Sharif Digital Repository

We present a new model and a new approach for solving fuzzy linear programming (FLP) problems with various utilities for the satisfaction of the fuzzy constraints. The model, constructed as a multi-objective linear programming problem, provides flexibility for the decision maker (DM), and allows for the assignment of distinct weights to the constraints and the objective function. The desired solution is obtained by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and study the effect of the control parameter on the solution. We also illustrate the efficiency of the model and present three algorithms for solving the FLP problem, the first of... 

The cutting stock problem is an important problem in the field of combinational optimization. In classic versions of this problem, the aim is to find a solution for cutting some equal-width mother rolls into smaller parts with given width so that the amount of trim-loss become as small as possible. There are plenty of works which addressed the classic cutting stock problem. However in real world applications there are usually some constraints which make the problem different form classical version and make it harder to solve. In this paper we investigate a special cutting stock problem in film industry and show that it can not be solved by using previous methods. We propose a new hybrid... 

We explore some duality properties in fuzzy number linear programming problems. By use of a linear ranking function we introduce the dual of fuzzy number linear programming primal problems. We then present several duality results. © 2006 Elsevier Inc. All rights reserved  

Recently, fuzzy variable linear programming problems have attracted some interests. We introduce the dual of fuzzy variable linear programming problem, and then deduce some important duality results. COPYRIGHT © ENFORMATIKA  

The problem of determining a shortest loop incident to each cell of a block layout is considered. A compact formulation is developed for this problem and a relatively simple algorithm is presented. It is shown that instances containing up to 60 cells can be solved optimally by using a commercial integer linear programming solver embedded within an iterative scheme. © 2005 Taylor & Francis Group Ltd  

This study develops a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-objective no-wait flow shop scheduling problem in a fuzzy environment. The proposed model attempts to simultaneously minimize the weighted mean completion time and the weighted mean earliness. A numerical example demonstrates the feasibility of applying the proposed model to no-wait flow shop scheduling problem. The proposed model yields a compromised solution and the decision maker's overall levels of satisfaction. © 2008 The#Franklin#Institute  

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach... 

In the last decade, technological innovations have resulted in considering distributed generation with heat recovery capability in addition to centralised generation. This work aims to develop a comprehensive model analysing techno-economic parameters of energy supply in an office building. The energy model is developed on the basis of the reference energy system with the linear programming technique. The objective function is the annual value of total costs of the energy supply system. The results of the model for the building of Sharif Energy Research Institute indicate that the most appropriate generation technology is an internal combustion engine of 461 kW and a water boiler of 152 kW.... 

To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search (VNS) algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a... 

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently,... 

Optimal production-distribution planning prevents capital accumulation, reduces costs, unemployment of machinery, and provides a good plan to satisfying customer needs. In this paper, a mixed-integer linear programming (MILP) model is developed to determine optimal production-distribution planning in electromotor manufacturing industries. The proposed model is a multi-product and multi-period one in which optimal amounts of production, inventory and distribution are determined in different periods. Also, the possibility of capacity expansion of facilities in different periods are modelled to optimally determine the capacity increase if necessary. To validate the proposed model, it is applied... 

Reliability cost is considered as an inevitable criterion in expansion planning studies of distribution systems. However, nonlinear expressions of reliability indices aggravate complexity of planning studies. To address this issue, this letter proposes a novel method to linearize mathematical model of the reliability-based distribution expansion planning problem. Using this variant of reliability indices, reliability costs can easily be involved in mixed-integer linear programming model of distribution expansion planning. Validity of the derived expressions is tested by simulation results. © 1969-2012 IEEE  

Standard mathematical-programming-based models have attracted considerable attention for optimizing distribution system planning and operation due to their salient advantages. More specifically, mixed-integer linear programming (MILP) has proven very effective in modeling such problems. The availability of optimization software for efficiently solving MILP problems with guaranteed convergence to optimality while providing a measure of the distance to the optimal solution has made MILP models more popular. Although a plethora of efficient MILP formulations have been proposed for planning and operating studies of distribution grids, incorporating reliability into such models is still... 

This paper presents a hierarchical demand response (DR) bidding framework in the day-ahead energy markets which integrates customer DR preferences and characteristics in the ISO's market clearing process. In the proposed framework, load aggregators submit aggregated DR offers to the ISO which would centrally optimize final decisions on aggregators' DR contributions in wholesale markets. The hourly load reduction strategies include load shifting and curtailment and the use of onsite generation and energy storage systems. The ISO applies mixed-integer linear programming (MILP) to the solution of the proposed DR model in the day-ahead market clearing problem. The proposed model is implemented... 

In this paper, a new market mechanism is proposed to quantify the value of emergency energy transactions in renewable-based multi-microgrid (MMG) systems. To reach this goal, main requirements and features of such emergency market are identified. Subsequently, a hybrid market framework is proposed which integrates pool emergency transactions and bilateral contracts in order to reduce the system risk in face of different contingency events. For settling different transactions in this market, the main procedure which should be followed by distribution system operator (DSO) to properly address bidding of microgrids (MGs) as well as system technical constraints are introduced. In addition, a... 

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally,... 

In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic spanning tree problem is presented. Then the proposed problem is formulated and solved by using the scalar expected value of fuzzy random variables. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper  

In this paper, we propose an optimization framework to retrieve an optimal group of experts to perform a multi-aspect task. While a diverse set of skills are needed to perform a multi-aspect task, the group of assigned experts should be able to collectively cover all these required skills. We consider three types of multi-aspect expert group formation problems and propose a unified framework to solve these problems accurately and efficiently. The first problem is concerned with finding the top k experts for a given task, while the required skills of the task are implicitly described. In the second problem, the required skills of the tasks are explicitly described using some keywords but each... 

We have recently proposed a structured algorithm for solving constrained nonlinear least-squares problems and established its local two-step Q-superlinear convergence rate. The approach is based on an earlier adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation makes use of the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians and adapts a structuring scheme due to Engels and Martinez. For robustness, we have employed a specific nonsmooth line search strategy, taking account of the least-squares objective. Numerical results also confirm the practical relevance of our special considerations for... 

We study the connection between biobjective mixed integer linear programming and normal form games with two players. We first investigate computing Nash equilibria of normal form games with two players using single-objective mixed integer linear programming. Then, we define the concept of efficient (Pareto optimal) Nash equilibria. This concept is precisely equivalent to the concept of efficient solutions in multi-objective optimization, where the solutions are Nash equilibria. We prove that the set of all points in the payoff (or objective) space of a normal form game with two players corresponding to the utilities of players in an efficient Nash equilibrium, the so-called nondominated Nash...