Multistage Method of Measuring Human Development through Improved Directional Distance Formulation of Data Envelopment Analysis: Application to Indian States

T.P.M. Pakkala

Mangalore University

Dept. of PG Studies and Research in Statistics

Mangalagangotri -574 199, Mangalore, INDIA

E-mail:  tpm_pakkala@yahoo.com

Uday Shetty

Directorate of Economics and Statistics

Govt. of Karnataka, Mangalore

E-mail: uday_kenjoor@yahoo.co.in

Abstract

United Nations Development Program (UNDP) introduced the Human Developmetn Index (HDI) in 1990 to measure human development of its member countires. Since then United Nations (UN) has been publishing HDI annually in its Human Development Report. The HDI is a composite index calculated on the basis of three major dimensions of human development; longevity, educational attainment and standard of leaving. To address the issue of regional disparities among the states in the countries in terms of human well beings a method to measure extent of disparity based on optimum combination of the indicators in required. In this paper we reassess the HDI through directional distance formulation of data envelopment analysis (DEA) of Indian states. Here, we re-estimate the HDI by finding relative efficiency of different states of india. Human development is benchmarked on the basis of empirical observations of states with best practice. A new estimation of HDI is made under the same assumptions as that of the original HDI. When the new measure of human development is compared with original HDI, it is found that they are highly correlated. Further, a new procedure, multistage reference technology is introduced to improve the performance of backward states in a stepwise approach. The paper develops a new method of computing HDI that aims at reducing regional disparities systematically.

Measuring Efficiencies in Indian Public Road Transit: A Data Envelopment Analysis Approach

Punita Saxena

Shaheed Rajguru College of Applied Sciences for Women

University of Delhi, India

e-mail: punita66@yahoo.com

Ratnesh Rajan Saxena

Deen Dayal Upadhyaya College, University of Delhi, India.

Abstract

 Efficiency evaluation is an important managerial tool for assessing the degree of resource utilization so as to give the desired outputs. The various approaches for this evaluation can be economietric or parametric by using a well difined productivity function or non-parametric by using Data Envelopment Analysis. This paper focuses on the performance of India’s Public Road Transport Undertakings. Data Envelopment Analysis is used to measure the technical scale and managerial efficiencies of Inter-state buses in India. Data was collected from the publication of Central Institute of Road Transport for 25 Transport undertakings that are run by the government departments or corporations. The private operators have been excluded from the study. The paper highlights certain important issues such as efficiency rankings and potential improvements for inefficient units. The undertakings have a great potential for efficiency improvement.

Data Envelopment Analysis:

An application to Turmeric Production in North western region of Tamil Nadu

L. Mary Louis

Dept. of Science and Humanities,Faculty of Engineering

Avinashilingam University of Woment

Coimbatore 641108

A. John Joel

Centre for Plant Breeding and Genetics,

Tamil Nadu Agricultural University

Coimbatore 641003, Tamil Nadu

E-mail: jnjoel@gmail.com

Abstract

The main objective of this research is to identify and analyze the sources of technical inefficiency in turmeric crop farming system in north western region of Tamil Nadu from a sample of 180 turmeric growing farmers. A non-parametric approach, Data Envelopment Analysis (DEA) has been used to estimate Technical Efficiency Scores (TES). Results indicate the presence of technical inefficiency in turmeric farming system. The average technical efficiency score is 79 percent with the maximum score of 95 per cent and minimum score of 59 per cent. The potential to increase the technical efficiency score of turmeric growing farms is found to be 17 per cent.

DEA Based Estimation of the Technical Efficiency of State Transport Undertakings in India

 Shiv Prasad Yadav

Indian Institute of Technology Roorkee

Department of Mathematics

Roorkee 247667

Mail: yadavfma@iitr.ernet.in

Shivi Agarwal

Department of Mathematics, BITS, Pilani-333031

E-mail: shividma@gmail.com

S. P. Singh

Dept. of Humanities and Social Sciences

IIT Roorkee, 247667

E-Mail: singhfhs@iitr.ernet.in

Abstract

This paper measures the technical efficiency of public transport sector in India. The study makes an attempt to provide an overview of the general status of the State Transport Undertakings (STUs) in terms of their productive efficiency. Data have been collected for 35 STUs for the year 2004-2005. Technical efficiency of the STUs is measured by applying Data Envelopment Analysis (DEA) technique with the use of four input and three output variables. Fleet size, Total staff, Fuel consumption and Accident per lakh kilometer are considered as inputs and Bus utilization, Passenger kilometers and Load factor as outputs. On the basis of the status of technical efficiency, it is concluded that the performance of the STUs are good but still very far from the optimal level. The mean overall technical efficiency (OTE) is 83.26% which indicates that an average STU has the scope of producing the same output with the inputs 16.74% lesser than their existing level. Significant variation in OTE across STUs is also observed.

Ranking Efficient DMUs Based on Single Virtual Inefficient DMU in DEA

Udaya Shetty

District Statistical Office

Directorate of Economics and Statistics

Government of Karnataka

Mangalore, INDIA

E-mail:  uday_kenjoor@yahoo.co.in

T.P.M. Pakkala

Mangalore University

Dept. of PG Studies and Research in Statistics

Mangalagangotri -574 199

Mangalore, INDIA

E-mail:  tpm_pakkala@yahoo.com      

Abstract

 This paper describes an approach to rank the efficient decision making units (DMUs) based on a single DMU, referred as virtual DMU. The virtual DMU is created in such a way that its inputs and outputs are the averages of the corresponding inputs and outputs of all the DMUs. It is shown that this DMU is always inefficient compared to the efficient DMUs in the set if there exists at least one inefficient DMU. The work in this paper proposes to rank efficient DMUs based on the influence of efficient DMUs on the efficiency of the virtual DMU. This paper also establishes some of the properties of the virtual DMU. Our proposed method of ranking is compared with the existing methods. This approach of ranking produces stable efficient DMUs in the higher order of the ranks. This method is simple and robust compared to existing methods.





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Partially observable Markov decision model for the

treatment of early Prostate Cancer.

John E.Goulionis and B.K.Koutsiumaris

Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou Street, 18534 Piraeus, Greece.

Abstract

Prostate cancer is second only to lung cancer as the leading cause of cancer deaths in the world Furthermore, policies are difficult to make because of the generally indolent nature of prostate cancer and because it tends to occur in older men who often have multiple, competing medical illnesses. In this paper we applied a Partially observable Markov decision processes (POMDP) formulation to the problem of treating patients with Early prostate Cancer (EPC). The purpose of this paper is to address the challenge of effectively managing Early Prostate cancer therapies. To solve this problem we used a procedure that take advantage of special problem structure, and we provide optimal policies to stochastic and dynamic decisions naturally arise in finding optimal disease treatment plans.

A Fuzzy Algorithm for Multilevel
Programming Problems

S.R. ARORA
Department of Mathematics, Hans Raj College,
University of Delhi, Delhi-110007, India

and

ANURADHA GAUR
Department of Mathematics, Maharaja Agrasen College,
University of Delhi, Delhi-110091, India

ABSTRACT

This paper presents a Fuzzy Mathematical Programming (FMP) approach for solving Multilevel Decentralized Programming Problems (ML(D)PPs). The higher level Decision Maker(DM) makes the decision first to provide preferred values of the decision variables under control and the follower reacts by optimizing the objective function conditioned on the higher level DM’s decision. A simple method is employed to find a satisfactory solution under fuzziness with linear fractional objectives overcoming the selection of membership functions and tolerance values and terminates in a finite number of steps. The methodology proposes small number of iterations and aims at reducing the feasible space of a decision variable at each level of the hierarchical system until a satisfactory solution is obtained at the last level. The Stackelberg strategy is employed as a solution concept when decision problems are modeled as two-level programming problems, whether there is a cooperative relationship between the decision makers or not. Illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

A Study on   Bulk Arrival Non Markovian Single Service Queue  With  State  Dependent Service

R. Arumuganathan¹, *S. Jeyakumar²

                ¹Department of Mathematics and Computer Applications,

PSG College of Technology, Coimbatore, -641 004. India

Email :  ran_psgtech@yahoo.co.in

²Department of Mathematics, Chikkanna Government Arts College,

Tirupur, 641602. India

E-mail: jeyakumar_19@yahoo.co.in

ABSTRACT

A M^x/G/1 Queueing system with two service modes under (a, c, b) policy is considered. A single server Poisson queue with state dependent service is considered for analysis. The service is rendered with different service patterns (different distributions) as singly or in bulk according to the queue length. If the queue length reaches the threshold value ‘a’ then the server does single service and if the queue length reaches the value     ‘c’(c > a), then the server selects batch service with variable batch size with a maximum batch size of ‘b’ (b > c). The server starts the service only if number of customers in the queue is at least  ‘a’.  The Server switches over from single service to batch service or vice-versa only at service initiation epochs depending on the queue length. The probability generating function of the queue size at an arbitrary time epoch is obtained using supplementary variables technique. Some important performance measures are also obtained. Numerical example is presented in order to illustrate the effectiveness of the model.

