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programming problem</title> <meta name="description" content="Search results for: linear programming problem"> <meta name="keywords" content="linear programming problem"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="linear programming problem"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 10597</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: linear programming problem</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10597</span> A Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujeet%20Kumar%20Singh">Sujeet Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Shiv%20Prasad%20Yadav"> Shiv Prasad Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=triangular%20intuitionistic%20fuzzy%20number" title="triangular intuitionistic fuzzy number">triangular intuitionistic fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming%20problem" title=" linear programming problem"> linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming%20problem" title=" multi objective linear programming problem"> multi objective linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20mathematical%20programming" title=" fuzzy mathematical programming"> fuzzy mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a> </p> <a href="https://publications.waset.org/abstracts/16411/a-fuzzy-programming-approach-for-solving-intuitionistic-fuzzy-linear-fractional-programming-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16411.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">566</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10596</span> Fuzzy Linear Programming Approach for Determining the Production Amounts in Food Industry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20G%C3%BCney">B. Güney</a>, <a href="https://publications.waset.org/abstracts/search?q=%C3%87.%20Teke"> Ç. Teke</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=food%20industry" title="food industry">food industry</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20linear%20programming" title=" fuzzy linear programming"> fuzzy linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20logic" title=" fuzzy logic"> fuzzy logic</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming "> linear programming </a> </p> <a href="https://publications.waset.org/abstracts/27880/fuzzy-linear-programming-approach-for-determining-the-production-amounts-in-food-industry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27880.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">650</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10595</span> Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qasim%20M.%20Kriri">Qasim M. Kriri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=parameter%20linear%20programming" title="parameter linear programming">parameter linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=objective%20function" title=" objective function"> objective function</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=optimize%20profit" title=" optimize profit"> optimize profit</a> </p> <a href="https://publications.waset.org/abstracts/86104/use-of-linear-programming-for-optimal-production-in-a-production-line-in-saudi-food-co" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86104.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">205</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10594</span> Sensitivity Analysis in Fuzzy Linear Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20H.%20Nasseri">S. H. Nasseri</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Ebrahimnejad"> A. Ebrahimnejad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20linear%20programming" title="fuzzy linear programming">fuzzy linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20numbers" title=" fuzzy numbers"> fuzzy numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=duality" title=" duality"> duality</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a> </p> <a href="https://publications.waset.org/abstracts/16916/sensitivity-analysis-in-fuzzy-linear-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16916.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">565</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10593</span> A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Mehdi%20Mazarei">Mohammad Mehdi Mazarei</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Asghar%20Behroozpoor"> Ali Asghar Behroozpoor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20derivative" title="general derivative">general derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a>, <a href="https://publications.waset.org/abstracts/search?q=smooth%20and%20nonsmooth%20functions" title=" smooth and nonsmooth functions"> smooth and nonsmooth functions</a> </p> <a href="https://publications.waset.org/abstracts/19425/a-new-approach-for-generalized-first-derivative-of-nonsmooth-functions-using-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19425.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">557</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10592</span> Three-Stage Multivariate Stratified Sample Surveys with Probabilistic Cost Constraint and Random Variance </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sanam%20Haseen">Sanam Haseen</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Bari"> Abdul Bari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper a three stage multivariate programming problem with random survey cost and variances as random variables has been formulated as a non-linear stochastic programming problem. The problem has been converted into an equivalent deterministic form using chance constraint programming and modified E-modeling. An empirical study of the problem has been done at the end of the paper using R-simulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chance%20constraint%20programming" title="chance constraint programming">chance constraint programming</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20E-model" title=" modified E-model"> modified E-model</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20programming" title=" stochastic programming"> stochastic programming</a>, <a href="https://publications.waset.org/abstracts/search?q=stratified%20sample%20surveys" title=" stratified sample surveys"> stratified sample surveys</a>, <a href="https://publications.waset.org/abstracts/search?q=three%20stage%20sample%20surveys" title=" three stage sample surveys"> three stage sample surveys</a> </p> <a href="https://publications.waset.org/abstracts/14515/three-stage-multivariate-stratified-sample-surveys-with-probabilistic-cost-constraint-and-random-variance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14515.