Originally posted by: Sultan_Niz7755

Hello everyone,

I have a problem with stochastic optimization. 
I have created a patient scheduling model. It is analogous to a dual bin-packing problem. The model assigns patients to OR by surgical specialties. 
My objective function tries to maximize number of assigned patients. 
// Decision variable
dvar boolean X[Patient][ORooms][Specialty][Day];
// Objective function
maximize sum(p in Patient, r in ORooms, s in Specialty, d in Day) X[p][r][s][d];
And I have several constraints. All parameters are discrete.  It is wroking fine.

In the next step, I should use random values for operation duration(stochastic duration). I have to implement the model with sample average approximation(SAA). I saw examples of stochastic optimization and added scenarios for operation duration and changed objective function like this: 
// Decision variables
dvar boolean X[Patient][ORooms][Specialty][Day][Scenario]; 

// Objective function
maximize (1 / scenarios) * sum(p in P, r in ORooms, s in S, d in Day, sc in Scenario) X[Patient][ORooms][Specialty][Day][Scenario];

I use operation duration only in one constraint to check capacity. Other constraints check is patient assigned correctly or not ... 
// this constrain checks: is the total duration of operations on exact day smaller than capacity of the selected operation room.
    forall(sc in Scenario, r in ORooms, s in Specialty, d in Day)
      constraint2:
      sum(p in Patient) DurationsWithScenario[p.id][sc] * X[p][r][s][d][sc] <= r.capacity * Y[r][s][d];  

MY PROBLEM IS THAT IS IT ENOUGH FOR SAMPLE AVERAGE APPROXIMATION? 

Hi,

as said at

https://en.wikipedia.org/wiki/Stochastic_programming

The SAA problem is a function of the considered sample and in that sense is random. For a given sample ξ 1 , ξ 2 , … , ξ N {\displaystyle \xi ^{1},\xi ^{2},\dots ,\xi ^{N}} the SAA problem is of the same form as a two-stage stochastic linear programming problem with the scenarios ξ j {\displaystyle \xi ^{j}} ., j = 1 , … , N {\displaystyle j=1,\dots ,N} , each taken with the same probability p j = 1 N {\displaystyle p_{j}={\frac {1}{N}}} .

So your approach looks good.

Tiny example of stochastic optimization at https://www.ibm.com/developerworks/community/forums/html/topic?id=7ce856ee-be78-4258-aede-fd9c4c9e464c&ps=25

regards

Originally posted by: Sultan_Niz7755

Hello, dear Alex Fleischer,

Thank you very much. 

I have to check it, I am not sure is it working correctly or not.

It is working fine with a small set of data, but it is difficult to represent the efficiency of stochastic optimization with the small data. Problem is that It takes too much time for a bigger set of data. Even I have not got a solution in 11 hours. 

Can you give me advice/

Thank you in advance.

Best regards,

Sherzod

Hi,

if the submodel has only float decision variables you may try automatic CPLEX Benders decomposition.

regards

Originally posted by: Sultan_Niz7755

Hi,

Ok, I will try. Thank you very much.

Best regards,

Sherzod