Serban Badila

Eindhoven University of Technology
e.s.badila@tue.nl

Supervisor Onno Boxma and Jacques Resing

Title On a bivariate insurance problem with coupled risks
Abstract We investigate an insurance risk model that consists of two reserves which receive income at  fixed rates. There are claims being requested at random epochs from each reserve and the inter-arrival times of a claim event are generally distributed.

The two reserves are correlated in the sense that at the epoch of a claim event, claims are being requested from both reserves and the amounts requested are correlated. For example car accidents generate simultaneously health claims and car insurance claims.

We allow in addition for the claim sizes of the current claim event to be correlated with the time elapsed since the previous claim event. A possible motivation is that unusually large claim sizes may be delayed due to regulatory policies for example.

We focus on the probability that this bivariate reserve process survives inde
finitely, as a performance measure for this insurance problem. It is shown that the infi
nite-horizon survival problem is related to the problem of determining the equilibrium distribution of a random walk with vector-valued increments which evolves as if the boundary of the positive quadrant is impenetrable. This 'reflected' random walk is actually the waiting time process 'dual' to the bivariate ruin process.

Under assumptions on the arrival process and on the nature of risks that specify the model, we explicitly determine the Laplace-Stieltjes transform of the survival function/equilibrium waiting time. The method used involves a factorization of a Wiener-Hopf type with a parameter.

Bart Beemsterboer
University of Groningen
b.j.beemsterboer@rug.nl

Supervisor Martin Land and Ruud Teunter

Title Planning of combined make-to-order/make-to-stock production
Abstract We consider a combined make-to-order (MTO) and make-to-stock (MTS) production system. The system produces the MTO orders one by one, while the MTS products are produced in batches. We are interested in the dependence of the inventory level at which a new MTS batch must be produced on the number of MTO orders, and in the benefits of this approach against a constant level.

In our model, demand for both products follows a Poisson process. MTS products are fulfilled from stock if possible and backordered otherwise. MTO products are ‘backordered’ in all cases. There are no lead times for the MTO products, but there is a ‘backorder’ cost per unit per time unit in order to motivate quick delivery. For the MTS products, there are both backorder costs and holding costs.

We modeled the system as a Markov Decision Process and we found that the inventory level at which the system should start producing an MTS batch varies between only two values. An optimal policy only discriminates between states with and states without MTO orders in the system, i.e. if there are orders in the system, the level at which the system starts producing an MTS batch is constant. Hence, the optimal policy can be described by only two values.

Further steps in this project are aimed at finding the dependence of the size of the MTS batches on the number of MTO orders, in case there is a setup required for these batches such that capacity can be gained by increasing the batch size.

Paul Bouman

Erasmus University Rotterdam

pbouman@rsm.nl

Supervisor Leo Kroon

Title Passenger Route Choice in Case of Disruptions
Abstract One of the major nuisances a passenger in railway transport can experience is a disruption, resulting in the cancellation of a number of train services. Not only do disruptions usually cause significant delays of the passengers' journeys, but they may also confront the passenger with a complicated question: “What is the best way to continue my journey?”

In such a situation, a little bit of information may be extremely valuable for making the right choice. As such, it is important that operators do the best they can in informing their passengers. However, even the operator himself may not have all information that would be required to give the best possible advice. In many cases it can take some time to assess the cause and severity of a disruption. In other situations the cause may have been resolved but the exact time before operations are back to normal is still uncertain.

In case good information is not available, the passenger faces a dilemma: should he be optimistic about the duration of the disruption and hope it is over soon enough to wait for the planned fast connection, or should he be pessimistic and take an alternative that might take much longer than the disrupted connection? Both approaches may lead to an unfortunate outcome, as the optimistic passenger might wait much longer than anticipated before the disruption is over, while the pessimistic passenger may find out that the disruption had vanished just after he departed on his lengthy detour.

In the past decades, algorithms for situations where the input arrives over time, have been investigated under the name of  “online algorithms”. Often the performance is measured by the so-called “competitive ratio”, which can be interpreted as the worst-case ratio of the obtained solution value to the best achievable solution value when having the required information in advance.

