Promoting
Ethics in OR Practice
Marc Le Menestrel
Department of Economics and Business
University Pompeu Fabra
Ramon Trias Fargas, 25-27
08005 Barcelona, Spain
E. Mail: Marc.Lemenestrel@upf.edu
Abstract
In 2003, a
group of OR scholars convened at INSEAD to study the relevance and importance
of ethics in Operations Research. The workshop was intended at promoting ethics
in the field of OR at the theoretical, practical and institutional levels.
Besides presenting our initiative and its rationale, this talk focuses on the
practical dimension of ethics and Operations Research. We start by arguing that
most of the ethical issues that we confront in OR can be resolved by following
tenets of good professional practice. In this sense, the question of ethics in
modelling can be viewed as a question of quality control. We present
principles to judge such quality during the different phases of the OR analysis. Second, we argue that although
ethical practice of OR necessitates good practice, it is not sufficient and essential
limitations remain. We present and illustrate the ethical limitations of OR
good practice, in an attempt to clarify the ethical dilemmas they may entail
for the OR analyst. This leads us to propose a synthesis.
While
the practice of OR consists mainly in finding solutions to solve well-defined
problems, we propose to put a direct emphasis on the role of the OR
practitioner in raising questions to uncover ill-defined problems. Indeed, the
analytical process of OR tends to reduce the problem to a structured and
solvable form from which ethical concerns may have to be abstracted. As a main
actor of this process, the OR practitioner is often well aware of what is
missing in his analysis. The idea is to sketch a methodological approach that
would help the OR practitioner to contribute to the uncovering of the hidden
and value-loaded issues, thus participating to a more exhaustive and ethical
process.
Usage of
the quantitative techniques in banking sector
R. B. Barman
Reserve Bank of
India, Bandra-Kurla Complex,
Mumbai 400051,
India.
Abstract
In this talk the author gives an overview of the use of
operations research and other quantitative techniques in the banking
sector. The banking sector needs to
take a number of investment decisions, while meeting the constraints of the
service expected of a bank. A central
bank like the Reserve Bank of India has to provide guidelines for investments
and also manage its foreign exchange resources, subject to the constraints imposed
by the service expected of such banks.
In deciding the policies, quantitative techniques are quite useful. The author presents his experience on the
use of such techniques from the point of view of a banker’s bank.
Efficiency of Indian Banks During
Post-Reform Period: A DEA Approach
Abhiman Das
Reserve Bank of India, Bandra-Kurla Complex,
Mumbai 400051, India.
Email: adas@rbi.org.in.
Abstract
The purpose of this paper is to investigate the performance of
Indian commercial banking sector during the post reform period 1992-02. We
evaluate several efficiency estimates of individual banks using the
nonparametric frontier methodology - Data Envelopment Analysis (DEA). Two
models based on two different approaches have been constructed to show how
efficiency scores vary with change in inputs and outputs. This analysis also
aims to explain the variation in calculated efficiencies to a set of variables,
i.e. bank size, ownership, capital adequacy ratio, risk-exposure and
management quality. We find that medium sized public sector banks performed
reasonably well and are more likely to operate at higher levels of technical
efficiency. We find a close relationship between efficiency and soundness as
determined by bank’s capital adequacy ratio. The empirical results also show
that the technically more efficient banks are those that have, on an average,
less non-performing loans.
JEL classification: D61; G21; G34
Keywords: Bank efficiency; DEA analysis, Indian banks
Fatal flaw of free-market system: lag residual examination
Diganta
Saikia Chitro Majumdar
M-20, GK-II, New
Delhi-48
India
E. mail:
s_diganta@yahoo.com, chitromajumdar@yahoo.com
Abstract
One of the most potent reasons for
expecting economic growth to remain sluggish is that it suits the policy objectives
of the two leading COUNTRIES . The constellation that seems to be emerging as a
sequence of the imperial circle deserves to be described as a golden age of
capitalism.
The fatal flaw of a free-market system is
its inherent instability. The belief that financial markets are self-regulating
is simply false. Fortunately, secretary Becker is aware of this fact and the
administration has begun to exert active economic leadership since he moved to
the treasury. We can grasp this anthology from the works of Wickshell.
