Multiobjective Stochastic Linear Programming Research Articles

Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems

This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology.

Towards a responsive-sustainable-resilient tea supply chain network design under uncertainty using big data

Nowadays, issues such as limited natural resources, environmental problems, social matters, and significance of resilience in agricultural supply chain (ASC) have dragged considerable attention worldwide. In this research, a five-level multi-objective stochastic mixed-integer linear programming model is designed for tea supply chain (TSC) in Iran. The objective functions of the suggested network are minimizing total costs of the supply chain (SC), the total water consumption, and non-resilience measures, and maximizing job opportunities of facilities. Literally, considering uncertainty for SC networks is extremely beneficial due to the existence of some variations in different parameters like demand. As a consequence, a robust possibilistic optimization (RPO) is implemented to manage the uncertainty. Due to the nature of the multi-objective optimization problem, the weighted-normalized-extended goal programming (WNEGP) approach is employed to solve the model. In order to credit the model, real data is collected from the tea organization of Iran. It is worth mentioning that parameters are gathered according to three aspects of big data: volume, velocity, and variety. The results validated the functionality of the model regarding planning strategy. In addition, it showed applying more costs on SC triggers an effective sustainable-resilient-responsive network. In terms of managerial insights, this study offers a far-reaching perspective to managers especially in ASC to develop their industries. Finally, some sensitivity analyses are discussed on key parameters such as demand, robustness coefficients, and also the value of the objective functions in various states. It is worth mentioning that sensitivity analyses on different states of the problem show how sustainability and resiliency affect the supply chain efficiency.

WEIGHTED ADDITIVE MODEL AND CHANCE CONSTRAINED TECHNIQUE FOR SOLVING NONSYMMETRICAL STOCHASTIC FUZZY MULTIOBJECTIVE LINEAR PROGRAM

The problems of linear programming are developing from time to time, and its complexity is constantly growing. Various problems can be viewed as a multi-objective fuzzy linear programming, multi-objective stochastic linear programming or a combination of both. This research is focused on examining Multi-Objective Fuzzy Stochastic Linear Programming (MOFSLP) with each of the objective functions has a different level of importance to decision makers, or better known as the nonsymmetrical model. The objective function of the linear program contains fuzzy parameters, while the constraint function contains the fuzzy parameters and random variables. The purpose of this study is to develop an algorithm to transform the MOFSLP be a Program of linear Single-Objective Deterministic Linear Programming (SODLP) so that it can be solved using simplex method. In the process of transforming MOFSLP to SODLP, several approaches have been used. They are; weighted additive model, analytic hierarchy process and chance constrained technique. An example of numerical computations has been provided at the end of the discussion in order to illustrate how the algorithm works. The resulted Model and algorithm are expected to help companies in the decision making process.

Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

A novel approach for solving stochastic problems with multiple objective functions

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

Fractile criterion iterative-interactive optimisation process for multi-objective stochastic linear programming problems in fuzzy environment

Present article focuses on one general fractile criterion iterative-interactive optimisation process in order to obtain the preferable Pareto optimal solution, subject to specified main objective function to multi-objective stochastic linear programming problems in fuzzy environment. This asks the managers to identify the main objective function among all objective functions without specifying any weights or utility functions. Unlike existing articles, the reference membership levels to conflicting objective functions are analytically determined by employing the trade-off ratios among objective functions in this process. Moreover, the necessity of only very few interactions with decision-makers saves the precious time and money of organisations. Numerical applications demonstrate the efficiency of proposed process. Finally, conclusions are drawn.

Fractile criterion iterative-interactive optimization process for multi-objective stochastic linear programming problems in fuzzy environment

Present article focuses on one general fractile criterion iterative-interactive optimisation process in order to obtain the preferable Pareto optimal solution, subject to specified main objective function to multi-objective stochastic linear programming problems in fuzzy environment. This asks the managers to identify the main objective function among all objective functions without specifying any weights or utility functions. Unlike existing articles, the reference membership levels to conflicting objective functions are analytically determined by employing the trade-off ratios among objective functions in this process. Moreover, the necessity of only very few interactions with decision-makers saves the precious time and money of organisations. Numerical applications demonstrate the efficiency of proposed process. Finally, conclusions are drawn.