In this paper we study the quality of strategies in an online passenger waiting problem, where a passenger has to decide between waiting for the end of the disruption or taking a detour. We characterize the strategies of the passenger and analyze the competitive ratios of these strategies. We apply the results to some realistic disruption scenarios in order to show the applicability of this approach in decision support systems that can improve passenger guidance in a disrupted situation. Additionally, we investigate a version of the problem where we perform an average case analysis using different probability distributions.

Hande Cetinay

Eindhoven University of Technology
H.Cetinay@tue.nl

Supervisor Fehmi Tanrisever and Jan Fransoo

Title Optimal Compensation for Newsvendor Managers
Abstract This paper, eliminating the single decision maker argument in a newsvendor inventory model, studies the effect of conflicting interests of different stakeholders on the operational and financial processes of the firm. Building up on a financial framework, we develop a modified agency problem, providing comprehensive analysis of executive compensation with its impact on the operations strategy, and the financial market. Incorporating shareholders, bondholders and manager's role and perspectives, the model reveals the dynamics of the optimal executive compensation for the newsvendor managers. The analysis emphasize the joint consideration of operational and financial flows in efficient compensation structure. We contribute to the operations management literature by providing optimal executive compensation for the firms, and to the finance literature by extending managerial compensation problem into an operations model. Apart from previous studies, we analyze the effect of market frictions (costly bankruptcy and asymmetric information) on the optimal contract terms. The findings reveal that for the firms with the outstanding risky debt, pure-equity compensation employed as a rule of thumb for the complete alignment of the manager's benefits to the shareholders', is suboptimal, resulting in an aggressive operations policy and value loss. Efficient compensation structures, which are designed to maximize the shareholder wealth, suggest the use of two counteracting motives on the operations policy, namely equity ownership and bonuses. In the optimal compensation structure, we acknowledge that the portion of equity-based incentives should increase in the profit margin of the newsvendor, yet decrease in the bankruptcy costs and the leverage ratio. When there is information gap between the stakeholders, the characteristic of the bondholders' belief shapes the compensation terms. However, the value loss is unavoidable when the shareholders do not possess the accurate market information.

Kamiel Cornelissen

University of Twente
k.cornelissen@utwente.nl

Supervisor Bodo Manthey

Title Smoothed Analysis of the Successive Shortest Path Algorithm
Abstract The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that both the problem and the algorithms are well understood. However, some of the algorithms' running times observed in empirical studies contrast the running times obtained by worst-case analysis not only in the order of magnitude but also in the ranking when compared to each other. For example, the Successive Shortest Path (SSP) algorithm, which has an exponential worst-case running time, seems to outperform the strongly polynomial Minimum-Mean Cycle Canceling algorithm. To explain this discrepancy, we study the SSP algorithm in the framework of smoothed analysis and establish a bound of O(mn\phi (m + n\log n)) for its smoothed running time. This shows that worst-case instances for the SSP algorithm are not robust and unlikely to be encountered in practice.

Sihan Ding

CWI
S.Ding@cwi.nl

Supervisor Rob van der Mei and Ger Koole

Title Fluid Approximation of a Call Center Model with Redials and Reconnects
Abstract In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). However, both customer behaviors have not yet been considered when making the staffing decisions. In this paper, we model call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations to the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such model is the unique solution to three differential equations. Furthermore, we use the outcome of the fluid limits to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a method is validated in the case of single intervals as well as multiple intervals with changing parameters.

Dwi Ertiningsih
Leiden University
dwiertiningsihd@math.leidenuniv.nl

Supervisor Floske Spieksma

Title A homogeneous Quasi-Skip-Free processes with level product form stationary distribution
Abstract We study QSF(Quasi-Skip-Free) processes, which are a generalization of QBD(Quasi-Birth-Death) processes, where transitions are allowed across several levels in one direction. In particular, we will study so-called skip-free to the left processes that are bounded to the right. We assume that each level of the QSF process contains one exit state. This means that each level contains precisely one state with a positive jump rate to the next lower level. This implies that jump matrix to the next lower level contains only single non-zero row. Under homogeneity and irreducibility assumptions, we will show that the stationary distribution has a product form as a function of the level. We apply this result on the PH/M/1-queueing model which can be modelled as a homogeneous QBD process. Further, for a fixed inter-arrival time, we show that the stationary distribution of PH/M/1 queue converges to D/M/1 queue.

