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 interarrival 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
nitehorizon survival problem is related to the problem of determining the
equilibrium distribution of a random walk with vectorvalued 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 LaplaceStieltjes transform of the
survival function/equilibrium waiting time. The method used involves a
factorization of a WienerHopf type with a parameter.
Bart
Beemsterboer
University of Groningen
b.j.beemsterboer@rug.nl
Supervisor Martin
Land and Ruud Teunter
Title Planning of combined
maketoorder/maketostock production
Abstract We consider a combined maketoorder (MTO) and maketostock
(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 socalled “competitive ratio”, which can be
interpreted as the worstcase 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, pureequity 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 equitybased
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 minimumcost flow
problem is a classic problem in combinatorial optimization with various
applications. Several pseudopolynomial, 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 worstcase 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 worstcase running
time, seems to outperform the strongly polynomial MinimumMean 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 worstcase 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
reattempts after abandonments (redials), and some are reattempts 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 QuasiSkipFree
processes with level product form stationary distribution
Abstract We
study QSF(QuasiSkipFree) processes, which are a generalization of
QBD(QuasiBirthDeath) processes, where transitions are allowed across
several levels in one direction. In particular, we will study socalled
skipfree 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 nonzero 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/1queueing model
which can be modelled as a homogeneous QBD process. Further, for a fixed
interarrival 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.dejong3@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 costoptimal 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
klevel 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 1.488approximation algorithm for the uncapacitated facility location
(UFL) problem by Shi Li is presented as a result of a nontrivial
randomization of a certain scaling parameter in the LProunding algorithm by
Chudak and Shmoys combined with a primaldual 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 klevel 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 klevel 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
ConditionBased Maintenance Policy for a Continuously Deteriorating
MultiUnit System with Aperiodic Inspections
Abstract In conditionbased 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 longrun 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 BloemhofRuwaard 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 multiechelon,
multiperiod mixed integer linear programming model. Additionally, the hybrid
mixed integer linear programmingconstraint 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. Sequencedependent 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, JeanPierre 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 BloemhofRuwaard
Title The timedependent twoechelon
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 largesize 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. trafficrelated air
pollution, accidents and noise). One way of achieving this objective is to
use multiechelon 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 twoechelon
capacitated vehicle routing problem (2ECVRP) 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 timedependent 2ECVRP 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 2ECVRP 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
fixeddegree polynomial optimization over the simplex
Abstract The problem of minimizing
a polynomial over the standard simplex is a wellknown NPhard nonlinear
optimization problem. It is known that the problem allows a polynomialtime
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 Markovmodulated infiniteserver 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 infiniteserver 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 timescaling.
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 OrnsteinUhlenbeck
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
FCLT is the usual sqrt{N}, whereas for alpha <= 1 the background process
is relatively slow, and the scaling in the FCLT is N^{1alpha/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 Timedependent Ambulance Location
Model with Startup 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 timedependent
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
timedependent models can result in better solutions than timeindependent
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 GeertJan van Houtum and Hao Peng
Title Optimal maintenance policies for a
safetycritical system and its deteriorating sensor
Abstract We consider the integrated problem of optimally maintaining an
imperfect, deteriorating sensor and the safetycritical 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 outofcontrol 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 FirstComeFirstServed (FCFS) basis. In this talk
we will study other local service policies like LastComeFirstServed
(LCFS), Random Order of Service (ROS), Processor Sharing (PS) and
ShortestJobFirst (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
randomaccess network, which yields a productform 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 highload 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 hardcore model in statistical physics and the sampling from independent
sets using singlesite update Markov chains.