Certainly, it is not laissez faire that has brought us to the threshold of a
new golden age of capitalism. But a concerted economic policy designed to
counteract the excesses of a free market system. Experience from Schumpeter and
Bohm-Bawerk (1891) and Fisher (1907), an eulogistic review introduced what was
at once a profound conception of the nature of advance production and at the
same time an over-simplification which made it slightly misleading where the
rate of interest in organised money markets has tended to be positive. And its
much better stated, and in a much more stimulating way, by K Wickshell in the
first volume of his Principles (1934-35). The heteeroskedasticity problem is
often solved by estimating the historical regression hypothesis in a log linear
form. In this paper, we’d like to say that the continuous residual functions
can be applied in an economy in the free market, post-globalisation economy. When we regress log y on log x, the proposed
estimated equation is :
Log y
= 0.0757 + 0.9562log x
(0.0574) (0.0183)
R2=0.9935
RSS=0.03757
Stochastic Investment
Modelling: A multiple time-series approach
Chitro Majumdar
M-20, GK-II, New Delhi-48
E. mail:
chitromajumdar@yahoo.com
Abstract
In this paper we take up the multiple
time-series modelling approach suggested by Tiao & Box (1981) to construct
a stochastic investment model for price inflation, share dividends, share
dividend yields and long-term interest rates in India. An approach for
dealing with aberrant observations is to perform a time-series outlier
analysis. This method has the
advantage of being direct and transparent. The sequential and iterative steps
of tentative specification, estimation and diagnostic checking parallel those
of the well-known Box-Jenkins method in the univariate time-series analysis. This research
might be useful for actuarial applications for which extreme stochastic
fluctuations are important. An alternative approach to dealing with extreme
observations in the data. It
is not required to specify any a priori causality as compared to some
other stochastic asset models in the literature.
Keywords: ARCH Models; Non-linear Threshold
Models; Wilkie Model; Vector Autoregressive-Moving Average Models; Time-Series
Outliers; Price Inflation; Long-Term Interest Rates; Share Dividend Yields;
Share Dividends
Pedigree Polytope
is a Combinatorial Polytope
Tiru Arthanari
Department of MSIS,
University of Auckland
7, Symonds Street, Auckland, New Zealand.
E.mail: t.arthanari@auckland.ac.nz
Abstract
Naddef and
Pulleyblank(1981) define a 0-1
polytope as combinatorial if
the midpoint of the line joining any pair of nonadjacent vertices
is the midpoint of the line joining another pair of vertices. They show
that some well-known classes of polyhedra, such as matching polyhedra, permutation polyhedra are combinatorial polyhedra. Arthanari (2002)
defined and studied a combinatorial object called a pedigree. Pedigrees
are in one-to-one correspondence with the Hamiltonian cycles in a complete
graph on n vertices. In this paper we
show that the pedigree polytope is combinatorial. As a consequence of this
we have the strong adjacency property for Pedigree polytopes., that is, the best valued pedigree is adjacent to some
second best valued pedigree for any weight vector.
Integral
version of Hahn Banach Theorem for Combinatorial
Optimization
H.Narayanan
Indian Institute of Technology
Bombay
Powai, Mumbai 400076
Abstract
A
set function f : 2S 
, is said to be
polyhedrally tight (pt) (dually polyhedrally tight (dpt)) iff in the set polyhedron (dual set
polyhedron) denoted by Pf (Pf)
defined by
x(X) 
f(X) 
X
S
x(X)
f(X) 
X
S
every inequality can be satisfied as an equality (not necessarily
simultaneously).
The Hahn - Banach
Separation Theorem states that if f is a convex function, g is a
concave function which take zero value on the zero vector and f 
g then there exists a linear function h s.t. f 
h 
g. In general, if f, g take integral values on
integral points then it is false that an h can be found such that it
takes integral value on integral points. However such a result is true
in the case of submodular set functions
( i.e., f(X)+f(Y) 
f(X
Y)+f(X
Y), 
X, Y 
S, f being
defined on subsets of S) and
supermodular set functions ( i.e., f(X)+f(Y) 
f(X
Y)+f(X
Y), 
X, Y 
S, f being defined on subsets of S).
Indeed, we have the `integral sandwich theorem for submodular
functions' which states 'if f,g
are integral submodular and
supermodular set functions respectively then h can be taken to be an
integral modular function.' In this talk we give sufficient conditions for such a
result to be true in the case of the general class of polyhedrally tight and dually polyhedrally tight set functions.
