View the model
Download the model

Minimize the unordered lexico-max of the X( j)
subject to given constraints on the X( j).
I.e., find the X(j) so largest X( j) is minimized,
subject to that, minimize the sum of the 2 largest,
subject to that, minimize the sum of the 3 largest, etc.
Variables:
X( i)) = penalty (less is better) incurred by party i,
klrgst( k) = kth largest X(i) when minimizing the
sum of the k largest X(i),
delta(i,k) = amount by which X(i)
is greater than klrgst(k) when minimizing the
sum of j largest, = 0 if <= klrgst( k);

References:
Serafini, P. (1996), "Scheduling Jobs on Several Machines with the Job Splitting Propert",
Operations Research, Vol. 44, No. 4, (July-August), pp. 617-628.
Maschler, M., B. Peleg, and L. S. Shapley (1979), "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts", Mathematics of Operations Research,
vol. 4, No. 4 (Nov), pp. 303-338.