For part of a coding project, I am trying to solve a nonlinear integer program, but my only experience is from school solving LPs and IPs. Here is the problem in words:
I am trying to assign n (in this case n = 1000) workers to 4 different stations. Each station produces a certain number of resources per hour (y1, y2, y3, y4), which is non-linearly dependent on the number of workers assigned. Find the number of workers in each station that will provide the highest total rate of resource production.
Let x1, x2, x3, x4 be the number of workers assigned to stations 1, 2, 3, 4, respectively. A-L are constants. Note that C, F, I, L are negative.
max y1 + y2 + y3 + y4 s.t. y1 = A*x1 + B + C/x1 y2 = D*x2 + E + F/x2 y3 = G*x3 + H + I/x3 y4 = J*x4 + K + L/x4 x1 + x2 + x3 + x4 <= 1000 x1, x2, x3, x4 are positive integers
I am considering solving this by assigning workers one at a time to the station that will provide the largest increase in resource production until either all 1000 are assign or until there is no net increase in production. I believe that this can method can achieve a near-optimal solution since each station's production is independent of other stations' productions.
My question is this: Given that I am fine with a solution that is only close to optimal, is this method good enough? If not, what should I do?
This is the first question that I have asked on math.stackexchange, so I apologize for any errors in formatting or clarity.