Using these we derive the (integral) Sandwich Theorem for
submodular/supermodular functions and (working with a (0,1,-1)
coefficient matrix generalization of set polyhedra), the 1/2-integral Sandwich
Theorem for pseudopolymatroids.
The
Alternating Cone of a 2-Colored Graph
Murali K. srinivasan
Indian Institute
of Technology Bombay
Powai, Mumbai 400076
Abstract
Suppose the edges of a graph G are colored red and blue.
Assign a nonnegative real weight to
every edge such that, at every vertex, the
sum of the weights of the red edges incident at that vertex is equal to
the sum of the weights of the blue egdes incident at that vertex. All such
nonnegative real weights define a convex polyhedral cone in the edge space,
called the Alternating Cone of the 2-colored graph G. We study basic properties
of this cone: extreme rays, integral vectors,
dimension, and flow theory. (This is joint work with Uri Peled and
Amitava Bhattacharya)
A 3-Neighborhood Heuristic Algorithm For Constrained
Redundancy Optimization In Complex Systems
Manju Agarwal and
Sudhanshu Aggarwal
Department of Operational
Research
University of Delhi
Delhi-110007.
Abstract
In the last four decades several heuristic algorithms have been developed
for solving constrained redundancy reliability optimization problems. Almost
all the algorithms search for the optimal solution iteratively, remaining
within the feasible region, in which a redundancy is added to only one
subsystem in each iteration; and the selection of the subsystem is based on a
sensitivity factor. Thus the solutions obtained are optimal only in
1-neighborhood. It was in 1982 that Kohda & Inoue (KI) presented a
heuristic algorithm in which two feasible solutions obtained in successive
iterations are in 2-neighborhoods of each other i.e a redundancy is added in
one subsystem and a redundancy is subtracted from another. Shi (1987) developed
a heuristic algorithm based on minimal path sets in which the feasible
solutions obtained in successive iterations are in 1-neighborhood or
2-neighborhoods of each other. Perhaps
the most interesting and efficient heuristic algorithm in terms of solution
quality is that given by Kim &Yum (KYA, 1993) in which the search is made
not only in the feasible region but also in the infeasible region. In this
algorithm two feasible solutions obtained in successive iterations need not
even be in 2-neighborhoods of each other.
This paper presents a new criterion to
improve redundancy optimization heuristically in 3-neighborhood. In the
proposed algorithm excursion into infeasible region is made only once and the search continues to explore the
feasible region by performing a series of selection and exchange operations by
subtracting (adding) a redundancy from (to) one subsystem and adding (subtracting)
a redundancy to (from) one or two subsystems. With some examples, the effect of
the proposed algorithm and existing algorithms (KI, Shi, KYA) are compared.
Computational results show that our algorithm can be used as an attractive
alternative in terms of solution quality.
Quadratic
Program with Homogeneous Constraints
Archana Khurana
E-mail:
archana2106@rediffmail.com, archana2106@yahoo.com
Abstract
In this paper an algorithm to solve a quadratic programming
problem when some of its constraints are homogenous is developed. Using the
homogenous constraints a transformation matrix T is constructed. With the help
of this matrix T the given problem is transformed into another quadratic
program but with fewer constraints. A relationship between the original problem
and the transformed problem is also established which ensures that the solution
of the original problem can be obtained from the transformed
problem. The algorithm is illustrated with the help of a numerical example.
The use of Genetic
algorithm for solving Multi-objective bi-level programming problems through
fuzzy goal programming
Bijay Baran Pal, Rabin Kumar Jana and Surapati Pramanik
Department of Mathematics,
University of Kalyani,
Kalyani- 741235, INDIA
Abstract
In MOBLPP, each of the two decision
makers (DMs) locating at two different hierarchical levels (upper- and
lower-levels) independently controls a separate set of decision variables and
is interested in optimizing a set of objectives of his /her own. It may be
noted that in fuzzy programming (FP) formulation of the problem with
multiplicity of objectives at each level, each DM is always faced with
computational difficulty of assigning an imprecise aspiration level to each of
the objectives due to the conflicting nature among themselves in the decision
making context. To overcome such a difficulty, the GA based solution approach
is used here to reach the individual decision for each level with the setting
of aspiration levels to the level-objectives.
