Writing an Objective Function in Python

[Justin O'Pella]

Hello,

I would like to repost a previous question but with additional critical information that was originally not included. 

I am looking for help coding the objective function (see attached). 

The decision variables are the x_sc's. There are two sets: set S and set C and each pair of the members from S and C form a decision variable x_sc, where x_sc is binary. K is a constant. (I have this value already programmed so this is a non-issue). The e_sc is a parameter obtained from the data supplied to the problem for each pairing of members from S and C. 

One attempt I tried was:

m.setObjective(

....... (quicksum(x_sc['*',c] for c in set_C)) /

....... ((K) - (quicksum(eligibility['*',c] for c in set_C))), GRB.MAXIMIZE)

If you were to expand, the objective function is linear with a fraction as each coefficient.

Any feedback or point toward some documentation is appreciated.

Thanks

Justin

[Daniel Espinoza]

Justin,

If each variable x[s,c] has an objective coefficient c[s,c], , i.e. you want to optimize 

max sum(x[s,c] * a[s,c]: s in S c in C)

then you could use 

m.setObjective(x.prod(a), GRB.MAXIMIZE)

Best,

Daniel

[Justin O'Pella]

Thanks, Daniel!