An Experimental Evaluation of Heuristic Algorithms for Bus-depot Matching Problem of Urban Road Transport Systems

M. Mathirajan, V. Ramachandran

Department of Management Studies, Anna University Tiruchirappalli, Tiruchirappalli 620024

C.V. Hariharakrishnan

Dept. of Mechanical Engg. National Institute of Technology, Karnataka, Surathkal 575025

Abstract

This research is motivated by a bus-depot matching problem observed in Urban Road transport Systems (URTS). In URTS, buses are parked overnight at depots. Starting points of routes are usually different from depot locations. A bus has to cover the distance from its depot to the starting point of its route before being engaged on regular service. Likewise, buses usually do not provide service to the depot at the end of the service period. The distance travelled by a bus in a day from a depot to a starting terminus and/or from the ending or last terminus back to the depot without carrying passengers in known as ‘dead kilometers’. The dead kilometers can be reduced by efficiently allocating the buses to depots. In the literature this problem is solved using mathematical model and heuristic algorithms. However, there is no detailed computational analysis to highlight the merits and demerits of various solution methodologies, so far addressed in the literature. In this study a set of heuristic algorithms are considered to make an efficient decisions in buses-depots matching problem. A computational experiment is carried out to understand the efficiency of the heuristic algorithms considered in this study for various large size problems in comparison with exact solutions. From the computational analysis, two out of the five heuristic algorithms considered in this study, resulted very close to exact solutions in most of the problem instances. All the heuristic algorithms considered in this study takes very meager computational time in Pentium IV for the large size problem of 30 depots and 5,031 buses considered in this study.

An EOQ Inventory Model for Weibull Distributed Deteriorating Items under Ramp Type Demand and Shortages

By

B. Mandal

Head, Department of Mathematics,

Bajkul Milani Mahavidyalaya, Purba Medinipur

email: mandal_biswaranjan12@yahoo.co.in

Abstract

       An inventory model is considered in which it is depleted not only by demand, but also by deterioration. The Weibull distribution, which is capable of representing constant, increasing and decreasing rates of deterioration, is used to represent the distribution of the time to deterioration. Hence, we derive the EOQ model for inventory of item that deteriorates at a Weibull distributed rate, assuming the demand rate a ramp type function of time. Finally a numerical example has been studied along with its sensitivity.

A Heuristic Algorithm for the Fixed Charge Problem

Veena Adlakha*

Merrick School of Business, University of Baltimore

1420 North Charles Street, Baltimore, MD 21201

E-mail: vadlakha@ubalt.edu

Telephone: (410) 837 - 4969 (USA)

 Krzysztof Kowalski

 Department of Transportation

State of Connecticut

121 Cimarron Road, Middletown, CT 06457

E-mail: kgwkowalski@yahoo.com

Telephone: (860) 638 - 3972 (USA)

Abstract

This paper describes some special properties of a fixed charge problem and develops a heuristic algorithm for its solution.  The algorithm is based upon the Balinski approximation solution method for a fixed cost transportation problem.  In light of the absence of a widely applicable exact method for solving fixed charge problems, the heuristic algorithm presented in this paper should prove useful in dealing with such fundamental nonlinear problems.  A numerical example is presented to illustrate the proposed method.

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Validating AHP, Fuzzy Alpha Cut & Fuzzy Preference Programming Method Using

Clustering Technique

Kalyan  Mitra

Indian Maritime University, Kolkata  Campus (MERI)

P- 19, Taratala  Road,  Kolkata 700 088

E-mail: kalyan_mitra_2000@yahoo.com

Abstract

Fuzzy multicriteria analysis (MA) methods suitable for a given decision problem usually differ in aggregation processes for handling the alternatives' performance ratings and criteria weights. Due to their structural differences, these methods often produce inconsistent ranking results for the same fuzzy MA problem. This paper presents a validation procedure using fuzzy clustering for selecting among inconsistent ranking results produced by AHP, Fuzzy Alpha Cut and Fuzzy Preference Programming methods for a given problem. The procedure compares the ranking results obtained by fuzzy MA methods using different aggregation algorithms with the clustering results of the alternatives by fuzzy clustering. An empirical study of evaluating Major Port Trusts of India is conducted to demonstrate the effectiveness of the validation procedure.

Selection of Vendor Using Analytical Hierarchy Process Based on

Fuzzy Preference Programming

Prabjot Kaur, Rakesh Verma and N. C.Mahanti

Department of Applied Mathematics

Birla Institute of Technology, Mesra,

 Ranchi, India.

Abstract

Modern businesses face a more severe and challenging environment than before. Selection of Vendor and evaluating its performance are decisions of strategic importance from business point of view. Selecting Vendors involve those that perform optimally on the desired multicriteria dimensions like cost, quality, delivery performance etc. In this paper we identify the major criteria for selecting vendors and develop a hierarchy through which decision maker can examine the relationship among these criteria. Some of these criteria possess characteristics of fuzziness. By applying AHP based on fuzzy preference programming (FPP) a pair wise comparison is made between criteria .The whole process of fuzzy AHP involves decomposition, pairwise comparison, interval comparison, derive priorities using optimization technique of FPP. An overall crisp priority is obtained for ranking the best Vendor. A numerical example illustrates our methodology

Silo Sizing and Mixing to Improve Outgoing Quality of Fertilizer

T.S. Arthanari

Department of Information Systems & Operations Management

The University of Auckland, Auckland, New Zealand.

D.K. Manna and A.K. Biswas

SQC & OR Unit, Indian Statistical Institute, Chennai, India.

Abstract

Because of prevailing large variability in the process, mean level of the nutrients is set at higher value to meet stringent specification.  Large variability has resulted in reprocessing leading to loss in saleable production, and increased cost for reprocessing.  Higher process average (mean level) gives rise to free-give-away of costly nutrients to the customers. In this article, we determine the required size of silo (primarily for storage) and study suitable stacking and mixing methodology to reduce variability in outgoing product.  As a result, it is expected that reprocessing would be eliminated completely, and process average could be reduced.  The consequential annual benefit is worked out as Rs. 50 million on direct savings.



Ranking Efficient DMUs Based on Single Virtual Inefficient DMU in DEA

Udaya Shetty

District Statistical Office

Directorate of Economics and Statistics

Government of Karnataka

Mangalore, INDIA

E-mail:  uday_kenjoor@yahoo.co.in

T.P.M. Pakkala

Mangalore University

Dept. of PG Studies and Research in Statistics

Mangalagangotri -574 199

Mangalore, INDIA

E-mail:  tpm_pakkala@yahoo.com      

Abstract

This paper describes an approach to rank the efficient DMUs based on a single DMU, referred as virtual DMU. The virtual DMU is created in such a way that its inputs and outputs are the averages of the corresponding inputs and outputs of all the DMUs. It is shown that this DMU is always inefficient compared to the efficient DMUs in the set if there exists at least one inefficient DMU. The work in this paper proposes to rank efficient DMUs based on the influence of efficient DMUs on the efficiency of the virtual DMU. This paper also establishes some of the properties of the virtual DMU. Our proposed method of ranking is compared with the existing methods. This approach of ranking produces stable efficient DMUs in the higher order of the ranks. This method is simple and robust compared to existing methods.



Parametric Approach and Genetic Algorithm for Multi Objective Linear Programming with Imprecise Parameters

M.Chakraborty  and   Ananya Ray*

   Department of Applied Mathematics

Indian School of Mines

Dhanbad – 826004, India

^*E-mail: ananya_ray_2000@yahoo.com

ABSTRACT

Many real world decision making problems are multi objective in nature. However, in some cases the model parameters are imprecise in nature. Such type of problems cannot be solved using classical techniques. These modelling complications can be handled with the help of the concept developed in the theory of fuzzy sets. For the imprecise parameters the model users are normally able to give realistic intervals. Using parametric approach the fuzzy multi objective model may be reduced to multi objective linear programming with crisp parameters. Genetic Algorithm is a powerful technique to solve multi objective decision making problems. A set of non-dominated pareto optimal solutions may be obtained with this approach. In this paper the multi objective linear programming with imprecise parameter has been considered and solved using parametric approach and Genetic Algorithm. To illustrate the procedure a numerical example has been solved. A case study has been done for the allocation of coal and its by-products from a mine establishment to different consumption sites. The transportation cost, availability and the demands are defined by a realistic interval. The problem is solved by GA approach and efficient numerical solution has been found.



Cost Analysis of the Unloader Queueing System with a Single Unloader Subject to Breakdown with Two Types of Trailers

K C Sharma and Archana Sirohi,

Department of Mathematics & Computer Science

MSJ College, Bharatpur - 321001 (Raj.), INDIA

E-mail: sharma_kc08@yahoo.co.in & archana_sirohi@rediffmail.com

Abstract

The main purpose of this paper is to develop a cost model for the unloader queueing system with a single unloader subject to breakdown with two types of trailers. The optimum value of number of trailers (taking two types together) is determined in two types of systems such that cost function per trailer per unit time is minimum. In type one system, the unloader can breakdown only when there is at least one trailer in the system. In type two system, the unloader can breakdown even when there is no trailer in the system. Related measures and parameters are evaluated and cost function is determined. Numerical evaluation is also given.

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A Simplex Algorithm for Network Flow Problems with Piecewise-Linear

Fractional Objective Function

Pooja Pandey

Department of Mathematical Sciences,

University of New Brunswick, Saint John,

New Brunswick,  E2L 4L5, Canada

Abraham P. Punnen

Department of Mathematics,

Simon Fraser University Surrey,

Central City, 250-13450 102nd AV,

Surrey, British Columbia,V3T 0A3, Canada

Email: apunnen@sfu.ca

Abstract

The simplex algorithm for network flow problems has been proposed for linear, piecewise linear, and linear fractional objective functions. Piecewise linear fractional network flow problems can be transformed into equivalent linear or linear fractional programs, but the resulting problems do not possess pure network flow structure and increase the number of variables significantly. We develop a simplex algorithm to solve network flow problems with piecewise linear fractional objective function, unifying and generalizing the network simplex algorithm, network simplex algorithm for piece-wise linear programs, and network simplex algorithm for linear fractional programs. Computational results using the proposed algorithm are also discussed.