In the FGP
formulation of the problem, the fuzzy objective goals at each level and the
decision vector controlled by the upper-level DM are defined first in terms of
their membership functions by introducing certain tolerance limits for
achieving the aspired levels of them. Then the membership functions are
transformed into membership goals by introducing under - and over – deviational
variables and assigning the highest
membership value (unity) to each of them. In the solution process, GA solution technique is introduced into
the framework of FGP model to reach a satisfactory decision for both the DMs
and thereby optimizing the overall benefit of the organization. The proposed
solution approach is illustrated by a numerical example and compared with the
solution of the conventional FGP approach.
A Comparative study of optimum design of a cone clutch using
genetic algorithm, geometric programming and graphical method
G.Balavenkata Reddy M.Mohan Reddy
C.S.Rao
Abstract
In the present study, optimum volume
design of a cone clutch, a widely used power transmission element in machine
drives automobiles etc has been investigated using Genetic Algorithm. The
ergodicity of evolution operators makes genetic algorithm very effective
performing global search compared to traditional optimization techniques. The
numerical results obtained agree extremely well with the solution of same
problem solved using Geometric programming which is a traditional non-linear
programming technique and also graphical method.
Key words: Cone Clutch, Genetic Algorithm, Geometric Programming
The Minimization
of waste through optimizing the panel
cutting strategy
U H
Acharya Boby John
Indian Statistical Institute
Bangalore Centre
E mail: uhacharya@hotmail.com
bobymon@hotmail.com
Abstract
The supplier of panels like Rear Door, Side Screen, Roof Plate
etc. to M/s Asia Brown Bovery, Bangalore was adopting the trial and error /
adhoc methods for cutting the large 2 mm sheets into sheets of smaller
dimensions. The sheets were available in standard size i.e. 2500 mm x 1250 mm
only. Compounded to this was the fact that the different panels required
different cut part sizes and all these panels are required in the same final
product. So naturally the company, due to the absence of a scientific approach,
was incurring large material waste as well as more time on finalizing the panel
cutting procedure. Every purchase order used to be a battle for the purchaser.
The authors developed a cutting plan (2 Dimensional), which minimized the waste
as well as the initial planning time.
An integer-programming model for deployment of highway
incident
Response Vehicles
Raktim Pal Indranil Bose
i2 Technologies, USA University of Hong Kong, Hong Kong
Abstract
Congestion caused by highway incidents
is a major concern for road users in urban areas. In order to minimize the
adverse effect of incidents, appropriate response strategies are required which
will clear incidents as quickly as possible. An important component of these
strategies is the deployment of incident response vehicles. These incident
response vehicles patrol a highway corridor in order to clear incidents as soon
as they occur and keep the traffic moving. Incident response vehicles may be
assigned to depots located in different parts of an urban area. Upon detection
of an incident at the traffic operation center, the response vehicles may be
dispatched to the incident site from a vantage depot location. In this study a
reliability-based mixed integer programming model has been developed. The model
is used to find the best location of depots and assignment of incident response
vehicles to each of these depots so that incidents at the demand nodes can be
attended from the feasible depot locations at a minimum cost. The proposed
model overcomes the limitations in the existing current literature on incident
response system by considering all types of major costs involved in operating
an incident response system like the fixed and variable costs of operation for
both response vehicles and depots. Again, this is the first time a distinction
between a major and a minor incident is made to accommodate prioritized service
provided by an incident response service. In addition, the reliability of the
response service is also modeled. Using a hypothetical problem, the model is
used to find the optimal location of depots at different probable sites and to
assign incident response vehicles to each depot. The response areas of each vehicle
are also determined. Further, the model gives guidelines regarding which type
of vehicle should cover what percentage of a particular type of incident in a
given zone. Detailed sensitivity analysis is performed to illustrate the impact
of various parameters on the design of the incident response system.
Metaheuristic approach for solving the
manufacturing problem
1G. Kannan, 2P. Nagaraj, 3S.
