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A utility function is an important tool for representing a DM’s preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utility functions. We induce the probability of the utilities for each objective function using Bayesian theory. Illustrative examples considering dependence and independence of variables are worked through to demonstrate the usefulness of the proposed model. © 2017, The Author(s)  

When a production facility is designed, there are various parameters affecting the number machines such as production capacity and reliability. It is often a tedious task to optimize different objectives, simultaneously. The other issue is the uncertainty in many design parameters which makes it difficult to reach a desirable solution. In this paper, we present a new mathematical model with two objectives. The primary objective function is considered to be the production capacity and the secondary objective function is total reliability. The proposed model is formulated on different units of production which are connected together in serial form and for each unit, we may have various... 

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... 

Satisfying the clients' uncompromising priorities is a challenge for decision makers of organizations that face multiple projects. This paper considers an organization with a multi-skilled workforce working on several predetermined projects under time-of-use energy tariffs where distributed load energy usage is the primary concern of energy suppliers. This paper also considers different time-of-use energy tariffs, which are among the most common strategies to reach a more balanced energy utilization. The problem is stated as a bi-objective mixed-integer programming model containing two conflicting objectives; to minimize the total cost of the multi-skilled workforce and obtain a sustainable... 

This study aims to investigate the hydrogen production process using an integrated system based on solar energy. This system includes an evacuated tube collector to absorb solar energy as input energy of the system. A parametric analysis was conducted to determine the most important design parameters and evaluate these parameters' impact on the system's objective functions. For identifying the optimum system conditions, multi-objective optimization was performed using particle swarm optimization (PSO) algorithm. The results obtained from the parametric analysis show that an increment in the collector mass flow rate and the turbine inlet temperature, as well as a decrement in the collector... 

Satisfying the clients' uncompromising priorities is a challenge for decision makers of organizations that face multiple projects. This paper considers an organization with a multi-skilled workforce working on several predetermined projects under time-of-use energy tariffs where distributed load energy usage is the primary concern of energy suppliers. This paper also considers different time-of-use energy tariffs, which are among the most common strategies to reach a more balanced energy utilization. The problem is stated as a bi-objective mixed-integer programming model containing two conflicting objectives; to minimize the total cost of the multi-skilled workforce and obtain a sustainable... 

Using Renewable Energy (RE) is growing day by day. We need to locate RE in the best place to maximize energy production and supplier profit. As a result, we propose a novel method for RE location (REL). This model suggests a Data-Driven Robust Optimization (DDRO) for multi-objective REL by considering Risk (DDROMORELR). We consider risk by adding min function in energy and profit objectives (government and supplier objectives). A DDRO approach is added to the model to tackle uncertainty and be close to the real world. We utilize an improved Augmented ε-constraint (AUGEPS2) to solve objectives and produce a Pareto front. We compare problems with DDRO and without considering DDRO, and the... 

Efficient management of supply chain (SC) requires systematic considerations of miscellaneous issues in its comprehensive version. In this paper, a multi-periodic structure is developed for a supply chain network design (SCND) involving suppliers, factories, distribution centers (DCs), and retailers. The nature of the logistic decisions is tactical that encompasses procurement of raw materials from suppliers, production of finished product at factories, distribution of finished product to retailers via DCs, and the storage of raw materials and end product at factories and DCs. Besides, to make the structure more comprehensive, a flow-shop scheduling model in manufacturing part of the SC is... 

This research deals with a model with better efficiency for selection of portfolio making use of cardinal constraints, which are explained in previous sections. Such a method, which is a combination of fuzzy models and MCDM considering the constraints intended by investors, has not been used in previous models. We have considered transactions cost, because they are among factors important for an investor, and their being ignored in a portfolio selection method will result in inefficient portfolio. Sector value constraint is among other constraints considered here. Such a constraint aims to raise investment rate in sectors with higher values. Cardinal constraints (number of shares existing in... 

