The MCknapuLexMxMn.lng Model


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Unordered Lexico Maximization of Muli-Criteria. ! (MCknapULexMxMn.lng)
Given a number of participants(parties/criteria), each with their own objective or utility function, we want to find a solution to a shared problem so that the smallest utility is maximized, given that, the second smallest utility is maximized, given that, the third etc...
It follows that the solution is Pareto optimal.
The specific shared problem is to allocate a number of discrete items from an inheritance to the heirs, with each heir having her own set of values for each of the items to be allocated;

Serafini, P. (1996), "Scheduling Jobs on Several Machines with the Job Splitting Property", 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.


Allocation | Knapsack Model | Pareto Optimal | Fair Allocation | Lexico-max | Minimax | Assignment Problem | Unordered Lexico max | Inheritance | Goal Programming | Preemptive Goal Programming | Multi-criteria | Nucleolus |