Jayabal, 4J. Varadarajan, 4M. Ramya:
1,4Department of Mechanical Engineering
Sethu Institute of Technology, Kariapatti-626106, Tamilnadu
2Department of Mechanical Engineering
Mepco Schlenk
Engineering College, Sivakasi-626005,
Tamilnadu
3Department of Mechanical Engineering
A.C College of
Engineering & Technology, Karaikudi-623004
E.mail: govindkannan_2001@rediffmail.com
Abstract
Planning is a must for the success of any industry in the
continuously changing environment. Management must work for the intermediate
range plant called as aggregate plan. Consistently with long range policies and
resources allocated by a long-range decision. Aggregate production plan (APP)
for any industry is done from 6 to 18 months usually. A mixed strategy
comprising of inventory, backorder, sub-contracting, overtime, firing and
hiring is formulated to solve the aggregate production-planning problem. To
attain an effective result of such plan various essential factors like
minimizing production planning cost, minimizing cost of manufacturing viz
production cost, sub contracting cost, overtime cost, hiring and firing cost,
and inventory cost, maximizing profit and maximizing the service to customers
are achieved. In this paper an attempt has been for solving the manufacturing problem through the Metaheuristic
approach(i.e Simulated Annealing and Genetic Algorithm) in which the mixed strategy is formulated to solve the aggregate production
plan.It is evident that the aggregate plan generated using SA is more cost
effective than the plan generated using conventional technique(LPP).
Optimization of “Coal Blending” in a Steel
Plant
using Non-linear Programming
S.K.Dutta J.Roy
Durgapur Steel Plant
Durgapur: 712 203
Abstract
Metallurgical
Grade Coke is the basic necessity for Blast Furnace Iron Making, in an
Integrated Steel Plant. Quality and
Cost of Hot Metal (Pig Iron) produced depends upon the quality of input coke in
general and coke Ash content in particular. This coke is produced at Coke Ovens
from input coal by carbonization process.
Ash content of
Indian Coal is very high, which is detrimental for Iron making with regards to quality
and cost. For this reason Indigenous
coal with high Ash content is suitably blended with Imported Coal containing
low Ash percentage. As per prevailing
practice blended input coal’s Ash content should be around 18% and moreover
there should be a consistency w.r.t. this parameter.
The Ash
content of Indigenous coal from different sources highly fluctuates between 35%
to 18%. Whereas Ash content of Imported coal is more or less stable
around 9%. To satisfy the
above-mentioned Technical Norms using a complex process of coal preparation in
the Coal Handling Plant (CHP) in terms of its Lay-out, physical facilities and
associated host of Technical Constraints, a Non-linear Programming Model is
developed. The model provides and
shift-wise Operational Plan to minimize the Ash content of the blend coal and
variation from shift to shift in terms Ash content.
On an
Inequality related to variational
inequality and its consequences
G. K. Panda
Department of
Mathematics,
National
Institute of Technology, Rourkrla – 769 008, Orissa, India
B. B. Sahoo
Department of
Mathematics, Cuttack College, Cuttack – 753 004, Orissa, India
and
G. K. Sahu
Department of
Mathematics, Seemanta Engineering College, Jharpokharia
(Mayur Bhanj) - 757 086, Orissa, India
Abstract
Let X be a Hausdorff topological vector space with dual X*, K
a nonempty subset of X, and f : K´K ® ℝ be any map. In this
paper we study the following problem: “Find
such that 
for all y Î K”. Some results on this problem was
studied by Takahasi, Park and Kim and Yen. Behera and Panda recognized this
problem as an independent problem and proved several results on the existence
of solution of this problem in the setting of a Banach space. This problem
includes as special cases, many problems on variational inequalities and
generalized variational inequalities studied by many authors. In this paper we also introduce and study
another problem, “Find 
such that 
for all 
” where S : K
® 2K is any point-to-set map. This problem
includes as a particular case the classical quasi-variational inequality
problem. A generalization of Minty’s Lemma is also studied.
A
Variational Inequality in
Semi-inner-Product Space
Sudarsan Nanda
Department of
Mathematics
Indian Institute
of Technology
Kharagpur, India
Abstract
The purpose of this paper is to give a brief review of known
results on Variational Inequality and to prove an existence theorem of
Variational Inequality in Certain Semi-inner-product Space under some
Contractive Type Conditions on the Operator.
Infact we prove the following theorem :
Theorem: Let 
be uniform convex and
strongly smooth (so that 
is a unique
semi-inner-product space ) and 
is a closed convex
subset of 
. Let 
satisfy any one of
the following conditions:
with 
with 
Then there exist a 
such that 
for all 
.