Caroline Jagtenberg
CWI
C.J.Jagtenberg@cwi.nl

Supervisor Rob van der Mei and Sandjai Bhulai

Title A polynomial time ambulance redeployment policy
Abstract In this talk we address an ambulance redeployment problem in which a given number of ambulances have to be dynamically distributed over a set of a set of base locations. The ambulances need to respect norm times to arrive at demand nodes where accidents can occur taking the travel time into account as well. The objective in the problem is to minimise the fraction of ambulances that arrive later than the norm time. We choose our cost function such that the problem is slightly simplified but at the same time leads to polynomial time computable solutions. Additionally, our choice also reduces errors compared to commonly used cost functions that need many sample paths in Monte Carlo simulations. We benchmark our method with the solution of the Maximum Expected Coverage Location Problem, which is a static solution. In a case study with one of the largest ambulance provider regions of the Netherlands, we show that our approach gives a significant improvement on the static MEXCLP solution.

Jasper de Jong

University of Twente
j.dejong-3@utwente.nl

Supervisor Marc Uetz

Title The sequential price of anarchy
Abstract The price of anarchy measures the costs to society due to the selfishness of players. More formally, it is a lower bound on the quality of any Nash equilibrium relative to the quality of the global optimum. However, in particular games some Nash equilibria are not realistic, therefore the price of anarchy gives an overly pessimistic view. Instead of assuming that all players choose their strategies simultaneously, we consider games where players choose their strategies sequentially. The sequential prices of anarchy is then a lower bound on the quality of any subgame perfect equilibrium of such a game relative to the quality of the global optimum. This idea was introduced in a recent paper by Paes Leme, Syrgkanis, and Tardos, where they indeed give examples where sequential decision making leads to better equilibria. We review some of their results, touch upon our own results for a throughput scheduling problem, and discuss some of our ongoing work on linear atomic congestion games.

Marlies de Keizer

Wageningen University
marlies.dekeizer@wur.nl

Supervisor Jack van der Vorst

Title Process and Inventory Allocation in a Perishable Product Logistic Network
Abstract Dynamics in time complicate the design of logistics networks. Customers require faster and more reliable delivery of their orders. This responsiveness requirement would argue for inventory of finished products close to the customer so that lead times are short and predictable. However, from a cost perspective, inventory of raw materials should be kept at a central location. For perishable products, like flowers and other agricultural products, dynamics in product quality complicate the design of logistics networks even more. Complications especially arise when different products from different origins have to come together for processes like bundling or consolidation. A network design (i.e. facility location with inventory and process allocation) obtained by traditional methods, which do not take quality decay and lead time at a detailed level into account, may result in too many products of low quality delivered too late to the final customer.

We present a new MILP model to identify a cost-optimal network design using an MILP model with constraints on approximated product quality and responsiveness. Small exemplary problems are solved using CPLEX which shows the added value of the additional constraints compared to traditional network design. As computation times increase rapidly with problem size, we also discuss possible heuristic approaches to solve our new MILP model.

Shanfei Li
Delft University of Technology

Shanfei.Li@tudelft.nl

Supervisor Karen Aardal

Title Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter
Abstract The state of the art in approximation algorithms for facility location problems are complicated combinations of various techniques. In particular, the currently best 1.488-approximation algorithm for the uncapacitated facility location (UFL) problem by Shi Li is presented as a result of a non-trivial randomization of a certain scaling parameter in the LP-rounding algorithm by Chudak and Shmoys combined with a primal-dual algorithm of Jain et al.. In this paper we first give a simple interpretation of this randomization process in terms of solving an auxiliary (factor revealing) LP. Then, armed with this simple view point, we exercise the randomization on a more complicated algorithm for the k-level version of the problem with penalties in which the planner has the option to pay a penalty instead of connecting chosen clients, which results in an improved approximation algorithm, even for the k-level uncapacitated facility location problem without penalties.

