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Multi-objective university rescheduling problem by fuzzy programming technique

EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2024年第6期18卷 885-909页

作者： Bhoi, Sunil B. Dhodiya, Jayesh M. Bharati Vidyapeeth Deemed Univ Coll Engn Pune MH India Sardar Vallabhbhai Natl Inst Technol Dept Math Surat Gujarat India

This study presents multi-objective university rescheduling assignment problem (MOURAP), when some faculty members have been left the institute due to unavoidable circumstances, i.e., disruptions. This presented model executed in two phases. The first phase discusses and formulates the university course rescheduling problem and allocates unassigned courses to available faculty members based on the preferences for course of the faculty members, administrators and the indirect students preferences computed on faculty feedback and student result analysis. In the second phase, faculty members and courses are assigned to time in pairs, based on the faculty member's preferences. The prime aim of rescheduling is to minimise the course allocation change from former and latter to faculty members and time slots allocations change from initial and new schedule to faculty members and students. To test the strength of the presented model, this study demonstrated the model with two numerical examples on hypothetical data. With hypothetical numerical data, the model has been executed and has generated a new schedule by fuzzy programming technique with linear and exponential membership functions. This technique always produced non-dominated/compromise solutions. Results are obtained using LINGO19.0 software. [Received: 14 January 2022;Accepted: 9 July 2023]

关键词： university scheduling rescheduling 0-1 integer programming fuzzy programming technique

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Solution of Uncertain Constrained Multi-Objective Travelling Salesman Problem with Aspiration Level Based Multi Objective Quasi Oppositional Jaya Algorithm

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2024年第2期32卷 209-253页

作者： Bajaj, Aaishwarya Dhodiya, Jayesh Sardar Vallabhbhai Natl Inst Technol Dept Math & Humanities Surat Gujarat India

Multi-Objective Travelling Salesman Problem (MOTSP) is one of the most crucial problems in realistic scenarios, and it is difficult to solve by classical methods. However, it can be solved by evolutionary methods. This paper investigates the Constrained Multi-Objective Travelling Salesman Problem (CMOTSP) and the Constrained Multi-Objective Solid Travelling Salesman Problem (CMOSTSP) under an uncertain environment with zigzag uncertain variables. To solve CMOTSP and CMOSTSP models under uncertain environment, the expected value and optimistic value models are developed using two different ranking criteria of uncertainty theory. The models are transformed to their deterministic forms using the fundamentals of uncertainty. The Models are solved using two solution methodologies Aspiration level-based Multi-Objective Quasi Oppositional Jaya Algorithm (AL-based MOQO Jaya) and fuzzy programming technique (FPT) with linear membership function. Further, the numerical illustration is solved using both methodologies to demonstrate its application. The sensitivity of the OVM model's objective functions regarding confidence levels is also investigated to look at the variation in the objective function. The paper concludes that the developed approach has solved CMOTSP and CMOSTSP efficiently with an effective output and provides alternative solutions for decision-making to DM.

关键词： Constrained Multi-Objective Travelling Salesman Problem Uncertain Environment fuzzy programming technique AL-based Multi-Objective Jaya Algorithm

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An approach to solve an unbalanced fully rough multi-objective fixed-charge transportation problem

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COMPUTATIONAL & APPLIED MATHEMATICS 2022年第4期41卷 1-27页

作者： Shivani Rani, Deepika Ebrahimnejad, Ali Dr BR Ambedkar Natl Inst Technol Dept Math Jalandhar 144011 Punjab India Islamic Azad Univ Dept Math Qaemshahr Branch Qaemshahr Iran