On the Lipschitz
continuity of the solution map in Semidefinite Linear Complementarity Problems
R. Balaji V. Vetrivel
Indian Institute of
Technology Madras
Chennai
Abstract
In the setting of Semidefinite Linear Complementarity
Problems, we consider the problem of Lipschitz continuity of its solution map.
It is shown that if the solution
map is Lipschitz continuous, then the i-th
diagonal entry of L(Eii)
is positive where Eii is the
diagonal matrix with the i-th diagonal entry 1 and rest are all 0. As an
application, we construct linear maps having P property, for which the solution
map is not Lipschitz continuous.
Improving
Efficiency of Winding in an Autoconer
A.Rajagopal
Indian Statistical Institute
Coimbatore
Abstract
Garment
manufacturers judge the quality of yarn by good finish which means, less joints
and higher productivity – the common benefits to both spinners and garment
manufacturers. Higher the number of
joints, more is the wasteful time and poor is the quality and
productivity. The cost is higher for
operators if work assignment is reduced in order to reduce waiting time. On the other hand if work assignments is increased due to increased
waiting time then the productivity is lower. Therefore one needs to assign work optimally to workers and improve
the finish quality of yarn.
In this paper we analyze and find that
an unit increase in operator cost by reducing work assignment shall not contribute
to higher productivity, but only escalates cost. The increase in productivity is only 190 Grams per frame per
shift, but the improvement in yarn quality by reducing 10% of joints is 17 Kg per frame per shift.
Further, the process parameters when
altered to achieve this results in
actual improvement of 10 Kg per frame per shift.
Techno
–Economic Viability of Sick Unit
By
Restructuring “NPA” and Rehabilitating
Through Breakthrough Approach
A.Rajagopal
SQC & OR
Unit
Indian
Statistical Institute
Coimbatore
Abstract
Textile
sector in India, is economically socially, technically and traditionally
contributing to foreign exchange earnings, embracing agriculture, industrial
and trading sector in India.
Many spinning units, were protected by sellers’ Market until a
decade ago. However under the present condition of a buyer’s market
“technological up-gradation” and quality consistency are vital factors forcing
a change.
In this paper we consider the case of a sick unit and describe how
quantitative techniques were used to evolve a turn around strategy for
reconstruction. As a result of this effort the sick unit is brought back to
viability.
Performance
Analysis of Cellular Networks
S. Dharmaraja
Department of Mathematics
Indian Institute of Technology Delhi
New Delhi 110016, India
Email: ~dharmar@maths.iitd.ac.in
Abstract
The rapid growth in the demand
for mobile communications has led to an
intense research effort to achieve an efficient use of the scarce
spectrum allocated for cellular communications. Two important Quality of
Service (QoS) measures have been defined in cellular networks. The first one is
the new call blocking probability, a measure similar to the one that we see in
telephone trunk systems. The second one, is the handoff call dropping
probability. Handoff dropping is extremely important in cellular systems since
it leads to the undesired phenomenon of a forced call termination. In this
paper, the recent work on closed form solutions to the above two performance
measures in cellular networks is reported.
Keywords: Call blocking
probability, Quality of Service,
Queuing models, Performance measures, Cellular networks
Computationally
Efficient Winner Determination Techniques for
Internet Multi-Unit
Auctions
Sandeep Juneja,
Tata Institute of Fundamental Research
Dr. Homi Bhabha Rd
Mumbai 400 005
Abstract
In this talk we develop algorithms for efficiently
processing bids in a single item,
N unit (N ³ 1) open cry auction for a large class of winner determination
rules. Existing techniques consider all previously submitted bids along with
the new arrivals to update the current set of winners. We propose that at most
N "potential winner bids"
amongst the previously submitted bids need to be used for such updates, thus
significantly reducing the computation
time and memory requirements. This is crucial when a large number of auctions
are being conducted simultaneously. For a commonly used greedy auction rule we
show that the expected number of potential winner bids may be much less than N
under reasonable probabilistic assumptions. (Joint work with Achal Bassamboo
and Manish Gupta)
Iterates
of semidifferentiable monotone homogeneous maps and Markov decision problems
Marianne Akian
INRIA, Domaine de Voluceau, 78153 Le Chesnay Cedex, France,
e--mail :
marianne.akian@inria.fr
S. Gaubert
INRIA, Domaine de
Voluceau, 78153 Le Chesnay Cedex, France,
e.mail: stephane.gaubert@inria.fr
Roger Nussbaum
Mathematics Department, Hill Center,
Rutgers University, 110 Frelinghuysen Road,
Piscataway, New Jersey, 08854-8019, U.S.A.,
e--mail : nussbaum@math.rutgers.edu
Abstract
In [AGN03], we consider the nonlinear eigenproblem for maps
satisfying certain conditions of monotonicity and homogeneity. We prove in
particular the following result. If C is a normal cone in a Banach space, and if f is a monotone multiplicatively homogeneous self-map of the
interior of C, then, an eigenvector v of f is unique (up to a
multiplicative constant) provided
that f is semidifferentiable at
v, that its semiderivative f’v has a unique
eigenvector (up to the addition of a multiple of v) and that f’v satisfies a
Fredholm type condition. Moreover,
every orbit of f converges to a scalar multiple of v at a geometric
rate, provided that f’v has a certain nonlinear spectral
radius strictly less than one. This extends earlier results proved by Nussbaum
for differentiable maps [Nus88]. The nonlinear spectral radius that we use
originates from the theory developed in [MPN02]. The semidifferentiability
notion comes from variational analysis (see [RW98]).