An Optimal Policy for Recovery and Procurement under Multiple Setups

Bhaba R. Sarker

Department of Industrial Engineering

Louisiana State University, Baton Rouge, LA 70803-6409

Phone: (225) 578-5370, FAX: (225) 578-5109

Email: bsarker@lsu.edu

Amrish D. Chawhan

Production Department

Bekaert Corporation

1881 Bekaert Drive, Van Buren, AR 72956-6801

Phone: 479-474-5211, Fax: 479-474-9075

Email: amrish.chawhan@bekaert.com

Pablo Biswas

Department of Industrial Engineering

Louisiana State University, Baton Rouge, LA 70803-6409

Phone: (225) 803-4231

Email: pbiswa1@lsu.edu

ABSTRACT

 This paper attempts to find the economic ordering quantity (EOQ) and economic procurement quantity (EPQ) for a system in which the demand can be satisfied by a combination of newly purchased products and recovered, used products. Used products are collected from customers and then they undergo recovery processes. These recovered products are regarded as perfectly new ones. The model developed here considers a realistic case where there can be multiple setups for both recoveries and procurements. We study cases where production/procurement rate is finite and infinite. We obtain the EOQ for newly procured products and the optimal inventory level of recoverable items to start the recovery process simultaneously. The total cost equation is found to be the function of the inventory level of recoverable items to start recovery and the ratio of orders for newly procured items to setups. Then, a search procedure to find the optimal control parameters is presented. The models have been validated with illustrating numerical examples and sensitivity analysis.

A Fully Polynomial Time Approximation Scheme for Weighted Job-dependent Earliness-Tardiness Problem with Agreeable Ratios

Sakib A. Mondal

India Science Lab, General Motors R&D

3rd Floor, Creator Building, ITPB, Whitefield Road

Bangalore – 560066, India, sakib.mondal@gm.com

Abstract:

This article considers a job scheduling problem arising in JIT context where a job may incur both earliness and tardiness penalty and these penalties are dependent on the job as well as amount of earliness and tardiness. Special cases of the problems have been shown to be NP-Complete.  To the best of our knowledge, there is no fully polynomial approximation scheme (FPTAS) for this problem. This article proposes a FPTAS for the problem.

Indefinite Quadratic Integer Bilevel Programming
Problem with Bounded Variables

Ruty Narang

Department of Mathematics, University of Delhi, India

Email: ritumaths_narang@yahoo.co.in

and

S.R. Arora

Department of Mathematics, Hans Raj College, University of Delhi, India

ABSTRACT

In this paper, an algorithm is developed to solve an indefinite quadratic integer bilevel programming problem with bounded variables. The problem is solved by solving the relaxed problem. A mixed integer cut for finding the integer solution of the given problem is developed. The algorithm is explained with the help of an example.

Selection of Warehouse Sites for Clustering Ration Shops to Them with Two Objectives through a Heuristic Algorithm Incorporating Tabu Search

Satya Prakash

Department of Mathematics, Amity School of Engineering and Technology,

 580, Delhi-Palam Vihar Road, Bijwasan, New Delhi–110061, India.

Email: a_satyaprakash @yahoo.com

 Mahesh K. Sharma and Amarinder Singh

School of Mathematics and Computer Applications, Thapar University,

Patiala–147004, India

Abstract

The problem of selecting upto a  fixed number of sites from among a given number of potential warehouse sites for clustering a given  number of ration shops to them  subject to several constraints with two objectives, is considered. One of the constraints is that each ration shop should be clustered to a unique warehouse site which is selected for locating a warehouse at it; however there is no restriction on the number of ration shops to be clustered to a selected warehouse site. Another constraint is that the total cost of the warehouses to be set up should not exceed a budgetary amount. The two objectives are to minimize the total cost and duration of meeting requirements of all the ration shops from their assigned warehouses at the selected sites. A heuristic iterative algorithm incorporating tabu search is developed to find the set of efficient solutions of this problem.

Maximum Entropy Condition In Multiserver Queueing System

S.N. Singh and Rekha Tiwari

Deptt. of Mathematics and Statistics

Dr. R.M.L. Avadh University, Faizabad – 224001 (U.P.)

Email: sks_5277@yahoo.com

Abstract

Maximum entropy condition in queueing theory due to SILVIU GUIASU has been subjected to further study in the present investigation. We have derived interarrival time by maximizing the entropy condition using gamma distribution. The chapter ends with interesting and useful results in   the form of two theorems, where the probability distribution and maximum entropy condition of the possible states of the system for multiserver queueing system has been derived.

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Optimization of Cropping Pattern Using Goal Programming Approach  - A Case Study

N. Vivekanandan

Assistant Research Officer

Central Water and Power Research Station, Pune 411024

K. Viswanathan

Reader

 NGM College, Pollachi 642001, Coimbatore 

Sanjeev Gupta

Assistant Engineer

Water Resources Department, Bhopal

Abstract

Irrigation planning and scheduling are essential components of water management in irrigated agriculture. For this purpose, optimal use of land and water is required for optimization of cropping pattern under a set of limitations. Number of approaches like Benefit-Cost, Functional, Programming, and Simulation are commonly used for optimization of cropping pattern. The paper presents three different cropping plans of Goal Programming (GP) approach, which was considered for maximization of net return, protein and calorie values with minimum land and water for the command area. The factors like amount of net return, utilization of surface and ground water by different plans were considered for selection of best cropping plan for optimization of cropping pattern for the command area under study. The paper gives the methodology adopted in optimizing the cropping pattern using GP approach and the results obtained from the study.

An Efficient Heuristic Algorithm for

the Bottleneck Traveling Salesman Problem

Ravi Ramakrishnan

Department of Applied Statistics, MA B1 453, EPFL, Lausanne, CH – 1015, Switzerland.

ravi.ramakrishnan@mail.com

Prabha Sharma

Department of Mathematics and Statistics, Indian Institute of Technology Kanpur,

Kanpur - 208016, India.

prabha@iitk.ac.in

Abraham P. Punnen

Department of Mathematics, Simon Fraser University Surrey, Central City,

250-13450, 102nd AV, Surrey, British Columbia,V3T 0A3, Canada.

apunnen@sfu.ca

Abstract.

This paper describes a new heuristic algorithm for the bottleneck traveling salesman problem (BTSP) which exploits the formulation of BTSP as a traveling salesman problem (TSP). Computational tests show that our algorithm is quite effective. It found optimal solutions for many problems from the standard TSPLIB problems. We also consider BTSP with an additional constraint and show that our BTSP heuristic can be modified to obtain a heuristic to solve this problem. Relationships between symmetric and asymmetric versions of BTSP are also discussed.

Call Processing Delay Analysis in Cellular Networks: A Queuing Model Approach

Vaneeta Jindal and S.Dharmaraja

Department of Mathematics, Indian Institute of Technology Delhi, India

(dharmar@maths.iitd.ac.in, vaneetajindal@yahoo.co.in)

Abstract

Mobile devices, which want to initiate calls, generate call request messages and then send them to a Base station (BS). A BS processes a call request message and then takes a decision of acceptance or rejection for the call. It is important to analyze the total time, which includes the waiting time and the processing time, spent by a call request message in the system. For if, this time is greater than the permissible delay, call will be blocked. Hence, the quality of service is degraded which is not acceptable to the service providers. Further, failures (such as hardware and software failures) and their recovery increase the delay. With this motivation, in this paper, we present queuing models for the analysis of delay experienced by a call request message for two cases: first, services of BS are not interrupted and second, services are interrupted due to the occurrence of failures at the BS. In the end, we discuss special cases of proposed queuing models for particular distributions of the processing times.

On Reserve Money for an EOQ Model in an Inflationary Environment under Supplier Credits

S.R. Singh*, Richa Jain

D.N.(P.G.) College, Meerut, U.P., India.

Email: *shivrajpundir@yahoo.com, arejae@rediffmail.com

ABSTRACT

We propose to derive a deterministic inventory model for a stock with time varying deterioration rate with a linear trend in demand over a finite planning horizon in this study. We assume that the supplier offers a credit limit to the retailer during which there is no interest charged. However, the retailer has the reserve capital with him to make the payments at the beginning of the transaction, but he decides to take the benefit of the credit limit. Each cycle has shortages which have been partially backlogged to suit present day competition in the market. Also, the whole study has been done in an inflationary environment using the Discounted Cash Flow (DCF) approach to impart economic feasibility to the model. Numerical examples have been presented to explain the theory, while sensitivity of the optimal solution of the system has been studied with respect to various system parameters.

A Discrete Time Bulk Service Queue with Accessible Batch: Geo/ NB ^(L,K) /1.

By

R. Sivasamy & N. Pukazhenthi

Statistics Department, Faculty of Social Sciences, University of Botswana,

P. Bag 00705, Gaborone, Botswana, E-mail: ramasamysr@mopipi.ub.bw

Abstract

This paper considers a discrete-time queue of packets awaiting movement according to the bulk service rule (L, K). Time is assumed to be divided into equal intervals called slots. The analysis has been carried out under the assumption that (i) service times of batches are independent of the number of packets in any batch and (ii) there is no simultaneous arrival of packets and departure of batch in a single slot. The packets arrive one by one and their inter arrival times follow geometric distribution. The arriving packets are queued in FIFO order. One server transports packets in batches of minimum number L and maximum K and service times follow negative binomial NB(α, p₁) distribution. The server accesses new arrivals even after service has started on any batch of initial number ‘j’ (L≤ j < K). This operation continues till the random service time of the ongoing batch is completed or the maximum capacity of the batch being served attains “K’ whichever occurs first. The distribution of system occupancy just before and after the departure epochs is obtained using discrete-time analysis (DTA). The primary focus is on the various performance measures of the steady state distribution of the batch server at departure instants and also on numerical illustrations.

