We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of...

We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the...

We consider the problem to price (digital) items in order to maximize the revenue obtainable from a set of bidders. We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we derive a PTAS. We also discuss a special case, the highway pricing problem.

We consider machine scheduling problems where jobs have to be processed on unrelated parallel machines in order to minimize the schedule makespan. The processing time of any job is dependent on the usage of a scarce resource that can be distributed over the jobs in process. The more of that...

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation...

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation...

We consider a Stackelberg pricing problem in directed networks:Tariffs (prices) have to be defined by an operator, the leader, for a subset of the arcs. Clients, the followers, choose paths to route their demand through the network selfishly and independently of each other, on the basis of...

We study the problem of scheduling maintenance services. Given is a set of mmachines and integral cost-coefficients ai and bi for each machine i (1 i m). Timeis discretized into unit-length periods; in each period at most one machine can beserviced at a given service cost bi. The operating...

This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as Group-TSP or TSP with neighborhoods. We prove that under the...

This paper is concerned with a special case of the Generalized Minimum Spanning Tree Problem. The Generalized Minimum Spanning Tree Problem is de¯ned on an undirected graph, where the vertex set is partitioned into clusters, and non-negative costs are associated with the edges. The problem is...