Consider a situation in which a company sells several different items to a set of customers. However, the company is not satisfied with the current pricing strategy and wishes to implement new prices for the items. Implementing these new prices in one single step mightnot be desirable, for...

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...

The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is (weakly) NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so...

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...

Mixed model assembly systems assemble products (parts) of differenttypes in certain prespecified quantities. A minimal part set is a smallestpossible set of product type quantities, to be called the multiplicities,in which the numbers of assembled products of the various types are inthe desired...

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 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...

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...

We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time...

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...