An Order Level Inventory Model Under Two Level Storage System with Time-Dependent Demand

S.Ghosh and T.Chakrabarty

Department of Applied Mathematics

University of Calcutta, 92, A.P.C Road

Kolkata-700009, IINDIA

E-mail: suchhandasen_2008@yahoo.com

Abstract

An order-level inventory model is considered with two levels of storage for deteriorating items. When stock level exceeds the capacity of own warehouse (OW), it is to be kept in additional rented warehouse (RW) with higher holding cost than OW. The inventory held in RW is transferred to OW in bulk size (K) where, K is less than the capacity of OW till the stock in RW gets exhausted and there is an associated transportation cost. In developing the model it is assumed that the demand is time-dependent and shortages are allowed.

Replenishment Policy for Single Item Inventory Model with Money Inflation

 R.Uthayakumar, K.V.Geetha

 Department of Mathematics, Gandhigram Rural University,

Gandhigram – 624 302, Dindigul, Tamil Nadu, India.

 uthayagri@gmail.com, geethagri@gmail.com

Abstract

Finding out the replenishment policy is a hot topic of research in inventory management.  In this article, we propose an optimal replenishment policy by considering stock dependent consumption rate for non instantaneous deteriorating items with money inflation and time discounting.  In this model shortages are allowed and backlogging is partial.  Solution procedure is given and explained with examples.  The impact of various parameters of the system on the optimal solution is analyzed by carrying out sensitivity analysis with perturbations in various parameters.

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An Algorithm for Constrained Global Optimization of Multivariate Polynominals Using the Bernstein Form and John Optimality Conditions

P.S.V. Nataraj;  M.Arounassalame

Systems and Control Engineering, CRNTS Building

Indian Institute of Technology, Bombay, Mumbai – 400076, India

nataraj@sc.iitb.ac.in, aroun@sc.iitb.ac.in  

Abstract

We propose an algorithm for constrained global optimization of multivariate polynomials using the Bernstein form of polynomials. The proposed algorithm is of the branch and prune type, where branching is done using subdivision and pruning is done using the John optimality conditions for constrained minima. A main feature of this algorithm is that the branching and pruning operatins are done with the Bernstein polynomial coefficients. The performance of the proposed algorithm is compared with those of existing global optimization techniques, on a few examples. The obtained results show the superiority of the proposed method over existing methods, in terms of number of iterations and computational time.

Parent-centric Differential Evolution Algorithm for Global Optimization Problems

Millie Pant;  Musrrat Ali;  V.P. Singh

Department of Paper Technology, Indian Institute of Technology Roorkee

Saharanpur Campus, Saharanpur – 247001, India

millifpt@iirt.ernet.in, musrrat.iitr@gmail.com, singhvp2@yahoo.co.in  

Abstract

Differential evalution (DE) is population based evolutionary search algorithm widely used for solving optimization problems. In the present article we investigate the application of parent-centric approach on the performance of classical DE, without tampering with the basic structure of DE. The parentcentric approach is embedded in the mutation phase of DE. We propose two versions of (DE) called differential evolution with parent-centric crossover (DEPCX) and differential evolution with probabilistic parent-centric crossover (ProDEPCX) in order to improve the performance of classical DE. The proposed algorithms are validated on a test bed of ten benchmark functions and the numerical results are compared with basic DE and a modified version called trigonometric differential evolution (TDE). Empirical analysis of numerical results on the benchmark problems show that the performance of proposed versions is either at par or better in comparison to TDE and basic DE in terms of convergence rate and quality of fitness function value.

Solving Bilevel Programming Problems with Multicriteria Optimization Techniques

C. O. Pieume

GERAD, Department of Computers Sciences and Operations Research

University of Montreal – Canada

Copieume2001@yahoo.fr, calice.oliver.pieume@umontreal.ac.

L. P. Fotso

Department of Cmputers Sciences

University of Yaounde I – Cameroon,

lpfotso@bsu.edu

 P. Siarry

Faculty of Science and Technologies

University of Paris 12 Val de Marne – France

siarry@univ-paris12.fr

 Abstract

We introduce in this paper a new relation between bilevel programming and multicriteria optimization. We show that solving a certain class of bilevel programming problem can be equivalent to solve two independents multicriteria optimization problems. The optimal solutins of the bilevel problem are then the Pareto optimal points corresponding to the nondominated points belonging to the intersection of the two efficient sets. Comment on the practical implementation of the obtained relation is discussed. A generalisation of the relation between bilevel programming optimization and multicriteria optimization, first presented by Fulop [1] is also discussed in the paper.

Differential Evolution Algorithm with Ensemble of Populations for Global numerical Optimization

R. Mallipeddi;  P. N. Suganthan

School of Electrical and Electronic Engineering

Nanyang Technological University, Singapore 639798

mallipeddi@ntu.edu.sg; epnsugan@ntu.edu.sg

Abstract

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving global optimization problems over contineous space, which has been widely applied in many scientific and engineering fields. However the success of DE to handle a specific problem crucially depends on the proper choice of various parameters including the size of the population. Employing the trial and error scheme to search for the most suitable parameter setting requires high computational costs. In this paper we propose a DE algorithm with an ensemble of parallel populations in which the number of function evaluations allocated to each population is self-adapted by learning from their previous experiences in generating superior solutions. Consequently, a more suitable population size takes most of the function evaluations adaptively to match different phases of the search process/evolution. Although the evolutionary algorithms have been investigated for about five decades, to our best of knowledge so far no effective population adaptation scheme has been proposed. The performance of the DE algorithm with an ensemble of parallel populations is extensively evaluated on a suite of 14 bound-constrained numerical optimization problems and compares favourably with the conventional DE with different single population sizes.

Interactive Fuzzy Multiobjective Reliability Optimization Using NSGA-II

Amar Kishor;  Shiv Prasad Yadav

Department of Mathematics, I.I.T. Roorkee,

Roorkee, India 247667

amarsdma@iitr.ernet.in, yadavfma@iitr.ernet.in

Surendra Kumar

Department of Electrical Engineering, I.I.T. Roorkee,

Roorkee, India 247667

Surendra_iitr@yahoo.com

Abstract

In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Presence of multiple objectives in a problem, in principle, gives rise to a set of optimal solutions (largely known as pareto – optimal solutions), instead of single optimal solution. This type of problem is known as multiobjective optimization problem (MOOP). In general, a MOOP can be solved using weighted sums or decision-making schemes. An alternative way is to look for the pareto-optimal front. Many evolutionary algorithms (EAs) like genetic algorithm (GA) have been suggested to solve MOOP, hence termed as multiobjective evolutionary algorithm (MOEAs). Nondominated sorting genetic algorithm (NSGA-II) is one such MOEA which demonstrates the ability to identify a pareto – optimal front efficiently. Thus it provides the decision maker (DM) a complete picture of the optimal solution space. This paper presents the reliability optimization of a life-support system in a space capsule where reliability of the system is maximized while minimizing the cost. An interactive fuzzy satisficing method for deriving a pareto-optimal solution preferred by the DM is presented here. Prior preference of the DM has been taken into account here. Using the concept of fuzzy sets and convex fuzzy decision making a multiobjective fuzzy optimization problem is formulated from the original crisp optimization problem. Different nonlinear membership functions based on the DM’s preference have been employed for the fuzzification. The Then, NSGA-II is applied to solv the resulting fuzzified MOOP. Resulting pareto-optimal solution gives the DM variety of alternatives to seek an appropriate solution by modifying parameters interactively according to his/her preference again. Various pareto-optimal fronts under different preferences of DM have been reported.

Optimal Advertising Control Policy for a New Product in Segmented Market

P.C. Jha;  Kuldeep Chaudhury;  P.K. Kapur

Department of Operatinal Research

Faculty of Mathematical Sciences, University of Delhi, Delhi

 jhapc@yahoo.com

Abstract

Market segmentation is the foundation of which all other marketing actions can be based. It requires a major commitment by management to customeroriented planning, research, implementation and control. The overall objective of using a market segmentation strategy is to improve company’s competitive position and better serve the needs of customers. In this paper, we use the concept of market segmentation in diffusion model for advertising a new product considering the external as well as internal influences and study the optimal advertising effectiveness rate in a segmented market. Firs, we discuss the evolution of sales dynamics in the segmented market. First, we discuss the evolution of sales dynamics in the segmented market under the assumption that the firm advertises in each segment independently. Further case of a single advertising channel, which reaches several segments with fixed spectrum, is also discussed. Such problems have not been discussed before. The optimal control theory is applied to study and solve both classes of problems.

Optimization of GIS Analysis Using Hybrid Genetic Algorithm

Mohamad M.Awad

National Counci for Scientific Research, Centre, for Remote Sensing

P.O. Box 11-8281, Beirut, Lebanon, 11072260

mawad@cnrs.edu.lb

Abstract

Geographic information system (GIS) analysis is used to help in finding solutions for the most important geographical issues. Several programming techiniques and methods are used to produce optimal solutions for GIS analysis. One of these techniques is the Solver in Microsoft Excel (MS Excel) which adjusts the values in the excel sheet cells to produce an optimal result. Hybrid genetic algorithm (HGA) which is a combination of genetic algorithm and Hill-climbing technique is an important optimization method to solve many combinatorial problems such as GIS analysis problems. The solutions provided by HGA are better than the one obtained by any linear programming tool such as the Solver in MS Excel. The solver produces one solution, which is most of the time not an optimal solution and leads to wrong GIS analysis. In order to prove this idea, several sites are selected as wildife habitat locations in Lebanon using GIS analysis software, then HGA and the Solver are compared to find the maximum area for a wildlife habitat with the lowest cost of managing the habitat. This comparison proved that HGA finds many optimal solutions for wild life habitat locations better than the solution produced by MS Excel Solver. In addition, the cost provided by HGA is always similar or less than the cost of solver solution.