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">457</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10591</span> Timetabling Communities’ Demands for an Effective Examination Timetabling Using Integer Linear Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20F.%20Jamaluddin">N. F. Jamaluddin</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20A.%20H.%20Aizam"> N. A. H. Aizam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=demands" title="demands">demands</a>, <a href="https://publications.waset.org/abstracts/search?q=educational%20timetabling" title=" educational timetabling"> educational timetabling</a>, <a href="https://publications.waset.org/abstracts/search?q=integer%20linear%20programming" title=" integer linear programming"> integer linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=scheduling" title=" scheduling"> scheduling</a>, <a href="https://publications.waset.org/abstracts/search?q=university%20examination%20timetabling%20problem%20%28UETP%29" title=" university examination timetabling problem (UETP)"> university examination timetabling problem (UETP)</a> </p> <a href="https://publications.waset.org/abstracts/49545/timetabling-communities-demands-for-an-effective-examination-timetabling-using-integer-linear-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/49545.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">337</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10590</span> Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahnaz%20Hosseinzadeh">Mahnaz Hosseinzadeh</a>, <a href="https://publications.waset.org/abstracts/search?q=Aliyeh%20Kazemi"> Aliyeh Kazemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20multi-objective%20linear%20programming%20problems" title="fuzzy multi-objective linear programming problems">fuzzy multi-objective linear programming problems</a>, <a href="https://publications.waset.org/abstracts/search?q=triangular%20fuzzy%20numbers" title=" triangular fuzzy numbers"> triangular fuzzy numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20ranking" title=" fuzzy ranking"> fuzzy ranking</a>, <a href="https://publications.waset.org/abstracts/search?q=supplier%20selection%20problem" title=" supplier selection problem"> supplier selection problem</a> </p> <a href="https://publications.waset.org/abstracts/54020/solving-fuzzy-multi-objective-linear-programming-problems-with-fuzzy-decision-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54020.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">383</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10589</span> Optimizing Human Diet Problem Using Linear Programming Approach: A Case Study</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=P.%20Priyanka">P. Priyanka</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Shruthi"> S. Shruthi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Guruprasad"> N. Guruprasad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Health is a common theme in most cultures. In fact all communities have their concepts of health, as part of their culture. Health continues to be a neglected entity. Planning of Human diet should be done very careful by selecting the food items or groups of food items also the composition involved. Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Linear programming techniques have been extensively used for human diet formulation for quiet good number of years. Through the process, we mainly apply “The Simplex Method” which is a very useful statistical tool based on the theorem of Elementary Row Operation from Linear Algebra and also incorporate some other necessary rules set by the Simplex Method to help solve the problem. The study done by us is an attempt to develop a programming model for optimal planning and best use of nutrient ingredients. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diet%20formulation" title="diet formulation">diet formulation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=nutrient%20ingredients" title=" nutrient ingredients"> nutrient ingredients</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=simplex%20method" title=" simplex method"> simplex method</a> </p> <a href="https://publications.waset.org/abstracts/19161/optimizing-human-diet-problem-using-linear-programming-approach-a-case-study" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19161.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10588</span> A Mixed Integer Linear Programming Model for Flexible Job Shop Scheduling Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Ziaee">Mohsen Ziaee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=scheduling" title="scheduling">scheduling</a>, <a href="https://publications.waset.org/abstracts/search?q=flexible%20job%20shop" title=" flexible job shop"> flexible job shop</a>, <a href="https://publications.waset.org/abstracts/search?q=makespan" title=" makespan"> makespan</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20integer%20linear%20programming" title=" mixed integer linear programming"> mixed integer linear programming</a> </p> <a href="https://publications.waset.org/abstracts/92281/a-mixed-integer-linear-programming-model-for-flexible-job-shop-scheduling-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/92281.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">184</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10587</span> Interval Bilevel Linear Fractional Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Hamidi">F. Hamidi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Amiri"> N. Amiri</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Mishmast%20Nehi"> H. Mishmast Nehi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s beneﬁt and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coeﬃcients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can ﬁnd the best and the worst optimal values of the leader objective function by two algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=best%20and%20worst%20optimal%20solutions" title="best and worst optimal solutions">best and worst optimal solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=bilevel%20programming" title=" bilevel programming"> bilevel programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional" title=" fractional"> fractional</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20coefficients" title=" interval coefficients"> interval coefficients</a> </p> <a href="https://publications.waset.org/abstracts/34778/interval-bilevel-linear-fractional-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34778.