Technical Sessions – Monday July 11

FB-06 IFORS 2011 - Melbourne
2 - Perils of the Advantage Set
Alan Brown, retired, 14 Rowell Street, Rosanna, 3084,
Melbourne, Victoria, Australia, abrown@labyrinth.net.au
In tennis, the stopping rules for an advantage set are poorly designed, and the
total number of games required to determine the winner is not well controlled.
When the advantage set is played, the standard deviation of the number of
games is a poor measure of risk of very long matches. Analysis of the distribution
of the number of games in an advantage set provides a simple practical
example where the Normal Power approximation fails. It is proposed that the
advantage set be replaced by short tie-breaker sets in tournament matches.
3 - Analyzing Tennis Scoring Systems: From the Origins
to Today
Tristan Barnett, School of Mathematics and Statistics, University
of South Australia, 1/11 Findon St, Hawthorn, 3122, Melbourne,
Victoria, Australia, strategicgames@hotmail.com
This paper investigates tennis scoring systems that have been used throughout
history — from Royal Tennis in 1490 to the most recent change to doubles
Lawn Tennis in 2006. By identifying how the game has changed (such as
technology in equipment) this helps to establish "reasonable’ scoring systems
that could be used for today. Based on this information and obtaining mathematical
results of scoring systems, recommendations are given for men’s and
women’s singles and doubles events. Actual matches are given to demonstrate
why changes in many scoring systems are necessary.
� FB-06
Friday, 13:15-14:45
Meeting Room 105
Logistics
Stream: Transportation
Invited session
Chair: Said Salhi, Kent Business School, University of Kent, Centre
for Heuristic Optimisation„ Canterbury, Kent, CT2 7PE, United
Kingdom, s.salhi@kent.ac.uk
1 - Pricing for Production and Delivery Flexibility
Martin Savelsbergh, CSIRO, NSW 1670, North Ryde, Australia,
Martin.Savelsbergh@csiro.au, George Nemhauser, Yaxian Li
Adjusting prices to influence demand to increase revenue has become common
practice. We investigate adjusting prices to influence demand to reduce cost.
We consider offering price discounts in return for delivery flexibility in a singleitem
uncapacitated lot-sizing context. Even though the resulting optimization
problem has a nonlinear objective function it can still be solved in polynomial
time under Wagner-Whitin cost conditions. Furthermore, we report results of a
computational study analyzing the benefits of offering price discounts in return
for delivery flexibility in various settings.
2 - Metaheuristics for Order Batching and Batch Sequencing
in Manual Order Picking Systems
Sebastian Henn, Faculty of Economics and Management,
Otto-von-Guericke University Magdeburg, Universitätsplatz 2,
39106, Magdeburg, Germany, sebastian.henn@ovgu.de
Order picking deals with the retrieval of articles from their storage locations
in order to satisfy customer requests. Major issues in manual picking systems
are the transformation of customer orders into picking orders and the determination
of picking tours. In practice, customer orders have to be completed by
certain due dates. The observance of these dates is influenced by the composition
of the batches, their tour lengths and by the sequence according to which
the batches are processed. It is presented, how metaheuristics can be used to
minimize the tardiness for given customer orders.
� FB-07
Friday, 13:15-14:45
Meeting Room 106
Healthcare Systems and Queues
Stream: Applied Probability
Invited session
Chair: Ilze Ziedins, University of Auckland, 1010, Auckland, New
Zealand, i.ziedins@auckland.ac.nz
118
1 - Some Observations Concerning Priority Queues
Mark Fackrell, Mathematics and Statistics, The University of
Melbourne, 3010, Melbourne, Victoria, Australia,
fackrell@unimelb.edu.au
We consider a single server queue with two types of customers, each type arriving
according to a Poisson process, with possibly different rates. One type of
customer is labelled “high priority”, the other “low priority”. Once a customer
arrives to the queue they begin accumulating priority at a fixed rate, depending
on their priority class. We present some theoretical and simulation results for
the nonpreemptive priority queue mentioned above, and extend the analysis to
queues with more than two priority classes of customers.
2 - A New Paradigm for Priority Patient Selection
David Stanford, Dept. of Statistical & Actuarial Sciences, The
University of Western Ontario, WSC 262, 1151 Richmond Street
N., N6A 5B7, London, Ontario, Canada, stanford@stats.uwo.ca,
Peter Taylor, Ilze Ziedins
In many health care systems: 1) Key Performance Indicators (KPIs) specify
the fraction of patients needing to be seen by some key time point. 2) Patient
classes present themselves for care in a fashion that is totally independent of
the KPIs. There is no reason to expect the resulting system performance will
adhere to the specified KPIs. The present work presents a new paradigm for
priority assignment that enables one to fine-tune the system in order to achieve
the delay targets, assuming sufficient capacity exists for at least one such arrangement.
3 - Modelling Patient Flow through a Cardio-vascular Intensive
Care Unit
Ilze Ziedins, University of Auckland, 1010, Auckland, New
Zealand, i.ziedins@auckland.ac.nz
We describe a simulation model of an intensive care unit, and an associated optimization
routine, that were developed for the Cardiovascular Intensive Care
Unit at Auckland City Hospital. Acute patients arrive as a time varying Poisson
process, while elective patients are modelled as deterministic arrivals. Lengths
of stay are drawn from the empirical distributions for different types of patients.
The model has been used to determine the number of beds that are needed in
the unit, and to explore the benefits of flexible rostering.
� FB-08
Friday, 13:15-14:45
Meeting Room 107
Natural Resource Management
Stream: Dynamic Programming
Invited session
Chair: Julia Piantadosi, School of Mathematics and Statistics,
University of South Australia, Mawson Lakes Campus, Mawson
Lakes Boulevard, Mawson Lakes, 5095, Adelaide, South Australia,
julia.piantadosi@unisa.edu.au
1 - Time Series Analysis of Daily Rainfall
John Boland, School of Mathematics and Statistics, University of
South Australia, Mawson Lakes Blvd., 5095, Mawson Lakes,
South Australia, Australia, john.boland@unisa.edu.au
How correlated is daily rainfall? It is common to model daily rainfall totals as a
Markov Chain. However, we conjecture that dependence at longer time scales,
typically of the order of one week, can be important. Standard procedures do
not capture this longer range dependence. We show the use of multiple regression
and principal component analysis in this problem.
2 - Effective Decision Making Polices for Multi-reservoir
Systems
Sara Browning, Mathematics and Statistics, University of South
Australia, Mawson Lakes Campus, Mawson Lakes, 5095,
Adelaide, SA, Australia, sara.browning@mymail.unisa.edu.au
We are interested in developing more effective decision making polices for
multi-reservoir systems using a variety of mathematical processes such as
stochastic dynamic programming (SDP) and decomposition. We have developed
an SDP formulation for the major storage areas of the Murray-Darling
basin using a decomposition procedure which compares favourably to SDP solutions
of the whole system. By incorporating methods of risk management we
aim to develop an efficient and comprehensible model to determine economic
water management policies whilst avoiding environmental damage to the water
system.