Intelligent Optimization Techniques Making Practical Emergency Responder Senior Networks

Lisa Osadciw;  Kalyan Veeramachaneni;

Weihua Gao;  Ganapathi Kamath

Department of Electrical Engineering and Computer Science

Syracuse University, NY – 13244

laosadic@syr.edu, kveerama@syr.edu, wgao03@syr.edu, gkamathh@syr.edu

Abstract

Swarm intelligence algorithms are developed to solve different aspect of the complex “First Responder Sensor Network” for emergency personnel. Swarm intelligence algorithms can solve both design problems as well as real-time processing problems. In this paper, two particle swarm optimization algorithms are developed to solve a complex design problem and, for contrast multilateration, a real-time signal-processing problem. A novel signal design technique is developed to design an ultra-wideband signal that supports communications as well as estimating location inside buildings and in hazardous conditions where GPS is unavailable. With the real-time processing in this network, propagation time is measured so that the location is estimated by a multilateration algorithm. The PSO based multilateration algorithm fuses time measurements from three or more sensors to locate a person in a two coordinate system.

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Hybridization of Particle Swarm Optimization with Quadratic Approximation

Kusum Deep;  Jagdish Chandra Bansal

Department of Mathematics

Indian Institute of Technology Roorkee

Roorkee – 247667 India

kusumfma@iitr.ernet.in, jcbansal@gmail.com

Abstract

Particle swarm optimization (PSO) has been extensively used in recent years for the optimization of nonlinear optimization problems. Two of the most popular variants of PSO are PSO-W (PSO with inertia weight) and PSO-C (PSO with constriction factor). Efforts have also been made to hybridize PSO with other methodologies to improve its performance. In this paper we present the hybridization of PSO with quadratic approximation operator (QA). The hybridization is performed by splitting the whole swarm into two subswarms in such a way that the PSO operators are applied on one subswarm, wherease the QA operator is applied on the other subswarm, ensuring that both subswarms are updated using the global best particle of the entire swarm. Based on the concept, two algorithms, namely qPSO –W and qPSO-C have been developed and their performance is evaluated with respect to PSO-W and PSO-C on the basis of 15 benchmark test problems and 3 real life problems taken from literature. The numerical and graphical results are a proof that the hybridized approach is a definite improvement in terms of efficiency, reliability and robustness.

Central Force Optimization: A New Deterministic Gradient – like Optimization Metaheuristic

Richard A. Formato

Registered Patent Attorney & Consulting Engineer

P.O. Box 1714, Harwich, MA 02645 USA

Rf2@ieee.org

Abstract

This paper introduces central force optimization as a new, nature-inspired metaheuristic for multidimensional search and optimization based on the metaphor of gravitational kinematics. CFO is a “Gradient-like” deterministic algorithm that explores a decision space by “flying” a group of “probes” whose trajectories are governed by equations analogoues to the equations of gravitational motion in the physical universe. This paper suggests the possibility of creating a new “hyperspace directional derivative” using the unit Step function to create positive-definite “masses” in “CFO space.” A simple CFO implementation is testd against several recognized benchmark functions with excellent results, suggesting that CFO merits further investigations.

The Flexi-PSO: Towards a More Flexible Particle Swarm Optimizer

M. Kathrada

Heriot-Watt University and Shell U.K. Limited

1 Altens Farm Road, Aberdeen, United Kingdom

Muhammad.kathrada@shell.com

Abstract

This paper presents some simple heuristics to increase flexibility in particle swarms. The particle velocities are updated with an extended inertia weight formulation, particles are also allowed to act as hill-climbers and the population is divided into exploration particles which are allowed to roam the search space more freely and exploitation particles which try to improve the fitness by fine tuning a local search, thus making the swarm much more flexible in its behaviour. These heuristics improve the traditional inertia weight PSO and show comparable performance in the computational results of benchmark functions to other state of the art techniques. The benchmark functions used are rigorous test bed for evaluating any optimization algorithm. An introduction and general overview of approaches to particle swarm optimizers is first presented, followed by a discussion of the proposed method. The result of the experiments is then discussed followed by proposals for future research directions.

A fuzzy Interactive Approach for Optimal Portfolio Management

Kusum Deep;  Krishna Pratap Singh

Depatrment of Mathematics, Indian Institute of Technology

Rorkee – 247667, Uttarakhand, India

kusumfma@iitr.ernet.in

M. L. Kansal

Department of Water Resources Development and Management

Indian Institute of Technology, Roorkee – 247667, Uttarakhand, India

C. Mohan

Ambala College of Engineering and Applied Research

Ambala, Haryana, India.

Abstract

Portfolio management problem is a multiobjective optimization problem in which some or all objectives are conflicting to each other. In real life, practitioners (investors) have an aim to choose his/her optimal portfolio with individual preferences for each objective. In this paper, a fuzzy interactive method is used to solve portfolio management problem. Using this approach, firstly, fuzzy goal is defined for each objective, keeping investor preferences in view, and then these fuzzy goals are aggregated using product operator. After that, the resultant problem is solved using a real coded genetic algorithm. An illustrated example is alos provided.

A Similarity-based Surrogate Model for Enhanced Performance in Genetic Algorithms

L. G. Fonseca;  H. J. C. Barbosa

LNCC, Av. Getulio Vargas, 333 Quitandinha

Petropolis, RJ Brazil, CEP 25651 – 075

goliatt@lncc.br, hcbm@lncc.br

A. C. C. Lemonge

UFJE, Department of Applied and Computational Mechanics,

Campus Universitario

Martelos, Juiz de Fora, MG Brazil, CEP 36036-330

afonso.lemonge@ufjf.edu.br

Abstract

In spite of their ability to deal with difficult optimization problems, genetic algorithms, in general require a large number of evaluations in order to find an optimal or a satisfactory near-optimal solution. When expensive simulations are involved in the optimization process, using genetic algorithms as optimization tools can become unattractive. The use of surrogate models is an interesting alternative to overcome that drawback, either by replacing expensive evaluations or allowing for exploration of the search space. In this paper we introduce a surrogate model based on similarity measures into genetic algorithms in order to enhance the performance in optimization problems, under a fixed budget of simulations. Numerical experiments are conducted in order to assess the applicability and the performance in constrained and unconstrained optimization problems. The results show that the present framework arises as an attractive alternative to improve the final solutions with a fixed budget of expensive evaluations.

Unit Commitment Scheduling Using Binary Differential Evaluation Algorithm

Aboalhassan Ghasemi, Malihe M. Farsangi, Hossein Nezamabadi-pour

Electrical Engineering Department

Shahid Bahonar University of Kerman, Kerman, Iran

aboalhassan_ghasemi@yahoo.com, mmaghfoori@mail.uk.ac.ir

nezam@mail.uk.ac.ir

Abstract

This paper presents a new approach for thermal generating units scheduling using binary differential evaluation (BDE) algorithm. Solving the unit commitment (UC) problem by BDE is a two stage process.In the first stage, the economic dispatch of the units are solved and hourly optimum solution of UC is obtained considering all constraints except the minimum up time (MUT) and minimum down time (MDT) constraints. In the second stage, the MUT and MDT are enforced by defining a probability function followed by modifying the schedule obtained in the first step. To validate the results obtained by BDE, a version of genetic algorithm (GA), namely as, PNUCO is applied for comparison. Also, the results obtained by BDE and PNUCO are compared with the previous approaches reported in the literature. The results show that the BDE produces optimal or nearly optimal solutions for the study systems.

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An Empirical Study of Stochastic Differential Equation Models Based on Component Importance Level for Open Source Software

Shigeru YAMADA

Department of Social Management Engineering, Graduate School of Engineering,

Tottori University

Minami 4-101, Koyama, Tottori-shi 680-8552, Japan

E-mail: yamada@sse.tottori-u.ac.jp

 Yoshinobu TAMURA

Department of Computer Science, Faculty of Applied Information Science,

Hiroshima Institute of Technology

Miyake 2-1-1, Saeki-ku, Hiroshima-shi 731-5193, Japan

E-mail: tam@cc.it-hiroshima.ac.jp

Abstract

Network technologies become increasingly more complex in a wide sphere. Especially, open source software systems which serve as key components of critical infrastructures in the society are still ever-expanding now. In this paper, we propose a new approach to software reliability assessment by creating a fusion of neural network and stochastic differential equations based on component importance levels.  Also, we analyze actual software fault-count data to show numerical examples of software reliability assessment considering component importance levels for an open source software. Moreover, we compare the goodness-of-fit of the proposed models with the conventional software reliability growth model for OSS.

A Unified Modeling Framework Incorporating Change-Point

for Measuring Reliability Growth During Software Testing

P. K. Kapur, Jyotish Kumar & Ravi Kumar

Department of Operational Research, Faculty of Mathematical Sciences,

University of Delhi, Delhi – 110007

E-Mail : pkkapur1@gmail.com

ABSTRACT

Reliability of software often depends considerably on the quality of software testing. By assessing reliability we can also judge the quality of testing. Alternately, reliability estimation can be used to decide whether enough testing has been done. Hence, besides characterizing an important quality property of the product being delivered, reliability estimation has a direct role in project management-the reliability models being used by the project manager to decide when to stop testing Jalote [12]. A plethora of software reliability growth models (SRGM) have been developed during the last three decades. Various software development environments and assumptions have been incorporated during the development of these models. From our studies, many existing SRGM can be unified under a more general formulation. In fact, model unification is an insightful investigation for the study of general models without making many assumptions. In the literature various software reliability models have been proposed incorporating change-point concept. To the best of our knowledge these models have been developed separately. In this paper we propose a general framework for deriving several software reliability growth models incorporating change-point concept based on non-homogeneous Poisson process (NHPP). In this paper some existing change-point models along with three new models have been derived from the proposed general framework. The models derived from the proposed general framework have been tested and verified using real data sets. Estimated Parameters and comparison criteria results have also been presented. 