Judith Mulder

Erasmus University Rotterdam

mulder@ese.eur.nl

Supervisor Rommert Dekker

Title Jointly optimizing sailing speed and buffer times in liner shipping
Abstract In liner shipping ships follow a fixed route within a fixed time schedule. However, ships can encounter delays both when they are sailing between ports and when they are berthing in a port. Additional costs are incurred when ships are delayed. We consider two different ways to manage delays: prevention and recovery. To prevent ships to incur delay, buffer times can be added to the schedule. The buffer time will then be used to capture (a part of) the obtained delay. However, when a ship does not encounter delay during the trip, it has to wait before it is allowed to start with the new trip. The total amount of buffer time that can be allocated to a schedule is limited. On the other hand, ships can increase the sailing speed to reduce the amount of delay. Since the buffer time is included in the published schedules, these decisions have to be made long before the route is sailed, while the determination of the sailing speed is a short run decision, which can be determined during the round tour and may depend on the observed amount of delay. The goal of the considered problem is to determine both the sailing speed and the buffer time allocation that minimize the total costs related to delays and fuel consumption. The difficulty of the problem is that long run and short run problems should be jointly considered, because they highly affect each other, while in practice the short run decisions are taken much later, when more information is available. For fixed buffer times, the problem can be formulated as a Markov decision process. We will prove some properties of the value function and use them to solve the problem for variable buffer times.

Minou Olde Keizer
University of Groningen

m.c.a.olde.keizer@rug.nl

Supervisor Ruud Teunter

Title A Condition-Based Maintenance Policy for a Continuously Deteriorating Multi-Unit System with Aperiodic Inspections

Abstract In condition-based maintenance (CBM), it is intended to perform maintenance right before a failure occurs by estimating the pending moment of failure based on monitoring a certain condition, such as vibration or temperature. We consider an existing CBM optimization approach that is advanced, compared to others, in that it optimizes both the inspection moments and the condition thresholds (on which the planning of maintenance actions is based) simultaneously. A discrete time system with two machines that operate in series is considered, where the objective is to minimize the long-run average maintenance cost per time unit. We analyze an adapted version of the system where two units operate in parallel, and provide new insights on CBM for systems with redundancy.

Martijn Onderwater
CWI

M.Onderwater@cwi.nl

Supervisor Rob van der Mei

Title Value function approximation with Evolutionary Algorithms

Abstract A numerical solution to a Markov decision process (MDP) can be obtained via, e.g., value iteration. This results in an approximation of the corresponding value function. After applying value iteration to the MDP for various combinations of parameters and inspecting the resulting value functions, one can formulate conjectures about the structure of the value function (e.g., the value function may resemble a quadratic function). However, proving such conjectures is often quite difficult.

In this presentation we illustate a novel approach for finding an analytic approximation to the value function. This approach is inspired by techniques from Evolutionary Computing, where an Evolutionary Algorithm is used to jointly `evolve' several analytic approximations to the value function. At the end of this process, the best approximation is retained, evaluated on the MDP, and compared to the optimal policy.

Research into this approach is in its initial stages and this presentation shows some early results that illustrate its potential.

Cagri Sel

Wageningen University

cagri.sel@wur.nl

Supervisor Jaqueline Bloemhof-Ruwaard and Jack van der Vorst

Title Shelf Life Integrated Production Scheduling and Distribution Planning of Yoghurt Production
Abstract The topic of supply chain management in dairy industry has received a great deal of attention in recent years due to its structural characteristics, such as long sequence dependent setup times, large changeover costs, numerous flavored and colored product types with the complicated changeover rules, limited shelf life restricting the storage duration and delivery conditions for each perishable raw material, intermediate and final product. Yoghurt is a perishable consumer good consisting of all these dairy characteristics that are coming into prominence. Furthermore, it has a relatively limited shelf life restricting the storage duration and delivery conditions for each of perishable raw materials, intermediate as well as the final products.

In this study, we deal with a production scheduling and distribution planning on set type yoghurt production within supply chain framework. We introduce a new multi-echelon, multi-period mixed integer linear programming model. Additionally, the hybrid mixed integer linear programming-constraint programming approach is proposed as a solution alternative. The problem under consideration is mainly focused not only on the packaging stage operating in parallel and sharing common resources, but also the timing and capacity constraints with respect to the fermentation/incubation stage. Sequence-dependent times and costs, perishability constraints, shelf life, working time, production overtime restrictions are explicitly taken into account and optimized by the proposed mathematical model.

