Extended introduction

The mission of the Stochastic Operations Research group (SOR) is to conduct mathematical education and research of internationally high standards in the areas of stochastic processes and mathematics of operations research, to contribute to the development of mathematics in a multidisciplinary engineering environment, and to contribute to a better understanding and functioning of our increasingly complex society.

Operations Research is the development of mathematical models and methods for the design, control and optimisation of complex systems. Within this broad field, SOR focuses on mathematical challenges in the area of stochastic processes and its engineering environment in societally relevant areas of application. SOR’s fundamental mathematical areas of expertise include probability theory, with emphasis on stochastic processes, and random graphs. The bridge to engineering applications is established through areas of expertise that include the theory of games, stochastic dynamic programming, queues, polling systems, large deviations and discrete event simulation. Typical application areas are in communications (wireless ad-hoc networks, sensor networks, energy minimization in networks, ranking algorithms in complex networks), social and professional networks (virus spread, collaboration, citation structure), transportation, production & logistics (facility location, supply chains, production systems, inventory management, road traffic), and health care (patient logistics and medication).

Communications systems

In modern communications systems, Internet and World Wide Web are closely intertwined with the telecommunications infrastructure. Connections in these systems may be wired or wireless, may have high or low bandwidth and may be reliable or unreliable. In modern networks, the connection infrastructure is of utmost importance for network reliability. Typical problems include the design of networks that allow reliable connections, design of energy efficient routing algorithms, and routing algorithms that guarantee delay constraints. The resulting networks have applications in smart dust sensor networks in which huge amounts of small sensors with limited communication capabilities are deployed to monitor remote areas, and in networks for emergency services where an area struck by a catastrophe is entered by emergency personnel connected via wireless devices with limited bandwidth rely on status reports. Performance modeling and analysis of these networks is based on properties of the underlying random graph structure combined with queueing models for network delays.

Social and professional networks

Social networks such as Facebook or LinkedIn are gaining importance in daily life. Searching the World Wide Web for desired information is part of our daily routine. Citation and collaboration networks become increasingly important to quantify the quality of research groups and individual researchers. The underlying networks are characterized by their scale-free topology in which hubs – the nodes with extremely high number of connections – play an important role. Typical problems include design and analysis of algorithms for web search and ranking, assessment of scholarly work, prevention of epidemics in computers and humans, and spread of trust and influence in social networks. Attacking these problems requires a careful combination of closely related but so far unconnected areas: development and empirical studies of network algorithms in computer science, and analysis of network connectivity and distances within the mathematical theory of random graphs.

Transportation, production & logistics

In modern society, work, living, leisure and the environment are becoming more and more intertwined. Households will use Internet for shopping, thus changing the entire supply chain from localized to distributed chains, which in turn affects mobility patterns. Road status information sent via the communications system will allow active steering of road traffic to minimize delay and pollution. This will also be the case in large transportation systems such as container or flower distribution, where next generation RFIDs (wireless sensor networks) build up a distributed communication system. Seemingly independent elements of societal and business life will become more and more interrelated. The modern urbanized society will become a single self-organizing system. Typical problems include development of cooperative distribution schemes for cities such that e.g. only a single truck will deliver goods in one street, and design of routing schemes for both messages and goods to minimize transportation delay (Internet of Things). Such problems may be addressed via a combination of game theory and queueing theory to integrated fair cost allocation into delay sensitive systems.

Health care logistics

Health care expenditures in the Netherlands may increase from roughly 10% of GDP in 2010 to roughly 20% in 2035. This increase is to a large extent due to our ageing population in which the percentage of people over 65 will increase from roughly 15% to roughly 25% in the same period. Sustaining the current quality of care seems to require a rapidly increasing percentage of the work force to be employed in the health care sector. However, there already is a shortage in health care staff such as nurses, and it is not likely that this shortage will be reduced. Typical challenges include efficient planning of operating theatres, balancing the number of patients in wards to reduce peaks and therefore increase the efficiency of nursing care, efficient rostering of staff to allow for more work to be done by the same number of people. Addressing these challenges may be based on queueing theory, dynamic programming, game theory, and discrete event simulation.

Application and implementation approach

Employing Operations Research techniques seems to be dedicated to improving efficiency, at the same time improved efficiency leads to increased job satisfaction as experienced work load is often dominated by those moments at which the work pressure is very high, and it also improves patient safety since errors due to peak work load will be avoided. Health care is in dire straits. Fortunately, more and more health care organizations are realizing that Operations Research may provide an approach to sustain our health care system. Such an approach requires close collaboration between Operations Research specialists and health care professionals to tackle resource optimization challenges of the health care sector and implement their solutions in health care organisations.