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">446</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10586</span> Production Plan and Technological Variants Optimization by Goal Programming Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tunjo%20Peri%C4%87">Tunjo Perić</a>, <a href="https://publications.waset.org/abstracts/search?q=Franjo%20Brati%C4%87"> Franjo Bratić</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper the goal programming methodology for solving multiple objective problem of the technological variants and production plan optimization has been applied. The optimization criteria are determined and the multiple objective linear programming model for solving a problem of the technological variants and production plan optimization is formed and solved. Then the obtained results are analysed. The obtained results point out to the possibility of efficient application of the goal programming methodology in solving the problem of the technological variants and production plan optimization. The paper points out on the advantages of the application of the goal programming methodolohy compare to the Surrogat Worth Trade-off method in solving this problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=goal%20programming" title="goal programming">goal programming</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20programming" title=" multi objective programming"> multi objective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=production%20plan" title=" production plan"> production plan</a>, <a href="https://publications.waset.org/abstracts/search?q=SWT%20method" title=" SWT method"> SWT method</a>, <a href="https://publications.waset.org/abstracts/search?q=technological%20variants" title=" technological variants"> technological variants</a> </p> <a href="https://publications.waset.org/abstracts/31123/production-plan-and-technological-variants-optimization-by-goal-programming-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31123.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">379</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10585</span> Application of De Novo Programming Approach for Optimizing the Business Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Z.%20Babic">Z. Babic</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20Veza"> I. Veza</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Balic"> A. Balic</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Crnjac"> M. Crnjac</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=business%20process" title="business process">business process</a>, <a href="https://publications.waset.org/abstracts/search?q=De%20Novo%20programming" title=" De Novo programming"> De Novo programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimizing" title=" optimizing"> optimizing</a>, <a href="https://publications.waset.org/abstracts/search?q=production" title=" production"> production</a> </p> <a href="https://publications.waset.org/abstracts/80556/application-of-de-novo-programming-approach-for-optimizing-the-business-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80556.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">222</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10584</span> Interactive Solutions for the Multi-Objective Capacitated Transportation Problem with Mixed Constraints under Fuzziness</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aquil%20Ahmed">Aquil Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Srikant%20Gupta"> Srikant Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Irfan%20Ali"> Irfan Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearization of fractional goal for solving the MOCTP. In this paper, imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=capacitated%20transportation%20problem" title="capacitated transportation problem">capacitated transportation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming" title=" multi objective linear programming"> multi objective linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20fractional%20programming" title=" multi-objective fractional programming"> multi-objective fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20goal%20programming" title=" fuzzy goal programming"> fuzzy goal programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20sets" title=" fuzzy sets"> fuzzy sets</a>, <a href="https://publications.waset.org/abstracts/search?q=trapezoidal%20fuzzy%20number" title=" trapezoidal fuzzy number"> trapezoidal fuzzy number</a> </p> <a href="https://publications.waset.org/abstracts/77380/interactive-solutions-for-the-multi-objective-capacitated-transportation-problem-with-mixed-constraints-under-fuzziness" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77380.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10583</span> Cars Redistribution Optimization Problem in the Free-Float Car-Sharing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amine%20Ait-Ouahmed">Amine Ait-Ouahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Didier%20Josselin"> Didier Josselin</a>, <a href="https://publications.waset.org/abstracts/search?q=Fen%20Zhou"> Fen Zhou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Free-Float car-sharing is an one-way car-sharing service where cars are available anytime and anywhere in the streets such that no dedicated stations are needed. This means that after driving a car you can park it anywhere. This car-sharing system creates an imbalance car distribution in the cites which can be regulated by staff agents through the redistribution of cars. In this paper, we aim to solve the car-reservation and agents traveling problem so that the number of successful cars’ reservations could be maximized. Beside, we also tend to minimize the distance traveled by agents for cars redistribution. To this end, we present a mixed integer linear programming formulation for the car-sharing problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=one-way%20car-sharing" title="one-way car-sharing">one-way car-sharing</a>, <a href="https://publications.waset.org/abstracts/search?q=vehicle%20redistribution" title=" vehicle redistribution"> vehicle redistribution</a>, <a href="https://publications.waset.org/abstracts/search?q=car%20reservation" title=" car reservation"> car reservation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a> </p> <a href="https://publications.waset.org/abstracts/67501/cars-redistribution-optimization-problem-in-the-free-float-car-sharing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67501.