The generalized assignment problem (GAP) examines the maximum profit assignment of jobs to processors such that each job is assigned to precisely one processor subject to capacity restrictions on the processors. Due to the fact that the GAP is an NP-hard integer program dual prices are not...

The multiple-choice nested knapsack problem (MCKP) is a generalization of the ordinary knapsack problem, where the set of items is partitioned into classes. The binary choice of selecting an item is replaced by taking exactly one item out of each class of items. Due to the fact that the MCKP is...

In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant...

Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices a set of item prices is called market clearing or equilibrium if all the winning bids are greater than or equal and if...

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity....

The thesis considers an investor's problem of optimal consumption and portfolio choice in a financial market. The model used for the financial market is the semimartingales model. The thesis shows that an optimal solution to this problem exists, even if the investor is contrained in the...