The uLexMinMax02.lng Model

Unordered LexicoMinMax procedure

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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.

Keywords:

Fair Allocation | Minimax | Goal Programming | Multi-criteria | Lexico-min | Unordered lexico-min |