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">347</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10582</span> An Efficient Approach to Optimize the Cost and Profit of a Tea Garden by Using Branch and Bound Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abu%20Hashan%20Md%20Mashud">Abu Hashan Md Mashud</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Sharif%20Uddin"> M. Sharif Uddin</a>, <a href="https://publications.waset.org/abstracts/search?q=Aminur%20Rahman%20Khan"> Aminur Rahman Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integer%20programming" title="integer programming">integer programming</a>, <a href="https://publications.waset.org/abstracts/search?q=tea%20garden" title=" tea garden"> tea garden</a>, <a href="https://publications.waset.org/abstracts/search?q=graphical%20method" title=" graphical method"> graphical method</a>, <a href="https://publications.waset.org/abstracts/search?q=simplex%20method" title=" simplex method"> simplex method</a>, <a href="https://publications.waset.org/abstracts/search?q=branch%20and%20bound%20method" title=" branch and bound method"> branch and bound method</a> </p> <a href="https://publications.waset.org/abstracts/2584/an-efficient-approach-to-optimize-the-cost-and-profit-of-a-tea-garden-by-using-branch-and-bound-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2584.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">623</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10581</span> Solving Linear Systems Involved in Convex Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yixun%20Shi">Yixun Shi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20programming" title="convex programming">convex programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interior%20point%20method" title=" interior point method"> interior point method</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20systems" title=" linear systems"> linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20division" title=" vector division"> vector division</a> </p> <a href="https://publications.waset.org/abstracts/39573/solving-linear-systems-involved-in-convex-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39573.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">402</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10580</span> Energy Management System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Periyadharshini">S. Periyadharshini</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Ramkumar"> K. Ramkumar</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Jayalalitha"> S. Jayalalitha</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20GuruPrasath"> M. GuruPrasath</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Manikandan"> R. Manikandan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a formulation and solution for industrial load management and product grade problem. The formulation is created using linear programming technique thereby optimizing the electricity cost by scheduling the loads satisfying the process, storage, time zone and production constraints which will create an impact of reducing maximum demand and thereby reducing the electricity cost. Product grade problem is formulated using integer linear programming technique of optimization using lingo software and the results show that overall increase in profit margin. In this paper, time of use tariff is utilized and this technique will provide significant reductions in peak electricity consumption. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cement%20industries" title="cement industries">cement industries</a>, <a href="https://publications.waset.org/abstracts/search?q=integer%20programming" title=" integer programming"> integer programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20formulation" title=" optimal formulation"> optimal formulation</a>, <a href="https://publications.waset.org/abstracts/search?q=objective%20function" title=" objective function"> objective function</a>, <a href="https://publications.waset.org/abstracts/search?q=constraints" title=" constraints"> constraints</a> </p> <a href="https://publications.waset.org/abstracts/29389/energy-management-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29389.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">593</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10579</span> Optimal Production Planning in Aromatic Coconuts Supply Chain Based on Mixed-Integer Linear Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chaimongkol%20Limpianchob">Chaimongkol Limpianchob</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work addresses the problem of production planning that arises in the production of aromatic coconuts from Samudsakhorn province in Thailand. The planning involves the forwarding of aromatic coconuts from the harvest areas to the factory, which is classified into two groups; self-owned areas and contracted areas, the decisions of aromatic coconuts flow in the plant, and addressing a question of which warehouse will be in use. The problem is formulated as a mixed-integer linear programming model within supply chain management framework. The objective function seeks to minimize the total cost including the harvesting, labor and inventory costs. Constraints on the system include the production activities in the company and demand requirements. Numerical results are presented to demonstrate the feasibility of coconuts supply chain model compared with base case. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aromatic%20coconut" title="aromatic coconut">aromatic coconut</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20management" title=" supply chain management"> supply chain management</a>, <a href="https://publications.waset.org/abstracts/search?q=production%20planning" title=" production planning"> production planning</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed-integer%20linear%20programming" title=" mixed-integer linear programming"> mixed-integer linear programming</a> </p> <a href="https://publications.waset.org/abstracts/6619/optimal-production-planning-in-aromatic-coconuts-supply-chain-based-on-mixed-integer-linear-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6619.