Data-Driven Software Reliability and Availability Modeling and Prediction

Xuemei Zhang

Alcatel-Lucent, Murray Hill, NJ 07974

Hoang Pham

Department of Industrial and Systems Engineering, Rutgers University

Piscataway, NJ 08854

Abstract

Traditional software deployment readiness criteria, such as “zero severity one defects”, do not provide any indication of how reliable the product will be in the field.  In this paper, we propose a software reliability prediction framework to achieve data-driven, customer focused reliability and availability assessment throughout the entire development life cycle. Focusing on front-end reliability and availability improvement, the framework starts with availability evaluations as early as the architecture design phases. Markov-based architecture reliability models are used to study the failure and failure recovery mechanisms of the systems and solutions. These early evaluations can help architecture design, reliability requirement setting and reliability budget allocation. The early phase models and predictions can be updated as testing data becomes available. Software reliability growth models (SRGMs) are used to estimate one of the most influential parameters, i.e., the failure rates of software. Estimation of other reliability parameters, such as coverage factor, silent failure detection times and recovery durations and success probabilities are also discussed in this paper. This framework also calibrates test data with field observations, and thus forms a close-loop approach to evaluate the reliability and availability of the software product to verify that the product meet specific reliability expectation.

Software Reliability Models Incorporating Testing Effort

Lance Fiondella & Swapna S. Gokhale

Department of Computer Science & Engineering,

University of Connecticut, Storrs, CT 06269, U.S.A.

Abstract

Explicitly relating the effectiveness of fault detection to the effort expended in testing, achieved by incorporating testing effort into software reliability models has been the focus of many research efforts. Although the literature is replete with these “testing effort models,” their development appears to be ad hoc and disconnected. The objective of this survey is to propose a framework to classify testing effort models, aimed at identifying their commonalities and highlighting their differences. We conclude the article with a brief discussion of the limitations of the prevalent works in this domain, which also identify directions for future research.

Empirical Bayesian Software Reliability Model using Rayleigh Distribution

D. Damodaran

Centre for Reliability, Govt. of India, Chennai, India, duraidamodaran@yahoo.com

G. Gopal

Department of Statistics, University of Madras, India

P. K. Kapur

Department of Operational Research, University of Delhi, India

Abstract

An Empirical Bayesian software reliability model is considered in this paper.  It is assumed that the times between failures follow Rayleigh distribution with the parameter in the failure rate function with stochastically decreasing order on successive failure time intervals. The reasoning for the assumption on the parameter is that the intention of the software tester to improve the software quality by the correction of each failure. With the Bayesian approach, the predictive distribution has been arrived at by combining Rayleigh time between failures and gamma prior distribution for the parameter. The expected time between failure measures has been obtained. The posterior distribution of the parameter and its mean has been deduced. For the parameter estimation, Maximum likelihood estimation (MLE) method has been adopted. The proposed model has been applied to two sets of actual software failure data and it has been observed that the predicted failure times as per the proposed model are closer to the actual failure times. The predicted failure times based on Littlewood-Verall (LV) model is also computed. Sum of Square Errors (SSE) criteria has been used for comparing the actual time between failures and predicted time between failures based on proposed model and LV model.

Quantitative Software Quality/Reliability Prediction Based on Project Management Data for Waterfall and Agile Development Paradigms

Shigeru YAMADA & Toshiki AOKI

Department of Social Management Engineering, Graduate School of Engineering,

Tottori University, Tottori-shi, 680-8552 Japan

Phone: +81 857-31-5303

E-mail: yamada@sse.tottori-u.ac.jp

m07t7001a@edu.tottori-u.ac.jp

Toshiyuki TOYOTA

Department of Information Systems, Faculty of Environmental and Information Studies, Tottori University of Environmental Studies

Kita 1-1-1, Wakabadai, Tottori-shi 689-1111, Japan

Phone: +81 857-38-6505

E-mail: toyota@kankyo-u.ac.jp

Abstract

Software development productivity and product quality are related to quality of the software development process. Therefore, if we can improve quality of software development process based on project management technologies, software development productivity and product quality will be increased. In this paper, we conduct a multivariate analysis by using process measurement data, and derive a relational expression based on statistically significant factors, which can quantitatively predict final product quality/reliability. Furthermore, we apply a method of collaborative filtering by using process measurement data to predict final product quality from the similarity of software projects. Finally, we compare the results of two methods, i.e., multiple regression analysis and collaborative filtering, in terms of predictive accuracy of final product quality/reliability.

Improvement of QoS in Process Centric Software Development and Application of Analytical Network Process (ANP) for the Estimation of Critical Phases

K. Krishna Mohan, A. Srividya & Hari Ravi

Indian Institute of Technology Bombay, Mumbai, India

kkm@ee.iitb.ac.in, asvidya88@gmail.com, ravireliable@gmail.com

Ravi Kumar Gedela

Centre of Excellence- SAP, Satyam Computer Services Limited, INDIA

Ravikumar_Gedela@satyam.com

Abstract

 In a competitive business landscape, large organizations such as insurance companies and banks are under high pressure to innovate, improvise and distinguish their products and services while continuing to reduce the time-to market for new product introductions. Generating a single view of the customer is vital from different perspectives of the systems developer over a period of time because of the existence of disconnected systems within an enterprise. Therefore, to increase revenues and cost optimization, it is important to build enterprise systems more closely with the business requirements by reusing the existing systems. While building distributed based applications, it is important to take into account the proven processes like Rational Unified Process (RUP) to mitigate risks and increase the reliability of systems. Experiences in developing applications in Java Enterprise Edition (JEE) with customized RUP have been presented in this paper. RUP is adopted into an onsite-offshore development model along with ISO 9001and SEI CMM Level 5 standards. This paper provides a basis to achieve increased reliability qualitatively with higher productivity and lower defect density along with competitiveness through cost effective custom software solutions of an application. Qualitative reliability is obtained, which is the expected number of defects in the software obtained from the PoC (Proof-of–Concept) through the RUP implemented prototype. Based on the prototype, the critical parameter(s) affecting the QoS is then estimated using Analytical Network Process (ANP) prior to actual implementation of the application development.

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Design and Operational Maintainability Importance Measures -

A Case Study

Xueli Gao 

Center for Industrial Asset Management, www.uis.no/ciam

Tore Markeset

University of Stavanger, N4036 Stavanger, Norway

Javad Barabady

Tromsø University College, Norway, www.hitos.no

Abstract

Performance of a system depends upon its components. Some components have major influences on system reliability and maintainability than others. Hence, several component importance measures have been well defined and widely used in the reliability area. These importance measures enable the weakest and most critical areas of a system to be identified, and which should be considered modified to improve the production plant performance. The aim of this paper is to define maintainability importance measures in order to find the criticality of each component or subsystem from the maintainability point of view. Such importance measures should be useful for resources allocation to improve production plant performance in both the design and operation phases.

Release Time Decision Policy of Software Employed for the safety of Critical System under Uncertainty

P. C.  Jha, Anshu Gupta & P. K. Kapur

Department of Operational Research, Faculty of Mathematical Sciences,

University of Delhi.

Deepali Gupta

Department of Mathematics, Jaypee Institute of Information Technology,

University, Noida.

Abstract

Critical systems exist all around us, from nuclear power plants to chemical processing plants to heart monitors and emergency phone systems etc. As software and processors encompass critical systems, the risk involved because of software failure is unimaginable. The main emphasis of software industries developing these systems is to put a great deal of deliberation and thought into making these systems as safe as possible. Safety is a nebulous concept, and is therefore difficult to define or measure. In our paper we measure safety in the form of risk and the costs associated with it. We have formulated an optimization problem for determining the optimal time at which the software testing is stopped and system is ready for use in operational phase with the prime objective of minimizing risk cost subject to budget constraints and failure intensity. We have also considered uncertainty and ambiguities in the definition of cost function and risk function coefficients, available budget, failure intensity due to intense competition in the global market, varying requirements of the client, rapid evolution of information technology, system complexity, intended flexibility, poor data base to name a few. For this we have defined the constrained optimization problem under fuzzy environment. Finally we have discussed fuzzy optimization technique for solving the problem with a help of numerical illustration.

A probabilistic approach for predicting corrosion initiation time for RC members considering effect of temperature and relative humidity

A. Srividya

Civil Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai: 400076, India, E-mail: asvidya88@gmail.com

Satish B. Allampallewar  

Basic Engineering Department, Maharashtra Academy of Engineering, Alandi (D), Pune: 412105, India, E-mail: sallampallewar@yahoo.co.in

Abstract

Corrosion initiation time of steel reinforcement in partially saturated concrete member subjected to chloride ingress is investigated at five geographic locations along Indian coasts. An approximate explicit method from literature is modified to incorporate additional variables affecting diffusion rate. The method accounts for uncertainties of input parameters and predict expected time of first corrosion for the chosen risk of corrosion.  Method is also utilized to study the sensitivity of the parameters to reinforcement corrosion. Previously proposed diffusion based chloride ingress model is used for the analysis of time to initiate corrosion (corrosion initiation time). Corrosion is initiated when the chloride concentration on steel reinforcement exceeds a threshold value. Considerable variation in corrosion initiation time is observed for same concrete structure at different geographic locations. Life-365 predicts the time to corrosion initiation considering full-saturated condition of concrete. Comparing the results of the analysis for partially saturated and fully saturated concrete, it was found that Life-365 underestimates the time to corrosion initiation. Corrosion initiation time in ascending order was found at places Colaba, Kanyakumari, Santacruz, Chennai and Vishakhapatnam. Knowledge of corrosion initiation time is useful for owner, designer, or to an organization to take decision about repair strategy and prioritize repair of structures for corrosion protection in order to optimize maintenance planning and budgeting, since planned maintenance at the optimum time is the safest and most cost effective approach.