We shall present here the applications of such results to optimal
control problems, and more generally, to zero-sum repeated games. In this
context, f is conjugate to a dynamic programming operator, and it is
semidifferentiable under rather general
assumptions, which include the case where the state and action spaces are finite.
We obtain as corollaries uniqueness results for the bias vector, as well
as geometric convergence results for the value function, which extend and
complete the results of [AG03] for ergodic optimal control problems.
References: [AG03] M.Akian and S. Gaubert: Spectral theorem for convex
monotone homogeneous maps, and ergodic control, Nonlinear Analysis. Theory,
Methods & Applications, 52, 2 (2003), 637--679.
[AGN03] M. Akian, S. Gaubert, and R. Nussbaum, Uniqueness
of fixed point of nonexpansive semidifferentiable maps, In preparation, 2003.
[MPN02] J. Mallet-Paret and Roger Nussbaum, Eigenvalues for a class
of homogeneous cone maps arising from max-plus operators, Discrete and
Continuous Dynamical Systems 8 (2002), no.3, 519--562.
[RW98] R.T. Rockafellar and R.J-B. Wets, Variational analysis, Springer, 1998.
Fast and Robust Learning Through
Fuzzy Linear
Proximal Support
Vector Machines
Jayadeva, Reshma Khemchandani and Suresh Chandra
Department
of Electrical Engineerging, Department of Mathematics
Indian Institute of Technology, Hauz Khas, New Delhi
– 110 016, India
Abstract
Traditional Support Vector Machines
assign data points to one of two classes, represented in the pattern space by
two disjoint half-spaces. In this
paper, we propose a fuzzy extension to proximal SVMs, where a fuzzy membership
is assigned to each pattern, and points are classified by assigning them to the
nearest of two parallel planes that are kept as distant from each other as
possible. The algorithm is simple and
fast, and can be used to obtain an improved classification when one has an
estimate of the fuzziness of samples in either class.
Multiparametric Sensitivity Analysis of the
Constraint Matrix in Linear-plus-Linear Fractional
Programming
Problem
Sanjeet Singh,
Scientist, SAG, DRDO, Metcalf House, Delhi-54
Pankaj Gupta,
Deen Dayal Upadhyaya College, University of Delhi,New Delhi-15
Davinder Bhatia, Dept. of OR, University
of Delhi, Delhi-7
Abstract
In this paper, we study multiparametric sensitivity analysis for
perturbations in a single row or a column of the constraint matrix in
programming problems with linear-plus-linear fractional objective function.
Such programming problems arise when a compromise between absolute and relative
terms is to be maximized. This type of problem has major applications in
areas like problems of optimizing enterprise capital, the production
development fund, transportation to name a few. We construct critical
regions for simultaneous and independent perturabtions using the concept of
maximum volume in the tolerance region. Necessary and sufficient conditions are
given to classify the perturbation parameters as "focal" and
"nonfocal". Nonfocal parameters can have unlimited variations,
because of their low sensitivity in practice these parameters can be deleted
from the final analysis. For focal parameters or more sensitive parameters, a
maximum volume tolerance region is characterized. Theoretical results of the
paper are illustrated with the help of a numerical example.