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">460</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10578</span> On Optimum Stratification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20G.%20M.%20Khan">M. G. M. Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20D.%20Prasad"> V. D. Prasad</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20K.%20Rao"> D. K. Rao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20variable" title="auxiliary variable">auxiliary variable</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20programming%20technique" title=" dynamic programming technique"> dynamic programming technique</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20programming%20problem" title=" nonlinear programming problem"> nonlinear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=optimum%20stratification" title=" optimum stratification"> optimum stratification</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20distribution" title=" uniform distribution"> uniform distribution</a> </p> <a href="https://publications.waset.org/abstracts/6677/on-optimum-stratification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6677.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">331</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10577</span> Solution of Nonlinear Fractional Programming Problem with Bounded Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mrinal%20Jana">Mrinal Jana</a>, <a href="https://publications.waset.org/abstracts/search?q=Geetanjali%20Panda"> Geetanjali Panda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20programming" title="fractional programming">fractional programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20valued%20function" title=" interval valued function"> interval valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20inequalities" title=" interval inequalities"> interval inequalities</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20order%20relation" title=" partial order relation"> partial order relation</a> </p> <a href="https://publications.waset.org/abstracts/22261/solution-of-nonlinear-fractional-programming-problem-with-bounded-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22261.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">519</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10576</span> Generalized Central Paths for Convex Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Li-Zhi%20Liao">Li-Zhi Liao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=central%20path" title="central path">central path</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20programming" title=" convex programming"> convex programming</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20central%20path" title=" generalized central path"> generalized central path</a>, <a href="https://publications.waset.org/abstracts/search?q=interior%20point%20method" title=" interior point method"> interior point method</a> </p> <a href="https://publications.waset.org/abstracts/58039/generalized-central-paths-for-convex-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58039.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">327</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10575</span> An Optimization Model for Maximum Clique Problem Based on Semidefinite Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Derkaoui%20Orkia">Derkaoui Orkia</a>, <a href="https://publications.waset.org/abstracts/search?q=Lehireche%20Ahmed"> Lehireche Ahmed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semidefinite%20programming" title="semidefinite programming">semidefinite programming</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20clique%20problem" title=" maximum clique problem"> maximum clique problem</a>, <a href="https://publications.waset.org/abstracts/search?q=primal-dual%20interior%20point%20method" title=" primal-dual interior point method"> primal-dual interior point method</a>, <a href="https://publications.waset.org/abstracts/search?q=relaxation" title=" relaxation"> relaxation</a> </p> <a href="https://publications.waset.org/abstracts/73224/an-optimization-model-for-maximum-clique-problem-based-on-semidefinite-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73224.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">222</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10574</span> A Linear Programming Approach to Assist Roster Construction Under a Salary Cap</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alex%20Contarino">Alex Contarino</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Professional sports leagues often have a “free agency” period, during which teams may sign players with expiring contracts.To promote parity, many leagues operate under a salary cap that limits the amount teams can spend on player’s salaries in a given year. Similarly, in fantasy sports leagues, salary cap drafts are a popular method for selecting players. In order to sign a free agent in either setting, teams must bid against one another to buy the player’s services while ensuring the sum of their player’s salaries is below the salary cap. This paper models the bidding process for a free agent as a constrained optimization problem that can be solved using linear programming. The objective is to determine the largest bid that a team should offer the player subject to the constraint that the value of signing the player must exceed the value of using the salary cap elsewhere. Iteratively solving this optimization problem for each available free agent provides teams with an effective framework for maximizing the talent on their rosters. The utility of this approach is demonstrated for team sport roster construction and fantasy sport drafts, using recent data sets from both settings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title="linear programming">linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=roster%20management" title=" roster management"> roster management</a>, <a href="https://publications.waset.org/abstracts/search?q=salary%20cap" title=" salary cap"> salary cap</a> </p> <a href="https://publications.waset.org/abstracts/155702/a-linear-programming-approach-to-assist-roster-construction-under-a-salary-cap" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/155702.