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We consider a Markov Chain in which the state space is partitioned into sets where both transitions within sets and between sets have a special structure. Transitions within each set constitute a finite level dependent quasi-birth-and-death-process (LDQBD), and transitions between sets are restricted to six types of transitions. These latter types are needed to preserve the sets structure in the reduction step of our algorithm. Specifically, we present a successive censoring algorithm, based on matrix analytic methods, to obtain the stationary distribution of this system of connected LDQBD-processes.

We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high down time costs. The inventory system consists of a central warehouse and multiple local warehouses, from where customers are served, and a central repair facility at an external supplier. When a part fails at a customer, his request for a ready-for-use part is immediately fullled by his local warehouse if it has a part on stock. At the same time, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part on stock. Otherwise, it is sent via a lateral transshipment from another local warehouse or the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a base-stock policy for the inventory control. Because our inventory system is too complex to solve for a steady-state distribution in closed form, we approximate it by a network of Erlang loss queues with so-called hierarchical jump-over blocking. We show that this network has a steady-state distribution in product-form. Further, this steady-state distribution and several relevant performance measures only depend on the distributions for the repair and replenishment lead times via their means (i.e., they are insensitive for the underlying probability distributions). The steady-state distribution in product-form enables an ecient heuristic for the optimization of base-stock levels, resulting in good approximations of the optimal costs.

Professionals often collaborate in projects. Some of these projects require funding, so before the collaboration can start a proposal for the project is submitted. This proposal will then be evaluated by a committee. The goal of the committee is to recognise proposals that are likely to be very successful. In this paper, we introduce a new numerical method to estimate the expected potential of a proposal. This method helps in identifying proposals that may turn out to be the most successful. The estimation is derived from the past performances of the professionals involved and takes into account the uncertainty of a contribution of a professional to a proposal. We apply our method to the Dutch film industry. We estimate the potential of proposals for new films released in 2010. The value of a film depends on the number of visitors in cinemas and the artistic prizes won. Our estimates are very good, indicating that past performances of filmmakers provide a very good indication of the potential of their new film. As a by-product of our method, rankings of producers, directors, and screenwriters of Dutch films up to 2011 are obtained.

Emergency department overcrowding is a widespread problem and often leads to ambulance offload delay. If no bed is available when a patient arrives, the patient has to wait with the ambulance crew. A recent Canadian innovation is the offload zone—an area where multiple patients can wait with a single paramedic–nurse team allowing, the ambulance crew to return to service immediately. Although a reduction in offload delay was anticipated, it was observed that the offload zone is often at capacity. In this study we investigate why this is the case and use a continuous time Markov chain to evaluate how interventions can prevent congestion in the offload zone. Specifically we demonstrate conditions where the offload zone worsens offload delay and conditions where the offload zone can essentially eliminate offload delay.

Around 40% of cured cancer patients in the European Union are treated with radiotherapy [2]. Delays in cancer treatment are associated with psychological distress and decreased cancer control. To this end, in the Netherlands standards for the access time for radiation treatment are set, which are currently not met in many Dutch oncological centers. The radiotherapy care process (i.e., preparation and treatment) consists of several consecutive stages, possibly related via time constraints. Inadequate capacity allocation may cause large delays, for example due to the capacity allocation of different stages not being aligned, or due to inadequate time division of single resources over different activities. The objective of this study is to increase compliance to access time standards without extending resource capacities, by developing a methodology for optimizing resource capacity allocation in the radiotherapy care process. For radiotherapy, time division of resources over different activities particularly applies to the doctors, who carry out consultations and scan contouring. Time slots for these activities are typically set for each doctor in a cyclic weekly scheme. We develop an integer linear programming (ILP) model to design a weekly doctors’ scheme that minimizes the expected access times of all patient types in the care process and that matches the number of consultation time slots with demand. In several experiments, the quality of the resulting doctors’ schemes is studied via a discrete event simulation model by evaluating the consequences of the schemes in a stochastic environment. Results from a case study in the Academic Medical Center (AMC) in Amsterdam show that the implementation of these schemes may result in a considerable access time reduction. The designed doctor’s schemes are being evaluated for implementation in the AMC.