Nowadays, rough set theory has become an invaluable tool to represent the uncertainty in different optimization problems because of its aspect of considering agreement and knowledge of all the experts and hence addressing more realistic decisions. Motivated by the nature of rough sets, in this study we investigate an unbalanced multi-objective fixed-charge transportation problem in which all the decision variables as well as coefficients of the objective functions and constraints are represented by rough intervals. A new method has been proposed to solve an unbalanced fully rough multi-objective fixed-charge transportation problem in which, firstly, an unbalanced fully rough multi-objective fixed-charge transportation problem transformed into a balanced fully rough multi-objective fixed-charge transportation problem. Then three approaches, namely, fuzzy programming technique, goal programming technique and weighted-sum method are applied for obtaining the Pareto-optimal solution of the transformed balanced fully rough multi-objective fixed-charge transportation problem. In weighted-sum method, analytic hierarchy process has been used to determine the weights corresponding to objective functions. A comparison is drawn between the Pareto-optimal solutions which are derived from different approaches. Since the obtained solution is in a rough environment, it provides a wide range to help the decision maker to extract the best compromise solution. Finally, a case study is solved to show the contribution of the article in the field of decision-making and transportation.

关键词： Unbalanced fixed-charge transportation problem Multi-objective optimization Rough interval coefficient fuzzy programming technique Goal programming technique Weighted-sum method Analytic hierarchy process Pareto-optimal solution

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Optimal solution for a single period inventory model with fuzzy cost and demand as a fuzzy random variable

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2015年第3期28卷 1195-1203页

作者： Dash, J. K. Sahoo, Anuradha Siksha O Anusandhan Univ Inst Tech Educ & Res Dept Math Bhubaneswar OR India

This paper presents the optimization of a single period inventory problem(SPIP) in particular a multi- item newsboy problem, where both fuzziness and randomness occur. Due to lack of data, the demand is subjectively determined. So demand is considered as a fuzzy random variable and the purchasing cost as a fuzzy number. The optimum order quantity and the expected profit have been obtained by using Buckley's concept of minimization of fuzzy numbers. The technique developed to transform a fuzzy single period inventory model into a crisp model and has been subjected to numerical verification.

关键词： Single period inventory model optimal order quantity fuzzy programming technique

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An attraction based particle swarm optimization for solving multi-objective availability allocation problem

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2018年第1期35卷 1169-1178页

作者： Samanta, Aniruddha Basu, Kajla NIT Durgapur Dept Math Durgapur 713209 W Bengal India

Reliability optimization and availability optimization are two classes of optimization problems in redundancy allocation problem (RAP). Contrary to reliability optimization, very few researchers have focused on availability optimization to find out the optimal redundancy. This paper proposes a multi-objective optimization problem of availability allocation in a series-parallel system with repairable components. The two objectives are maximizing the system availability and minimizing the total cost of the system. In real life situation, due to complexity of the systems and non-linearity of their behaviour, most of the data are usually uncertain and imprecise. Hence in order to make the model more reliable, fuzzy theory has been introduced in terms of triangular data for handling the uncertainties. Thus in fuzzy environment a fuzzy multi-objective availability allocation problem is formulated. In order to solve the problem a crisp optimization problem has been reformulated using fuzzy programming technique and finally an attraction based particle swarm optimization (APSO) has been proposed to solve this crisp optimization problem. The proposed APSO is compared with the traditional Particle swarm optimization (PSO) to show the efficiency and consistency of the proposed approach. Based on a numerical example, the statistical analysis of the experimental results establish that the proposed APSO has a better and consistent performance compared to traditional PSO.

关键词： Series-Parallel System availability allocation problem fuzzy programming technique Attraction based particle swarm optimization (APSO)

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Uncertain multi-objective multi-product solid transportation problems

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2016年第5期41卷 531-539页

作者： Rani, Deepika Gulati, T. R. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

The solid transportation problem is an important generalization of the classical transportation problem as it also considers the conveyance constraints along with the source and destination constraints. The problem can be made more effective by incorporating some other factors, which make it useful in real life situations. In this paper, we consider a fully fuzzy multi-objective multi-item solid transportation problem and present a method to find its fuzzy optimal-compromise solution using the fuzzy programming technique. To take into account the imprecision in finding the exact values of parameters, all the parameters are taken as trapezoidal fuzzy numbers. A numerical example is solved to illustrate the methodology.

