Assigning individuals to the roles.

[PaigeMiller]

What is the "total score" in this problem?

[RobPratt]

The total score is the sum of the researcher-paper scores when researcher r is assigned to paper p (that is, when the binary decision variable X[r,p] takes the value 1):

max TotalScore = sum {r in RESEARCHERS, p in PAPERS} score[r,p]*X[r,p];

The input score[r,p] could represent the amount of familiarity researcher r has with the topic of paper p.  Such measures are typical in assignment problems.

[Reeza]

@PaigeMiller it was posted in OR/MS so an OR solution seems appropriate. 

[PaigeMiller]

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@Reeza wrote:

@PaigeMiller it was posted in OR/MS so an OR solution seems appropriate. 

---

I think that something like Occam's razor ought to be used here. Occam's razor adjusted for programming: The simplest code that meets the requirements is the winner. PROC OPTMODEL is fine if it is necessary, but I don't see any statement from the OP that requires a PROC OPTMODEL solution.

[t75wez1]

Hello Rob,

Could you demystify the constraint statement below?

What does the "card" mean here?

Thanks,

" con EqualWorkload {r in RESEARCHERS}:
floor(2*card(PAPERS)/card(RESEARCHERS)) <= sum {p in PAPERS} X[r,p] <= ceil(2*card(PAPERS)/card(RESEARCHERS)); "

[RobPratt]

The CARD operator returns the cardinality of the set.  For your example, card(RESEARCHERS) = 3 and card(PAPERS) = 400, so that ratio is the target workload of each researcher.  More explicitly:

   num targetWorkload = 2*card(PAPERS)/card(RESEARCHERS);
   put targetWorkload=;
   con EqualWorkload {r in RESEARCHERS}:
      floor(targetWorkload) <= sum {p in PAPERS} X[r,p] <= ceil(targetWorkload);

The PUT statement reports targetWorkload=266.66666667 in the log, and the constraint enforces the assignment of either 266 or 267 papers to each researcher.

[t75wez1]

Hello Rob,

What does X[r,p]>0.5 (in the CREATE statement below) exactly function here?

I tried changing it to 0.1 or 0.3 then it makes no difference in result.

Could you enlighten me?

Thanks,

"create data SolutionData from [researcher paper]={r in RESEARCHERS, p in PAPERS: X[r,p].sol > 0.5} score;"

[RobPratt]

That is just a safe check for which binary decision variables take the value 1 in the resulting optimal solution.  The variable's value can differ from 0 or 1 by a small integer feasibility tolerance (default value is 1e-5).  Yes, you should see the same behavior if you use > 0.5 or > 0.1 or > 0.3 or > 0.99 or > 0.0001, etc.  But you should not use instead X[r,p].sol = 1 as the logical condition unless you first round the solution.  Alternatively, round(X[r,p].sol) = 1 would also be safe.

[t75wez1]

Thanks so much for the superb solution!

[Reeza]

And the SURVEYSELECT method.

data want;
set sashelp.class;


array _ran(3) a b c; *a, b, c are the names of the reviewers;

do i=1 to 3;
    _ran(i) = ranuni(25);
end;

first_reviewer = vname(_ran(whichn(smallest(1, of _ran(*)), of _ran(*))));
second_reviewer = vname(_ran(whichn(smallest(2, of _ran(*)), of _ran(*))));


drop a b c i;

run;

Problem is formulated as choose 2 per paper, where you've created a data set with all three reviewers per paper. 

[WarrenKuhfeld]

A design that approximates a balanced incomplete block design should do the trick. A fully balanced design is not possible with 400 papers and your other constraints. All you need is one simple line:

%mktbibd(b=400,k=2,v=3)