Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Algorithms for optimal price regulations

Since summer 2007, mobile phone users in the European Union (EU) are protected by a ceiling on the roaming tariff when calling or receiving a call abroad. We analyze the effects of this price regulative policy, and compare it to alternative implementations of price regulations. The problem is a three-level mathematical program: The EU determines the price regulative policy, the telephone operator sets profit-maximizing prices, and customers choose to accept or decline the operator’s offer. The first part of this paper contains a polynomial time algorithm to solve such a three-level program. The crucial idea is to partition the polyhedron of feasible price regulative parameters into a polynomial number of smaller polyhedra such that a certain mprimitive decision problem can be written as an LP on each of those. Then the problem can be solved by a combination of enumeration and linear programming. In the second part, we analyze more specifically an instance of this problem, namely the price regulation problem that the EU encounters. Using customer-data from a large telephone operator, we compare different price regulative policies with respect to their social welfare. On the basis of the specific social welfare function, we observe that other price regulative policies or different ceilings can improve the total social welfare.\u