In this paper, an extension of the recently developed Crow Search Algorithm (CSA) to multi-objective optimization problems is presented. The proposed algorithm, called Multi-Objective Crow Search Algorithm (MOCSA), defines the fitness function using a set of determined weight vectors, employing the max-min strategy. In order to improve the efficiency of the search space, the performance space is regionalized using specific control points. A new chasing operator is also employed in order to improve the convergence process. Numerical results show that MOCSA is closely comparable to well-known multi-objective algorithms. © 2017 IEEE  

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests... 

In many projects, multi-skilled workforces are able to perform different tasks with different quality levels. In this paper, a real-life version of the multi-skilled resource constrained project scheduling problem is investigated, in which the reworking risk of each activity depends on the assigned level of multi-skilled workforces. The problem is formulated mathematically as a bi-objective optimization model to minimize total costs of processing the activities and to minimize reworking risks of the activities, concurrently. In order to solve the resulting problem, three cuckoo-search-based multi-objective mechanisms are developed based on non-dominance sorting genetic algorithm,... 

One of the basic requirements of the companies to survive in real-world competitive environments is to make their supply chains as efficient as possible. Due to recent governmental regulations, environmental issues, and the development of the concept of social responsibility, the closed-loop supply chain management has been focused by many researchers. A closed-loop supply chain includes both forward and reverse supply chain networks with the purpose of combining environmental considerations with the traditional supply chain network designs through the collection of used products and activities related to their reuse. In this paper, a bi-objective, multi-period, multi-product, closed-loop... 

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  

Usually, resources are short in supply when earthquakes occur. In such emergency situations, disaster relief organizations must use these scarce resources efficiently to achieve the best possible emergency relief. This paper therefore proposes a multi-objective, multi-mode, multi-commodity, and multi-period stochastic model to manage the logistics of both commodities and injured people in the earthquake response. Also, a robust approach is developed and used to make sure that the distribution plan performs well under the various situations that can follow an earthquake. Afterwards, it proposes a solution methodology according to hierarchical objective functions and uses it to illustrate the... 

The aim of the present work is to propose an eco-design method for sustainable development of methanol production by implementing a multi-objective optimization model based on CO2-efficiency. Two different approaches for the methanol production, i.e. a conventional reference methanol case (RMC) and proposed green integrated methanol case (GIMC) were compared from the view point of eco-design. Using life cycle assessment and process simulation, the environmental features as well as operational decision variables of the RMC and GIMC were assessed. Based on the inventory analysis of LCA, it was found that carbon dioxide is the major emitted pollutant from methanol production. Thus the... 

This article proposes a multi-objective goal programming based approach with two objectives of maximizing the reliability and minimizing the placement cost of Phasor Measurement Units (PMUs) for full observability in power systems. The weighted sum goal programming formulation incorporates the reliability of individual PMUs and finds a placement to resolve the conflicting objectives of minimum number of PMUs cost-wise and maximum level of system-wide reliability. This multi-objective problem is formulated as a nonlinear goal programming model in which weights are associated with the objectives. The model is solved for several weight scenarios for the IEEE 14, 30, 57 and 118 bus test systems.... 

The characteristics of integrating distributed generation (DG) in a distribution network have changed. These electrical resources are used as an alternative energy source to the main grid. The technical and economical benefits of such units are achieved only when they are optimally sized and placed in the network. In this paper, a static mixed integer non-linear model for distributed generation planning is defined and solved using a modified NSGA method (Non-dominated Sorting Genetic Algorithm). Different DG technologies are considered and the objective functions for minimization are defined as the total active loss, investment and operational costs, and environmental pollution. The method... 

Humanitarian logistics is regarded as a key area for improved disaster management efficiency and effectiveness. In this study, a multi-objective integrated logistic model is proposed to locate disaster relief centers while taking into account network costs and responsiveness. Because this location problem is NP-hard, we present a genetic approach to solve the proposed model