is the weight of each partner?
• V_{i,j} is the added value of partner i collaborating with partner j?
• OF1= Total Collaboration Value?
• OF2= Total individual weight Value?
• x_i is a binary variable to select/not select partner i?
• Z_{i,j} is a real value (0,1) to linearize x_i * x_j?
• epsilon is a threshold for OF2 which is gradually updated to obtain all pareto optimal solutions

Here is the pyomo code :

As a result, a set of Pareto optimal solutions are found and the PI can select the appropriate one (depending on how he/she cares about the individual skills or collaborative gains)

I know some might say why don't you sum the OF1 and OF2 and then maximize the overall objective, Unfortunately, I could not add oranges to the apples. If you can please kindly let me know.

The same approach can be followed for selecting any team members, how to fill your backpack for a trip, how to select the animals to be saved by your ship, selecting your friends for a party, etc.

Here is the photo of PI after solving the problem.

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