Recent mathematical and statistical modeling of leprosy incidence data provides estimates of the current undiagnosed population and projections of diagnosed cases, as well as ongoing transmission. Furthermore, modeling studies have been used to evaluate the effectiveness of proposed intervention strategies, such as postleprosy exposure prophylaxis and novel diagnostics, relative to current approaches. Such modeling studies have revealed both a slow decline of new cases and a substantial pool of undiagnosed infections. These findings highlight the need for active case detection, particularly targeting leprosy foci, as well as for continued research into innovative accurate, rapid, and cost-effective diagnostics. As leprosy incidence continues to decline, targeted active case detection primarily in foci and connected areas will likely become increasingly important.

Green waves in urban settings are seen to be beneficial both for the drivers and the environment because they lower delays and reduce pollution. To obtain these benefits, it is important to determine the optimal network parameters, e.g., green splits and offsets, that yield the desired traffic behaviour. We consider two possibilities for network optimization. The first one is minimising the average lost time per vehicle; the second one is maximizing the green wave efficiency. We compare the results with the MAXBAND algorithm, which is used at the design stage of arterial traffic light settings to facilitate green waves. Using our optimisation method, the average delay per vehicle can be reduced by up to 10% and more vehicles can encounter a green wave compared to the MAXBAND approach. The reduction of the average delay for the main stream reaches 20%.

Frequency and duration of follow-up for patients with breast cancer is still under discussion. Current follow-up consists of annual mammography for the first five years after treatment and does not depend on the personal risk of developing a locoregional recurrence (LRR) or second primary tumor. Aim of this study is to gain insight in how to allocate resources for optimal and personal follow-up. We formulate a discrete-time Partially Observable Markov Decision Process (POMDP) with a finite horizon in which we aim to maximize the total expected number of quality-adjusted life years (QALYs). Transition probabilities were obtained from data from the Netherlands Cancer Registry (NCR). Twice a year the decision is made whether or not a mammography will be performed. Recurrent disease can be detected by both mammography or women themselves (self-detection). The optimal policies were determined for three risk categories based on differentiation of the primary tumor. Our results suggest a slightly more intensive follow-up for patients with a high risk and poorly differentiated tumor, and a less intensive schedule for the other risk groups.

Noise load reduction is among the primary performance targets for some airports. For airports with a complex lay-out of runways, runway selection may then be carried out via a preference list, an ordered set of runway combinations such that the higher on the list a runway combination, the better this combination is for reducing noise load. The highest safe runway combination in the list will actually be used. The optimal preference list selection minimises the probability of exceeding the noise load limit at the end of the aviation year. This paper formulates the preference list selection problem in the framework of Stochastic Dynamic Programming that enables determining an optimal strategy for the monthly preference list selection problem taking into account future and unpredictable weather conditions, as well as safety and efficiency restrictions. The resulting SDP has a finite horizon (aviation year), continuous state space (accumulated noise load), time-inhomogeneous transition densities (monthly weather conditions) and one-step rewards zero. For numerical evaluation of the optimal strategy, we have discretised the state space. In addition, to reduce the size of the state space we have lumped into a single state those states that lie outside a cone of states that may achieve the noise load restrictions. Our results indicate that the SDP approach allows for optimal preference list selection taking into account uncertain weather conditions.

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load.

In this paper we present a new method on how to compute the expectation and distribution of the queue length for a particular class of systems. We apply this method and prove its time-efficiency for models in road traffic such as the fixed-cycle traffic light (FCTL) model and for the bulk-service queue model. We give several generalizations of the FCTL queue, which model right-turns, disruptions of the traffic and uncertainty in departure times. We also consider different ways of green time allocation, which are based on either minimizing the maximum expected delay per vehicle or minimizing the total expected queue length. We compare these methods to proportional allocation.

