Operational Research Society of India - for Management Decision

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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