关键词： Solid transportation problem fuzzy optimal-compromise solution fuzzy programming technique trapezoidal fuzzy number multi-product (item)

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Multi-objective multi-item solid transportation problem in fuzzy environment

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APPLIED MATHEMATICAL MODELLING 2013年第4期37卷 2028-2038页

作者： Kundu, Pradip Kar, Samarjit Maiti, Manoranjan NIT Dept Math Durgapur 713209 WB India Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 India

A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of "minimum of fuzzy number" is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Solid transportation problem fuzzy sets Expected value Minimum of fuzzy number fuzzy programming technique Global criteria method

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Multi-objective solid transportation problems with budget constraint in uncertain environment

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2014年第8期45卷 1668-1682页

作者： Kundu, Pradip Kar, Samarjit Maiti, Manoranjan Natl Inst Technol Dept Math Durgapur India Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore India

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.

关键词： solid transportation problem multiple objective programming uncertain variable chance-constrained programming fuzzy programming technique

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Stochastic programming problems involving Pareto distribution

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JOURNAL OF INTERDISCIPLINARY MATHEMATICS 2011年第1期14卷 39-56页

作者： Barik, S. K. Biswal, M. P. Chakravarty, D. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Indian Inst Technol Dept Min Engn Kharagpur 721302 W Bengal India

Stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are considered, where the right hand side parameters follow Pareto distribution with known mean and variance. Both the stochastic programming methods namely, chance constrained programming and two-stage stochastic programming are used. In order to solve these stochastic programming problems;we convert these problems into some equivalent deterministic models. Then we use standard mathematical programming techniques for solving single-objective deterministic model. We use fuzzy programming technique to solve the multi-objective deterministic model. The solution procedures are illustrated with an example.

关键词： Stochastic programming Chance constrained programming Two-stage stochastic programming Pareto distribution fuzzy programming technique

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Entropy based solid transportation problems with discounted unit costs under fuzzy random environment

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OPSEARCH 2014年第4期51卷 479-532页

作者： Giri, Pravash Kumar Maiti, Manas Kumar Maiti, Manoranjan Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Medinipur W Bengal India Mahishadal Raj Coll Dept Math Medinipur 721628 W Bengal India

This paper investigates some multi-objective fixed charge solid transportation problems (FCSTPs) under fuzzy-random environment with fuzzy-random fixed charges and transportation times. Here objectives are total transportation cost and time which are minimized. Unit transportation costs are crisp and three types of discount i.e. All Unit Discount (AUD), Incremental Quantity Discount (IQD), IQD within AUD are applied upon these costs. In the first model (Model-I) supplies, demands and capacities of conveyances are assumed to be fuzzy-random in nature. These quantities are fuzzy in the second model (ModelII). Imprecise objectives of the models are transformed into equivalent crisp ones using random expectation and fuzzy possibility/necessity measures on fuzzy event. Imprecise constraints are reduced to equivalent crisp constraints using two different fuzzy-random chance constraint methods. Similarly constraints of Model-II are reduced to equivalent crisp constraints with the use of possibility and necessity measures on fuzzy events. Models are also formulated with and without entropy function. Finally transformed constrained multi-objective deterministic problems are solved using a multi-objective genetic algorithm (MOGA) based on arithmetic crossover and boundary mutation. Moreover, Model-IA1 is converted to a single objective non-linear programming (SONLP) problem following fuzzy non-linear programming (FNLP) technique and the reduced ModelIA1S is solved using generalized reduced gradient (GRG) method (using LINGO software). Numerical examples are used for illustration and comparison of the models.

关键词： Solid transportation problem fuzzy random variable All unit discount Incremental quantity discount Entropy fuzzy programming technique Multi-objective genetic algorithm

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