Duality in Multiobjective fractional programming
involving ρ-convexity
Reddy, P.R.S. and Varalakshmi, G.
University of Sri Venkateswara, Tirupati, A.P., India
E. mail: gvlsvu@yahoo.co.in
Abstract
In this paper, we derive necessary and sufficient conditions for a multiobjective fractional programming
with respect to ρ- generalized convexity. In addition, weak and strong
duality results are proved in this context.
Key Words: Multiobjective fractional programming problem,
ρ-generalized convexity, duality.
Multi-Machine Scheduling Problem
for A General Class of Job Value Deterioration Function
Sumit Raut1 Sanjeev Swami2
1PhD Scholar, Department of Industrial and
Management Engineering
Indian
Institute of Technology, Kanpur- 208016, INDIA
E-mail:
rsumit@iitk.ac.in, Phone No: 0512-2597101
2Assitant Professor, Department of
Industrial and Management Engineering
Indian
Institute of Technology, Kanpur- 208016, INDIA
E-mail: sswami@iitk.ac.in, Phone No:
0512-2597460, Fax: 0512-2597553
Abstract
In this paper, we study a class
of machine scheduling problems in which the critical scheduling parameter, job
value, is dependent on the starting time of the job in a schedule. The
objective is to maximize the cumulative value of the jobs in a schedule.
Voutsinas and Pappis (2002) have earlier considered the case of job value
deteriorating exponentially over time for a single machine problem. In the
proposed work, we consider more generalized job deterioration functions (e.g.,
linear, exponential, Weibull) for the following cases: (i) single machine, (ii)
identical parallel machines and (iii) parallel machines with unequal capacity.
Complexity boundary results are presented for each model. We also introduce
some efficient heuristics for these models and investigate their properties.
Numerical results are provided to compare the performance of various approaches
proposed.
Key words: Scheduling;
Deteriorating jobs; Heuristics; Combinatorial Optimization
Machine
Shop Scheduling -- An Application
Surajit
Pal, S. Mondal, and D. K. Manna
Indian
Statistical Institute,
110
Nelson Manickam Road,
Aminjikarai,
Chennai – 600029.
|
Email: surajitpal@hotmail.com |
Abstract
This article deals with the development
of a scheduling system for the machine shop in a company that manufactures
automotive equipments. The scheduling problem under consideration involves more
than 130 jobs and 50 machines. The scheduling problem has limited planning
horizon. The length of planning cycle is normally one week, and the processing
requirement varies from cycle to cycle. The system draws schedule after taking
into consideration the existing finished/semi-finished stock and availability
of machines with the objectives of meeting due-date demand as well as
maximizing shop utilization. The development of the system is accomplished with
the help of a computer-software that requires about one minute on a PIII
processor for deriving weekly schedule.
Keywords: Early due-date principle, make
span minimization, shop utilization.
On the least cost testing sequence problem for quality inspection.
K.V.S.Sarma & K.Sekhar
Department of Statistics
S.V University, Tirupati. 517502.
Abstract
The Least cost Testing Sequence
(LCTS) problem is one application of the well-known Weighted Shortest
Processing Time (SPT) sequencing problem.
A manufactured item has to pass each of the n-tests at the final
inspection, where ith test has an associated cost Ci of inspection and a non
zero probability pi of passing that test. The testing will be terminated if the
item fails on any one test. When there
is no constraint on the technical ordering of conducting the tests, it has been
established that the optimal sequence that minimizes the expected inspection
cost is obtained by
sequencing the tests such that
C[i]/(1-p[i]) £ C[i+1]/(1-p[i+1]) for all i.
The new aspect studied in this paper is the provision for rework. We admit a non-zero probability ri of rework
for the ith test and a maximum of m-reworks allowed for the item. The probability of termination of testing
process at the end of the ith test is the sum of probabilities of normal fail,
fail after rework and that of the reaching the mth rework. This probability will become the weight Wi
to be given for the ith test. An
interesting probability structure
has been identified to derive Wi under the condition that all the probabilities
are non identical. An array called Probability Position Matrix (PPM) has been
developed and a spreadsheet has been designed to workout the Wi and the
sequence. This model will have
applications to project evaluation studies, final testing in satellite
launching cases etc.