On the multicriteria allocation problem
We consider multicriteria allocation problems with linear sum objectives. Despite the fact that the single objective allocation problem is easily solvable, we show that already in the bicriteria case the problem becomes intractable, is NP-hard and has a non-connected efficient set in general. Using the equivalence to appropriately defined multiple criteria multiple-choice knapsack problems, an algorithm is suggested that uses partial dominance conditions to save computational time. Different types of enumeration schemes are discussed, for example, with respect to the number of necessary filtering operations and with regard to possible parallelizations of the procedure.
multicriteria optimization combinatorial optimization location-allocation problem