Het veertigjarig jubileum van de ‘Lunteren Conference on the Mathematics of Operations Research’ vormt de aanleiding voor een interview met Wim Klein Haneveld en Jan Karel Lenstra, die nauw betrokken zijn geweest bij de ontwikkeling van landelijke samenwerking in de mathematische besliskunde. Naast de conferentie is ook het onderwijsprogramma dat wordt verzorgd door het Landelijk Netwerk Mathematische Besliskunde een belangrijk onderdeel van het succes van deze samenwerking. De afweging tussen lokale universitaire en nationale belangen bij het opzetten van dit programma dertig jaar geleden vertoont een grote overeenkomst met de huidige discussie rond Mastermath in het Deltaplan voor de Nederlandse wiskunde. Richard Boucherie en Johann Hurink spraken Wim Klein Haneveld en Jan Karel Lenstra op 29 januari 2016.

We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high down time costs. The inventory system consists of a central warehouse and multiple local warehouses, from where customers are served, and a central repair facility at an external supplier. When a part fails at a customer, his request for a ready-for-use part is immediately fullled by his local warehouse if it has a part on stock. At the same time, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part on stock. Otherwise, it is sent via a lateral transshipment from another local warehouse or the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a base-stock policy for the inventory control. Because our inventory system is too complex to solve for a steady-state distribution in closed form, we approximate it by a network of Erlang loss queues with so-called hierarchical jump-over blocking. We show that this network has a steady-state distribution in product-form. Further, this steady-state distribution and several relevant performance measures only depend on the distributions for the repair and replenishment lead times via their means (i.e., they are insensitive for the underlying probability distributions). The steady-state distribution in product-form enables an ecient heuristic for the optimization of base-stock levels, resulting in good approximations of the optimal costs.

In the Dutch context we see similar problems as outlined in Linda Green’s commentary and, due in part to the redesign of the healthcare financing structure in the Netherlands, we have also seen a tremendous increase in the demand for operations analysis. The major redesign of the financial structure is described below, but for now, it is sufficient to state that its principal purpose is to achieve better value for the money spent on healthcare. Achieving more value for money is certainly an area where operations analysis can play a leading role. As a result, the demand for both our research capacity and recent graduates has been increasing. Furthermore, since healthcare providers are truly engaged, implementations of our results and recommendations have likewise increased. In this paper, we discuss recent projects to build on Linda Green’s commentary and to argue how to apply operations analysis in healthcare in a scientifically and practically relevant way.

In large-scale distributed applications, a loosely-coupled event-based style of communication as in publish-subscribe systems eases the integration of autonomous, heterogeneous components. In a publish subscribe-system, content-based routing - where routing is based on the content of the messages - is an alternative to address-based delivery. In this paper we provide a time-dependent analysis of the identity-based routing scheme. Our analytical approach is based on continuous-time Markov chains and extends the steady-state approach by Jaeger and Mühl [7] to systems with time-fluctuating parameters. For $m$-ary trees with $k$ levels, with a single publisher at the root and subscribers at the leaves, we obtain explicit closed form solutions for the time-dependent distribution of the traffic rates in the network. The results allow us to investigate, for example, the impact of time-fluctuating request rates versus time-independent request rates, and the switching point between optimality of flooding and identity-based routing.

We consider the problem of retrieving a reliable estimate of an attribute monitored by a wireless sensor network, where the sensors harvest energy from the environment independently, at random. Each sensor stores the harvested energy in batteries of limited capacity. Moreover, provided they have sufficient energy, the sensors broadcast their measurements in a decentralized fashion. Clients arrive at the sensor network according to a Poisson process and are interested in retrieving a fixed number of sensor measurements, based on which a reliable estimate is computed. We show that the time until an arbitrary sensor broadcasts has a phase-type distribution. Based on this result and the theory of order statistics of phase-type distributions, we determine the probability distribution of the time needed for a client to retrieve a reliable estimate of an attribute monitored by the sensor network. We also provide closed-form expression for the retrieval time of a reliable estimate when the capacity of the sensor battery or the rate at which energy is harvested is asymptotically large. In addition, we analyze numerically the retrieval time of a reliable estimate for various sizes of the sensor network, maximum capacity of the sensor batteries and rate at which energy is harvested. These results show that the energy harvesting rate and the broadcasting rate are the main parameters that influence the retrieval time of a reliable estimate, while deploying sensors with large batteries does not significantly reduce the retrieval time.