Dirk Sierag
CWI

D.D.Sierag@cwi.nl

Supervisor Ger Koole, Rob van der Mei, Jean-Pierre van der Rest and Bert Zwart

Title Revenue Management under Customer Choice Behaviour with Cancellations and Overbooking

Abstract Revenue management is the practice of deciding which products to sell to which customers at what price under capacity constraints, such as the number of rooms of a hotel. A realistic revenue management model allows overbooking and incorporates customer buying behaviour and cancellations. The latter is motivated by our research using real data, which shows that for a hotel a large proportion of the reservations are cancelled. However, existing revenue management models do not take cancellations into acount. We propose a new revenue management model which takes cancellations into account in addition to both overbooking and buying behaviour of customers. This model is based on the customer choice model introduced by Talluri and van Ryzin (2004). We model the customer choice cancellation model as a Markov decision process and propose a dynamic programming formulation to solve the problem. The state space and action space of the problem are too large, such that the problem is intractable to solve for all practical purposes. Therefore we propose a heuristic to solve the problem. Numerical results show that that the heuristic does perform well and the customer choice model without cancellations does not.

Laurens Smit

Leiden University

laurens@pipe.nl

Supervisor Floske Spieksma and Michael Katehakis

Title On Successive Thinning and Lumping of Markov Chains

Abstract We present a procedure to decompose Markov processes into separate, often easier to solve, processes by eliminating transitions. We show how the solution of the original process can be recovered from the solutions of these newly created thinned chains. We discuss applications of this procedure for cases where the thinned processes are successively lumpable and the original process is not. Successive lumping is a solution procedure for Markov Chains introduced in Katehakis and Smit (2012), where the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains.

Furthermore, we apply this thinning based decomposition procedure to Markov decision processes and we derive conditions under which these processes are successively lumpable. We use the method of thinning and successive lumping to calculate discounted rewards in Markov decision processes. We study applications of these methods to classical reliability and queueing models.

Mehmet Soysal
Wageningen University
mehmet.soysal@wur.nl

Supervisor Jaqueline Bloemhof-Ruwaard

Title The time-dependent two-echelon capacitated vehicle routing problem with emissions consideration
Abstract The growth in freight traffic and increase in traffic congestion on popular urban routes necessitate introducing legal restrictions on the use of large-size vehicles with high loads. The desired objective of keeping large vehicles away from congested areas aims not only to reduce the environmental externalities of freight distribution (e.g. energy usage and congestion), but also to improve the social performance of such activities (e.g. traffic-related air pollution, accidents and noise). One way of achieving this objective is to use multi-echelon distribution strategies in which freight is delivered to customers via intermediate depots rather than direct shipments from the origin (Crainic et al., 2004; Perboli et al., 2011). The two-echelon capacitated vehicle routing problem (2E-CVRP) is a distribution system where intermediate capacitated depots, called satellites, are placed between a supplier and final customers (Feliu et al., 2007). This paper presents an emissions integrated MILP model for the generic time-dependent 2E-CVRP that accounts for vehicle type, traveled distance, vehicle speed, load, and multiple time zones. A case study in a supermarket chain operating in the Netherlands shows the applicability of the model to a real life problem. Different variations of the model each of which differs only in terms of objective function are employed to compare the performances with respect to the selected key performance indicators of total distance, total time, total fuel consumption and total cost.

Results of the computational experiments show that the resulting routes and the performances of the solutions with respect to the aforementioned key performance indicators change according to the variation of the model. The use of the cost minimizing objective, which breaks away from the traditional objective functions used in the 2E-CVRP due to explicit fuel consideration, enabled cost reductions though it did not guarantee the best sustainable solution in terms of emissions. The most environmentally friendly solution was obtained from the fuel minimizing objective, but it came at a cost. The sensitivity analyses conducted on handling fee in the satellites and demand of the customers showed the potential impacts of several changes on the resulting routes and the key performance indicators under different objectives.

Zhao Sun
Tilburg University
sunzhao1987@gmail.com

Supervisor Monique Laurent and Etienne de Klerk

Title An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex
Abstract The problem of minimizing a polynomial over the standard simplex is a well-known NP-hard nonlinear optimization problem. It is known that the problem allows a polynomial-time approximation scheme (PTAS) for polynomials of fixed degree. We provide an alternative proof of the PTAS property for one simple scheme that only evaluates the polynomial on a regular grid, and the proof relies on the properties of Bernstein approximation on the simplex.