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">111</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10573</span> Mathematical Programming Models for Portfolio Optimization Problem: A Review</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mazura%20Mokhtar">Mazura Mokhtar</a>, <a href="https://publications.waset.org/abstracts/search?q=Adibah%20Shuib"> Adibah Shuib</a>, <a href="https://publications.waset.org/abstracts/search?q=Daud%20Mohamad"> Daud Mohamad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=portfolio%20optimization" title="portfolio optimization">portfolio optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20programming" title=" mathematical programming"> mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20programming" title=" multi-objective programming"> multi-objective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=solution%20approaches" title=" solution approaches"> solution approaches</a> </p> <a href="https://publications.waset.org/abstracts/2654/mathematical-programming-models-for-portfolio-optimization-problem-a-review" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2654.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">348</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10572</span> Bounded Solution Method for Geometric Programming Problem with Varying Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullah%20Ali%20H.%20Ahmadini">Abdullah Ali H. Ahmadini</a>, <a href="https://publications.waset.org/abstracts/search?q=Firoz%20Ahmad"> Firoz Ahmad</a>, <a href="https://publications.waset.org/abstracts/search?q=Intekhab%20Alam"> Intekhab Alam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=varying%20parameters" title="varying parameters">varying parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20programming%20problem" title=" geometric programming problem"> geometric programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=bounded%20solution%20method" title=" bounded solution method"> bounded solution method</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20reliability%20optimization" title=" system reliability optimization"> system reliability optimization</a> </p> <a href="https://publications.waset.org/abstracts/131804/bounded-solution-method-for-geometric-programming-problem-with-varying-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131804.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">133</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10571</span> Spatial Interpolation Technique for the Optimisation of Geometric Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debjani%20Chakraborty">Debjani Chakraborty</a>, <a href="https://publications.waset.org/abstracts/search?q=Abhijit%20Chatterjee"> Abhijit Chatterjee</a>, <a href="https://publications.waset.org/abstracts/search?q=Aishwaryaprajna"> Aishwaryaprajna</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=geometric%20programming%20problem" title="geometric programming problem">geometric programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20optimisation%20technique" title=" multivariate optimisation technique"> multivariate optimisation technique</a>, <a href="https://publications.waset.org/abstracts/search?q=posynomial" title=" posynomial"> posynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spatial%20interpolation" title=" spatial interpolation"> spatial interpolation</a> </p> <a href="https://publications.waset.org/abstracts/70385/spatial-interpolation-technique-for-the-optimisation-of-geometric-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70385.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">371</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10570</span> Benders Decomposition Approach to Solve the Hybrid Flow Shop Scheduling Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ebrahim%20Asadi-Gangraj">Ebrahim Asadi-Gangraj</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20flow%20shop" title="hybrid flow shop">hybrid flow shop</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20integer%20linear%20programming" title=" mixed integer linear programming"> mixed integer linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=Benders%20decomposition" title=" Benders decomposition"> Benders decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=makespan" title=" makespan"> makespan</a> </p> <a href="https://publications.waset.org/abstracts/106041/benders-decomposition-approach-to-solve-the-hybrid-flow-shop-scheduling-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/106041.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">188</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10569</span> A Study of Using Multiple Subproblems in Dantzig-Wolfe Decomposition of Linear Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=William%20Chung">William Chung</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximate%20subproblem" title="approximate subproblem">approximate subproblem</a>, <a href="https://publications.waset.org/abstracts/search?q=Dantzig-Wolfe%20decomposition" title=" Dantzig-Wolfe decomposition"> Dantzig-Wolfe decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=large-scale%20models" title=" large-scale models"> large-scale models</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20subproblems" title=" multiple subproblems"> multiple subproblems</a> </p> <a href="https://publications.waset.org/abstracts/110435/a-study-of-using-multiple-subproblems-in-dantzig-wolfe-decomposition-of-linear-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110435.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">166</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10568</span> Solving the Quadratic Programming Problem Using a Recurrent Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20Behroozpoor">A. A. Behroozpoor</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20M.%20Mazarei"> M. M. Mazarei </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=REFERENCES%20%20%0D%0A%5B1%5D%09Xia" title="REFERENCES [1] Xia">REFERENCES [1] Xia</a>, <a href="https://publications.waset.org/abstracts/search?q=Y" title=" Y"> Y</a>, <a href="https://publications.waset.org/abstracts/search?q=A%20new%20neural%20network%20for%20solving%20linear%20and%20quadratic%20programming%20problems.%20IEEE%20Transactions%20on%20Neural%20Networks" title=" A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks"> A new neural network for solving linear and quadratic programming problems. 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