Uncertainty Consideration in Power System Well-being

Assessment Using Fuzzy Set Approach

M. V. Bhatkar

Department of Electrical Engineering, A.C.Patil College of Engineering,

Navi Mumbai, India-410210, Email: mvbhatkar@ee.iitb.ac.in

A. K. Verma

Department of Electrical Engineering, Indian Institute of Technology Bombay,

Powai, Mumbai, India -400076, Email: akv@ee.iitb.ac.in

Abstract

With increased energy demand, less new transmission, and open access, the power system is experiencing a much greater level of power transfer. These new requirements push the system to its limits for maximum economic benefit, while maintaining sufficient security margins that require network analysis. A practical interconnected system can collapse due to a number of different limits being exceeded such as thermal and operating reserve. Usually probabilistic methods are used in the conventional reliability assessment. The large amount of uncertainty is implicit in the estimate of system reliability because of insufficient failure data and variation in environmental conditions. In practice, limits are imposed by the operators on power system parameters, like line flows and bus voltages  are crisps when dealing the deterministic technique, but in real, these limits are no longer of a crisp nature and are considered as soft constraints. The reliability parameters such as failure and repair rates used in the probabilistic models basically come from historical operation records, and leads to considerable data uncertainty. In this paper an approach to assess the health of the bulk power system by incorporating the fuzzy sets is suggested. To deal with the issue of large number of contingencies, a fuzzy logic based ranking of outages is also illustrated. This paper provides an approach to extend the conventional probabilistic reliability analysis by including fuzzy set for the assessment of wellbeing of a composite power system in the adequacy domain.





Application of AHP to Fire Safety Based Decision Making of a Passenger Ship

S.W. Kim,  A. Wall & J. Wang

School of Engineering, Liverpool John Moores University, UK.

Y. S. Kwon

School of Aerospace and Naval Architecture, Cho-Sun University, Korea.

Abstract

Ship fire safety is increasingly attracting attention from both researchers and engineers. This paper develops an approach to integrate ship fire safety assessment and decision-making using the Analytical Hierarchy Process (AHP) method. The approach can be used to help reduce the probability of fire occurrence and severity of possible consequences during the operational phase of a passenger ship. It utilises the AHP theory to rank the fire events and further integrates the available control options (to minimise these fires) within the analysis. A test case on the operation of a passenger ship is used to demonstrate the approach.





Warranty System-Cost Analysis Using Quasi-Renewal Processes

Minjae Park & Hoang Pham

Department of Industrial and Systems Engineering

Rutgers University Piscataway, New Jersey USA

Abstract

In this paper, we present two alternative quasi renewal processes based on the quasi-renewal process recently developed by Wang and Pham [17]. The first alternative process is an altered quasi-renewal process with random parameter and the other is a mixed quasi-renewal process considering replacements and repairs. These mixed and altered quasi-renewal processes are used for developing the warranty cost models, reliability and other measures for k-out-of-n systems. A numerical example is discussed to demonstrate the applicability of the proposed methodology.





Design for High Performance Assurance for Offshore Production Facilities in Remote Harsh and Sensitive Environments

Tore Markeset

University of Stavanger, Center for Industrial Asset Management, 4036 Stavanger, Norway tore.markeset@uis.no

Abstract

During the last years there has been increasing interest in developing oil and gas fields in the Barents Sea north of the Polar circle, in the Arctic. However, there exists little experience and data with respect to operating in such a harsh climate, a sensitive environment and remote location. Hence, it is expected that one will face many challenges in developing offshore production facilities with respect to production regularity. The aim of this paper is to discuss production regularity for production facilities used in Arctic conditions and locations. Furthermore, we propose a model for decision-making with respect to regularity during the design phase. The model highlights important aspects to consider when deciding on what equipment to choose for achieving the regularity goals in the Arctic.





Optimal Maintenance Decision for Line Reparable Units (LRU’s) for an Aircraft System – A Conceptual Approach

Rajiv Dandotiya, Yuan Fuquing & Uday Kumar

Division of Operation and Maintenance Engineering,
Luleå University of Technology, Luleå, SE-97187, Sweden
rajiv.dandotiya@ltu.se

yuan.fuqing@ltu.se, uday.kumar@ltu.se

Abstract

Maintenance decisions for the repairable units (LRU’s) for an aircraft fleet are needs to be considered carefully while phasing out of an aircraft fleet in terms of cost effectiveness and fleet availability. Discard rate and phasing out period for an aircraft are the critical parameters for determining optimum time to stop the maintenance. The remaining economic value of useful life of an aircraft fleet should be taken into consideration by salvaging the LRU’s at the end of phasing out. These units can often be utilized for the aircraft staying in operation and this can influence the maintenance strategy for the units and the aircraft fleet. By salvaging units with remaining service life from retired aircraft, the relative stock level of units compared to operational aircraft will increase. This will give an opportunity to modify the maintenance strategy due to the increased number of units in the stock; units are discarded instead of being maintained which is a cost-effective strategy. In this paper a methodology has been suggested to optimize the availability of repairable units at a lowest life cycle cost, in order to decide at which point further maintenance can safely be stopped, and maintenance resources should be discarded. A mathematical formulation has been derived for the discard rate of aircrafts based on failure rate, mission life and remaining life of the aircrafts in the fleet that helps in managing demand rate of the units during the phase out of the aircraft fleet.





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Revisiting Dinkelbach-Type Algorithms for

Generalized Fractional Programs

Jean-Pierre Crouzeix

LIMOS, CNRS-UMR 6158, Université Blaise Pascal,

Clermont-Ferrand, France

Jacques A. Ferland

DIRO, Université de Montréal, Montréal, Canada.

Van Hien Nguyen

Département de mathématiques,

Facultés Universitaires Notre-Dame-de-la-Paix,

Abstract

In this paper we introduce a new Dinkelbach-type algorithm where the new iterate is determined using the information given by previous iterates and not only by the last one. The new algorithm is compared numerically with previous algorithms for generalized fractional programs.

On the Solution of Fuzzy Parametric Bicriterion Programming Problems

M. S. A. Osman

Dept.. of Mathematics, Higher Technology Institute,

Tenth of Ramadan City, Egypt.

A. M. A. Abdel -Fadel

Dept. of Mathematics, Faculty of Science,

Suez Canal University, Ismailia, Egypt

K. F. El-Sersy

Dept. of Mathematics, Faculty of Engineering,

Suez Canal University, Port- Said, Egypt

N. M. A Ibraheem

Dept. of Mathematics, Faculty of Engineering,

Suez Canal University, Port-Said, Egypt.

Abstract

This paper deals with Bicriterion mathematical programming problems with fuzzy numbers in the two objectives and free parameters in the right hand side of the constraints. An algorithm is proposed to find an  -Pareto Optimal Solution and the corresponding Stability Set of First Kind. Some basic stability notions are defined and characterized for the problem of concern. Finally, an illustrative nonlinear numerical example is given to clarify the algorithm.







A Branch and Bound Algorithm for the Partial Coverage Capacitated

Plant Location Problem.

Sudha Arora

Dept. of Mathematics, Deen Dayal Upadhyaya College, University of Delhi,

Shivaji Marg, Karam Pura, Delhi 110015.

S.R. Arora

Department of Mathematics, Hansraj College,

University of Delhi, Delhi-110007

                                                Abstract

In this paper, a branch and bound algorithm for the partial coverage capacitated facility locations problem is developed. We have to fix open a set of warehouses which are economically feasible.  It is an extension of the algorithm given by B. M. Khumawala [2] and Sudha Arora and S.R. Arora [10]. The case when the demand of the customer may not be satisfied completely, giving rise to “opportunity demand” is also discussed. This is illustrated with the help of examples and their computational results.







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An  Algorithm  for Multi-Level   Programming
Problem Using Goal Programming

S.R.Arora 
Department of Mathematics, Hans Raj College University of Delhi, Delhi
Ritu Gupta
 Department of Mathematics, University of Delhi, Delhi

Abstract

       This paper presents an algorithm for solving a multi-level programming problem using a linear pre-emptive goal programming model. The higher level decision maker (DM) provides the preferred values of the decision variables under his control and the target value of his objective function to the next level DM to formulate a goal programming problem equivalent to the given multi-level programming problem. It is illustrated with the help of an example of a tri-level programming problem.

Inventory Models wth Mixture of  Backorders Involving Reducible
Lead Time and Setup Cost

R.Uthayakumar
Department of Mathematics, Gandhigram University,
Gandhigram – 624 302, TamilNadu, India.
Email: uthayakavi@rediff.com

P. Parvathi
Department of Mathematics,
M.V.M. Government Arts College, Dindigul – 624 001, TamilNadu, India.


Abstract

    Lead time and setup cost are controllable variables in our continuous review inventory model. In this study we assume that only the first and second moments, of the probability distribution of lead time demand, are known, order quantity and backorder price discount are decision variables in our problem with mixture of backorders and lost sales. As a result of reducing lead-time we can significant savings and it is made know through numerical examples.

