grant-strategy.jl

# Purpose: This is just a play model to think about time spent on large and big grants/opportunities and 
#    overall likelihood of a successful result (undefined, just general feel).
#    2080 is the hours in a year if working 40 hours (because everyone does that...)

using JuMP
using Ipopt
model = Model(Ipopt.Optimizer)

p1 = .05 # Probability of winning grant 1
sx1 = .4 # Probability of successful work (class 1)
sx2 = .85 # Probability of successful work (class 2)

"""
maximize x*p1*sx1 + y * p2*sx2 (probability of a successful project)
s.t. 
    # Time to building proposals (i.e. 160 per small, 320 per large, work = time * success*number)
    x * 160 + y * 320 + p1*x*400 + p2*y*1000 <= 2080

    # No more than 12 small opportunities, no more than 5 large opportunities
    12 >= x >= 0
    5 >= y >= 0
    p1 = .1
    p2 = .01
"""

@variable(model, 12 >= x >= 0)
@variable(model, 5 >= y >= 0)
@variable(model, p2 >=.01)
@objective(model, Max, x*p1*sx1 +  y * p2*sx2)
@constraint(model, c1, x * 160 + y * 320 + p1*x*400 + p2*y*1000 <= 2080)
@constraint(model, c2, p2 == .01)
print(model)
optimize!(model)
@show termination_status(model)
@show primal_status(model)
@show dual_status(model)
@show objective_value(model)

println("apply to:", round(value(x)), " small grants\napply to:", round(value(y))," large grants")
println("Win: ",round(value(x)*p1, digits = 2), " small grants")
println("Win: ",round(value(y)*value(p2), digits = 2), " large grants")
println("success probability: ", round(objective_value(model)*100),"%")

apply to:12.0 small grants
apply to:0.0 large grants
Win: 0.58 small grants
Win: 0.0 large grants
success probability: 23.0%