Halldora Thorsdottir
CWI

H.Thorsdottir@cwi.nl

Supervisor Michel Mandjes and Joke Blom

Title A functional central limit theorem for a Markov-modulated infinite-server queue

Abstract We model the production of new molecules in a chemical reaction network as a Poisson process with a varying arrival rate, which depends on an external Markov process. It is assumed that the molecules decay after an exponential time, independently of other molecules present, thus the system is essentially an infinite-server system. We show how one can represent the counting process we need, that is, the number of molecules, M(t), in terms of the Poisson process. The goal is to analyze the distributional properties of M(t), under a specific time-scaling. In this scaling, the background process is sped up by a factor N^alpha, for some alpha>0, whereas the arrival rates are scaled by N, for N large. The value of alpha determines which one goes faster in the limit of N, the background process or the arrival process.

Using the simple construct of Poisson processes, we apply the law of large numbers to obtain a fluid limit and in what follows, we obtain a functional central limit theorem for M(t), by applying the martingale central limit theorem. Namely, we show that M(t), after centering and scaling, converges weakly to an Ornstein-Uhlenbeck process.

An interesting dichotomy is observed, namely, if alpha > 1 the background process jumps faster than the arrival process, and consequently the arrival process behaves essentially as a (homogeneous) Poisson process, so that the scaling in the F-CLT is the usual sqrt{N}, whereas for alpha <= 1 the background process is relatively slow, and the scaling in the F-CLT is N^{1-alpha/2}.

Martin van Buuren
CWI

M.van.Buuren@cwi.nl

Supervisor Rob van der Mei

Title Simulation of Ambulance Services

Abstract Ambulance care is of paramount importance in today's society. For good service, Dutch ambulances should be at an incident location within a response time threshold of 15 minutes for high urgency calls. Applied mathematicians can help ambulance providers to achieve a higher service with the same capacity.

Using simulation software, we can evaluate the impact of different policies. The model can for example show the influence of closing hospitals, give insight into the effect of changing base locations or evaluate dispatch strategies including dynamic ambulance management.

The model makes use of powerful routing software dedicated for both ambulances and helicopters. This gives us an unique precision that can be helpful for both scientists and ambulance practitioners.

Pieter van den Berg

Delft University of Technology

P.L.vandenBerg@tudelft.nl

Supervisor Karen Aardal

Title Time-dependent Ambulance Location Model with Start-up and Relocation Cost
Abstract Since Emergency Medical Vehicles are responsible for providing adequate care in case of an emergency, and time is limited in these situations, it is important to determine a good distribution of the ambulances over a geographical region. In this paper we introduce a time-dependent probabilistic location model to determine such a distribution. We want to maximize the expected coverage throughout the day and at the same time minimize the number of opened facilities and the number of relocations. We take into account that travel times, demand, and ambulance availability fluctuate over the day. We apply the model to both randomly generated test instances and to data provided by different ambulance providers. We address some issues that arise when the model is applied in practice. We see that time-dependent models can result in better solutions than time-independent models and that the current set of base locations is not always optimal. Furthermore, we see that minor adjustments in the model allow us to incorporate the additional requirements for specific ambulance providers.

Chiel van Oosterom
Eindhoven University of Technology
C.D.v.Oosterom@tue.nl

Supervisor Geert-Jan van Houtum and Hao Peng

Title Optimal maintenance policies for a safety-critical system and its deteriorating sensor
Abstract We consider the integrated problem of optimally maintaining an imperfect, deteriorating sensor and the safety-critical system it monitors. The sensor's costless observations on the binary state of the system become less informative over time. The state of the system can be identified perfectly by a costly full inspection, after which the system is replaced if it is identified to be in the out-of-control state. A full inspection additionally provides the opportunity to replace the sensor. We formulate the problem of adaptively scheduling full inspections and sensor replacements using a partially observable Markov decision process (POMDP) model. The objective is to minimize total expected discounted cost due to system operation, full inspection, system replacement, and sensor replacement. We characterize the structure of the optimal policy and provide numerical examples to illustrate our structural result.