Chance Constrained Programming with Fuzzy Inequality Constraints

S. Nanda,  G. Panda,  J. K. Dash
Department of Mathematics, Indian Institute of Technology,
Kharagpur-721302, West Bengal, India

Abstract

This paper deals with a methodology for solving a Chance Constrained Fuzzy linear programming problem. The methodology is applied to the Chance Constrained model where the constraints have two different types of fuzzy inequalities and the method is justified through numerical examples.

Optimum Skiplot Sampling Plans Using Spread Sheets

P.Lavanya Kumari
S.P.W.Degree College, Tirupati, India

K.V.S.Sarma
S.V.University, Tirupati, India

Abstract

The characteristics of Skip Lot Sampling Plans (SkSP) originally developed by Dodge and Perry are reconsidered in this paper from a computational point of view.  The reference plan plays an important role in the performance of SkSP.  A Single Sampling Plan (SSP) is normally used as reference plan and a number of procedures are available to determine the SSP.  We focus on the algorithm-based procedures instead of methods based on statistical tables to determine the SSP and its effect on the performance indicators of SkSP.  Spreadsheet solutions are nowadays more user-friendly than customized programs written in specific languages.  We present a case of using Excel worksheet functions to handle statistical distributions required in the determination of the plan.  The performance of SkSP is compared by generating a SSP as reference plan using algorithms due to i) Guenther, ii) Modified Graf et al.   It is shown that an admissible reference plan can always be generated with Excel functions and templates are developed to obtain the characteristics of SkSP.

A Quadratic Regression Model with an Application to Business School Ranking


Pritibhushan Sinha
Quantitative Methods & Operations Management Area
Indian Institute of Management Kozhikode
Kozhikode – 673570, Kerala,  India.

E-mail: pritibhushan.sinha@iimk.ac.in



Abstract

We present a blocked, quadratic regression model in this article. The model has a predictor variable which does not allow direct measurement but may be estimated from other observations. A solution method is outlined to find the estimated values of the model parameters and such a predictor variable. The model has substantial scope of application. Such an application, in business school ranking, is discussed.

Optimal  Strategy Analysis of an  N-Policy M[X]/M/1 Queueing System                
with  a  Removable  and  Non-Reliable  Server

S. Anantha Lakshmi
Faculty of Engineering, Avinashilingam University, Coimbatore 641108
M.I. Afthab Begum & S. Swaroopa Rani
Department of Mathematics, Avinashilingam University, Coimbatore - 641 043.

Abstract

This paper analyses the modeling of a production system, which is designed as an N policy M[x]/M/1 queueing system with a removable and non-reliable server. The server spends a random period for startup procedure before each new service. The server does not start the production until some specified number of raw materials ‘N’ are accumulated in the queue and it stays idle when there is no input unit to process. The server is susceptible for random breakdown and in such a case it is repaired at once and it resumes the service. The units are assumed to arrive in batches of random size. Various system measures and stochastic decomposition property are obtained using generating functions.Optimal operating policy is achieved under a linear cost structure and a sensitivity analysis is  presented through numerical illustrations

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Title of the paper: Ranking of Decision Making Units: A Review and Development of New Model Using Data Envelopment Analysis Approach

Authors:
OmPal Singh
Assistant Professor, Mechanical & Production Engg. Dept.
Beant College of Engg. & Tech. Gurdaspur-143521, ompal@lycos.ecom

Satish Chand
Professor Mechanical Engineering Department,
Motilal Nehru National Institute of Technology, Allahabad –211004, India.

Abstract:
A key limitation of Data Envelopment Analysis (DEA) models are their inability to rank the decision making units (DMUs) particularly efficient ones. In this paper a systematic review of literature concerned to ranking of DMUs is presented. Thereafter a new model has been developed by extending the DEA model using merger methodology. According to this methodology in a set of n DMUs, one DMU is merged in another DMU simply by adding their inputs and outputs linearly while keeping the inputs and outputs of unmerged DMUs unaltered. These DMUs are then reanalyzed to get the relative efficiency of newborn DMU (achieved by merging two DMUs) and revised efficiencies of unmerged DMUs. Thereafter the same merging process is iterated for all possible combinations of mergers in a systematic manner. By doing this process we obtain nC2 total number of efficiencies for each DMU. Out of this set of results the frequency of occurrences of 100% efficiency for each DMU is counted. The DMU which has the maximum frequency of such occurrence has been assigned the top rank and others are put under lower rankings in order of occurrence of frequencies. In this approach maximum numbers of DMUs are assigned the ranking except few DMUs where there is a tie in the frequency. The ranking of such DMUs is decided on the basis of frequency of occurrences of higher efficiency scores.

Title of the paper: Fuzzy Logic Model for Cotton Grading

Authors:
P.A.Thakre
Department of Mathematics
Jayavantrao Sawant College of Engg.,Pune (MS)-India
Email:thakrepa@rediffmail.com

P.G.Khot
Department of Statistics
Department of Statistics, RTM Nagpur University, Nagpur (MS)-India
Email:pgkhot@sancharnet.in

Abstract:
This paper describes the applications of Fuzzy Logic (FL) to cotton grading. In order to improve the accuracy obtained by human experts and available testing instruments, this decision making tool will offer a new approach to classify ideal, excellent, good, average, below average and poor quality of cotton. Various quality features like length, strength, maturity, fineness, trash percentage and colour have been taken in to consideration and prepared fuzzy inference system (FIS) to grade cotton in to the categories such as Ideal, Excellent, good, average, below average and poor.

Title of the paper: Solution of Rectangular Fuzzy Games

Authors:
Prasun Kumar Nayak
Bankura Christian College, Bankura, INDIA, 722 101,
Email: nayak_prasun@ rediffmail.com.

Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Programming,
Vidyasagar University, Midnapore – 721 102, INDIA.

Abstract:
A solution of m´n rectangular fuzzy game with payoff as imprecise numbers instead of crisp real numbers namely interval and triangular fuzzy numbers is considered here. Solution of such fuzzy games with pure strategies and the algebraic method to solve 2´2 fuzzy game without saddle point by using mixed strategies is also discussed. Here the m´n payoff matrix is reduced to 2´2 payoff matrix by dominance method. In this paper, we discuss a saddle point solution from an uncertain payoff matrix. Moreover solution method for fuzzy games has also been developed. Numerical example is provided to illustrate the method.

Title of the Paper: An Inventory Model with Stock Dependent Demand and General Rate of Deterioration Under Conditions of Permissible Delay in Payments

Author:
Manisha Pal and Sanjoy Kumar Ghosh
Department of Statistics
University of Calcutta, India

Abstract:
In this paper a deterministic inventory model is developed for deteriorating items with general rate of deterioration and with stock dependent demand when shortages are observed. Conditions of permissible delay in payments are also taken into consideration. Numerical examples are cited to illustrate the model.

Title of the Paper: An EOQ Inventory Model with Ramp Type Demand, Weibull Distribution Deterioration and Starting with Shortage

Authors:
Sanjay Jain
Department of Mathematics
Government College, Ajmer – 305 001, INDIA
E-mail: drjainsanjay1@rediffmail.com

Mukesh Kumar
Department of Mathematics
Government College, Kishangarh, INDIA

Abstract:
An economic ordering quantity (EOQ) is developed for the model incorporating items with ramp type demand, starting with shortage and two – parameter Weibull distribution deterioration.

Title of the Paper: EOQ Model for Deteriorating Items Having Constant and Time-Dependent Demand Rate

Authors:
Meenakshi Srivastava
Reader, Department of Statistics, Institute of Social Sciences,
Dr. B.R. Ambedkar University, Agra.

Ranjana Gupta
Research scholar, Department of Statistics, Institute of Social Sciences,
Dr. B.R. Ambedkar University, Agra.

Abstract:
In this paper, an infinite time-horizon inventory model has been developed for deteriorating items assuming the demand rate to be constant for some time and then as a linear function of time. The theoretical expressions are obtained for optimum inventory level and total average cost. The model is illustrated with the help of numerical example. Sensitivity analysis has also been conducted to study the effect of the parameter on optimum policies.

Title of the Paper: Fuzzy Set Solutions for Optimal Maintenance Strategy Selection

Authors:
A. K. Verma
Reliability Engineering Group,
Indian Institute of Technology Bombay, Powai,
Mumbai-400076 (INDIA),
E-Mail: akv@ee.iitb.ac.in

A. Srividya
Reliability Engineering Group,
Indian Institute of Technology Bombay,
Powai, Mumbai-400076 (INDIA)
E-Mail: asvidya@ee.iitb.ac.in

Rajesh S. Prabhu Gaonkar
Mechanical Engineering Department
College of Engineering, Goa
Farmagudi, Ponda, Goa-403401 (INDIA
E-Mail: rpg@gec.ac.in

Abstract:
Selecting optimal maintenance strategy under fuzzy environment is not a trivial task. This paper presents an illustration of multi-criteria maintenance strategy selection under fuzzy environment. Three most common maintenance strategies and eight maintenance decision criteria’s have been considered and most appropriate/ optimal strategy selection process is demonstrated using three different techniques/ methods. Fuzzy linguistic terms have been used to rate and weigh the maintenance decision criteria’s. Linguistic terms/ variables are represented by triangular fuzzy sets/ number and fuzzy set operations have been carried out using – cut method. The basic technique used is rating and ranking method using fuzzy set theory wherein ratings of alternatives/ strategies is determined first and then ranking is carried out to decide the optimal strategy. Other methods i.e. ranking fuzzy sets using cardinal utilities and by maximizing and minimizing sets are also established to confirm our choice of optimal maintenance strategy.

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