Morten Riis

Capacitated Network Design with Uncertain Demand

We consider a capacity-expansion problem arising in the design of telecommunication networks. The problem is to install capacity on links of the network so as to meet customer demand while minimizing total costs incurred. When studying this and related problems it is customary to assume that point-to-point demands are given. This will not bethe case in practice, however, since future demand is generally unknown and the decision must be based on uncertain forecasts. We develop a stochastic integer programming formulation of the problem and propose an L-shaped solution procedure based on well-known cutting-plane procedures for the deterministic problem. The algorithm was tested on two sets of real-life problem instances and we present results of our computational experiments.

Applying the Minimum Risk Criterion in Stochastic Recourse Programs

In the setting of stochastic recourse programs, we consider the problem of minimizing the probability of total costs exceeding a certain threshold value. The problem is referred to as the minimum risk problem and is posed in order to obtain a more adequate description of risk aversion than that of the accustomed expected value problem. We establish continuity properties of the recourse function as a function of the first-stage decision, as well as of the underlying probability distribution of random parameters. This leads to stability results for the optimal solution of the minimum risk problem when the underlying probability distribution is subjected to perturbations. Furthermore, an algorithm for the minimum risk problem is elaborated and we present results of some preliminary computational experiments.

Multiperiod capacity expansion of a telecommunications connection with uncertain demand

We consider multiperiod capacity expansion of a telecommunications connection with uncertain demand. We present a new preprocessing rule which drastically reduces computation time of an existing algorithm for a two-stage formulation of the problem. Also, an alternative multistage formulation of the problem is given and we elaborate a recursive solution procedure. Both algorithms have been implemented in C++, and we present the results of a series of computational experiments, demonstrating the effect of the new preprocessing rule and the practicability of the multistage procedure.

Applying the minimax criterion in stochastic recourse programs

We consider an optimization problem in which some uncertain parameters are replaced by random variables. The minimax approach to stochastic programming concerns the problem of minimizing the worst expected value of the objective function with respect to the set of probability measures that are consistent with the available information on the random data. Only very few practicable solution procedures have been proposed for this problem and the existing ones rely on simplifying assumptions. In this paper, we establish a number of stability results for the minimax stochastic program, justifying in particular the approach of restricting attention to probability measures with support in some known finite set. Following this approach, we elaborate solution procedures for the minimax problem in the setting of two-stage stochastic recourse models, considering the linear recourse case as well as the integer recourse case. Since the solution procedures are modifications of well-known algorithms, their efficacy is immediate from the computational testing of these procedures and we do not report results of any computational experiments.

A bicriteria stochastic programming model for capacity expansion in telecommunications

Abstract. We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the probability of future capacity requirements to be violated are simultaneously minimized. Assuming the existence of a finite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm determines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three different problem instances, one of which is a real-life problem faced by SONOFON, a Danish communications network operator.

Deployment of Mobile Switching Centers in a Telecommunications Network: A Stochastic Programming Approach

We consider a network design problem arising in mobile communications. At the core of the network is a number of mobile switching centers (MSCs), each serving a number of base station controllers (BSCs). The network design problem involves three major groups of decisions – deployment of a number of new MSCs, allocation of BSCs to new and existing MSCs, and capacity expansion of transmission links interconnecting the MSCs. These decisions must be made so as to minimize the incurred costs while meeting customer demand and observing the capacity restrictions. We formulate the problem as a two-stage stochastic program with mixed-integer recourse. To solve the problem we apply a dual decomposition procedure, solving scenario subproblems by means of branch and cut. The solution procedure has been tested on a real life problem instance provided by SONOFON, a Danish mobile communication network operator, and we report results of our computational experiments.

Internet protocol network design with uncertain demand

We present a case study concerning the design and dimensioning of the internet protocol network of TDC, the largest Danish network operator. Due to historical reasons the number of points of presence (POPs) in the network has reached a level, believed to be too high. To point out potential POPs for dismantling, we consider a network planning problem concerning dimensioning of the POPs and capacity expansion of the transmission links of the network. This problem is formulated as a two-stage stochastic program using a finite number of scenarios to describe the uncertain outcome of future demand. The problem is then solved by an L-shaped algorithm, and we report results of our computational experiments.

Audio Satellites: Overhearing Everyday Life

The project “Audio Satellites – overhearing everyday life” consists of a number of mobile listening devices (audio satellites) from which sound is distributed in real time to a server and made available for listening and mixing through a web interface. The audio satellites can either be carried around or displaced arbitrarily in a given landscape. In the web interface, the different sound streams from the individual satellites can be mixed together to form a cooperative soundscape. The project thus allows people to tune into and explore the overheard soundscape of everyday life in a collaborative and creative process of active listening.