Petra Vis
VU University Amsterdam

petra.vis@vu.nl

Supervisor René Bekker and Rob van der Mei

Title Waiting time distributions for polling systems in heavy traffic
Abstract In a polling model there is one server that has to serve multiple queues. We consider a polling model with cyclic server routing and exhaustive service. This means that the server serves the queue until it is empty and then switches to the next queue. In the vast majority of papers that appeared on polling models, it is assumed that at each of the individual queues, customers are served on a First-Come-First-Served (FCFS) basis. In this talk we will study other local service policies like Last-Come-First-Served (LCFS), Random Order of Service (ROS), Processor Sharing (PS) and Shortest-Job-First (SJF). For each of these local policies we derive the scaled waiting time distribution in heavy traffic. For FCFS the scaled waiting time distribution is known to be a uniform times gamma distribution. For other service disciplines, the gamma distribution remains unaffected but we obtain a galaxy of results as alternative for the uniform distribution. In particular, we get uniforms with a point mass in zero, trapezoidal distributions and mixtures of these. Compared to the gated service discipline, we notice that the waiting time results in heavy traffic are now more involved.

Joris Wagenaar
Erasmus University Rotterdam

jwagenaar@rsm.nl

Supervisor Leo Kroon

Title Disruption management in passenger railway transportation
Abstract Passenger railway transportation in the Netherlands is confronted with disruptions on a daily basis. A disruption blocks (a part of) a track, causing the resource schedules, such as the timetable, the rolling stock circulation and the crew schedule, to become infeasible. Effective disruption management is required to uphold as much of the passenger service as possible. In disruption management the
first step, after a disruption occurred, is to reschedule the timetable, secondly with the new timetable as input the rolling stock circulation is rescheduled and fi
nally with both the new timetable and the new rolling stock schedule as input the crew schedule is adjusted.

Mathematical models have been created to solve all three steps individually. However, there has never been a model or heuristic that solves all three steps either at once or one after another. In this paper we show results of running all three models one after another, with using the output of the previous model as the input for the next model. However, if, for instance, in the crew rescheduling process an additional trip needs to be cancelled, then it is no longer certain that the rolling stock schedule is still feasible. So, we have added feedback loops to the heuristic. The information in the feedback loops consists of the additional cancelled trips in both the rolling stock circulation and the crew schedule. With this new information, the resource schedules are rescheduled once again. This is repeated until no additional trips are cancelled and in this way a feasible solution for all three the resource schedules is guaranteed.

Guanlian Xiao
Erasmus University Rotterdam

xglian@gmail.com

Supervisor Joris van de Klundert

Title The adaptive operating room schedule with overtime cost: application of knapsack problem
Abstract The schedule of surgeries to operating rooms(ORs) is a challenging optimization problem. Many uncertainties in service time make the schedule problem complicated. Most literature so far assume that surgical service time follows some given random distributions or even is a constant to make it tractable, which keeps a distance from the reality. In our paper, we assume service time are stochastically distributed and all patients are available at the very beginning of the decision epoch. After every realization of previous stages, we update the current system state and select one patient for the following surgery. We first apply this thought to normally distributed service time to gain some insights about the quality of the solution. Then we extend it to general stochastic distributions with given samples and employ sample average approximation (SAA) to get solutions.

Alessandro Zocca

Eindhoven University of Technology
a.zocca@tue.nl

Supervisor Sem Borst and Johan van Leeuwaarden

Title Delays due to long hitting and mixing times
Abstract We consider a stylized stochastic model for a wireless random-access network, which yields a product-form stationary distribution of the activity process for the various users and provides useful estimates for the user throughputs. We focus on partite network topologies, for which we investigate the deep interplay that exists in a high-load regime between long transition times among different components, poor delay characteristics and starvation issues, and slow mixing times of the Markov process. In particular, we establish the asymptotic order of magnitude and the scaled asymptotic distribution of the transition time when the activation rates grow large. Moreover we exploit these results for the transition times to obtain lower bounds for delay and mixing times. Our proof framework is also relevant for the hard-core model in statistical physics and the sampling from independent sets using single-site update Markov chains.