Decentralized rainwater harvesting program for rural cities considering tax incentive schemes under stakeholder interests and purchasing power restrictions

Abstract This paper focuses on implementing a decentralized rainwater harvesting (DRH) program for rural cities under stakeholder interests and purchasing power restrictions. The study is conducted by considering: (1) a no tax incentive scheme (NTIS); (2) a flat rate tax incentive scheme (FTIS); and (3) a progressive tax incentive scheme (PTIS). A three-stage decision framework is proposed. In the first stage, a water balance simulation model is developed to estimate the amount of rainwater that can be collected at individual households using different capacity rain barrels and to determine the threshold rain barrel capacity. In the second stage, the water balance simulation model is run multiple times with varying input parameters to obtain the probability distributions for rainwater used and water demand for different households using different capacity rain barrels, which are then used to generate scenarios for the third stage optimization model. In the third stage, a multi-objective stochastic mixed integer linear programming (Mo-SMILP) model is proposed that aims to determine the household participation rate and cumulative city-wide DRH capacity considering tax incentive schemes, stakeholder interests, and purchasing power restrictions. The proposed Mo-SMILP model is solved by using an improved augmented epsilon constraint method (AUGMECON 2) in order to understand the trade-off between city-wide household reliability, city-wide household savings, and city government savings. A case study of a small rural city in the State of Texas in the US is used to illustrate the effectiveness of the proposed decision framework. The results shows a significant decrease in city-wide household reliability when stakeholder interests and purchasing power are considered. In addition, the PTIS is best at improving city-wide household reliability and savings. NTIS and FTIS are best at improving city government savings depending on the household preference for reliability and savings.

Multi-objective stochastic programming energy management for integrated INVELOX turbines in microgrids: A new type of turbines

In this paper, a new type of wind turbine that is called INVELOX has been used. INVELOX has many advantages such as six times more power generation than previous types, work at low speed, inconsiderable maintenance and investment costs, and reduce the environmental effects of previous wind turbines. Moreover, other renewable and nonrenewable generators are used in the energy management and scheduling of the microgrid. The test case is a microgrid with selling and buying energy capability in which the cost and pollution are considered as the objective functions. In the following, Uncertainties of wind speed, solar radiation and electrical-thermal loads are investigated and a multi-objective stochastic mixed integer linear programming is solved in the first scenario. Then, in the second scenario, the effects of fuel cost uncertainty on generation units and objective functions have been studied. The Epsilon constraints method and fuzzy satisfying are utilized to solve the problem and choose the best solution, respectively. By using of INVELOX turbines, total cost and pollution of the microgrid in both deterministic and stochastic planning are reduced from 192.68 $ to 97.23 $ and 249.28 $ to 126.38 $, as well 3334.76 Kg to 3302.7 and 3925.63 to 3910.2 Kg respectively.

Bi-Level Multi-Objective Stochastic Linear Fractional Programming with General form of Distribution

This paper deals with the stochastic approach of bi-level multi-objective linear fractional programming problem.In this type of bi-level programming problem stochastic nature the right hand side resource vector is considered to follow a general form of distribution F (bi) = 1 − Bi^exp(Aih(bi))[13], which in itself includes many well known distributions such as Pareto distribution, Weibull distribution etc. After converting the problem into an equivalent deterministic form, each level of the problem is transformed into a single objective by using K-T conditions. Finally the problem is solved by Taylors series approach. A numerical example is also presented to illustrate how the proposed approach is utilized.

A compromise solution method for the multiobjective minimum risk problem

We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.

Iterative Solution Process for Multiple Objective Stochastic Linear Programming Problems Under Fuzzy Environment

This article presents one interactive algorithm, and thereby determines the Pareto optimal solution to multi-objective stochastic linear programming (MOSLP) problems in real-life oriented fuzzy environment. Among the various objective functions, there always exists one objective function, referred to as the main objective function in this article, to multi-objective models, whose optimal value is most vital to decision-makers. When the optimal value to main objective function meets the pre-determined aspiration level, and the corresponding values to other objective functions are satisfactory in nature, that Pareto optimal solution is acceptable to decision-makers. Again, in several existing interactive fuzzy optimisation methods to MOSLP models, all reference membership levels of expectations to objective functions are considered as a unity. However, this seems to be less rational that the expectation of each conflicting objective function simultaneously attains the individual goal. So, the present article proposes to employ the trade-off ratios of membership functions to analytically determine reference membership levels in a fuzzy environment. Numerical applications further illustrate this algorithm. Finally, conclusions are drawn.

Designing a sustainable stochastic electricity generation network with hybrid production strategies

This paper aims to design a sustainable stochastic electricity production network where fossil fuels-based, biomass-based, and co-firing-based production strategies are simultaneously considered in order to take advantage of all the three production strategies. A multi-objective stochastic mixed integer linear programming model is proposed to achieve economic feasibility, as well as environmental and social benefits under multiple uncertainties. The model is solved by using the improved augmented epsilon constraint method. A case study is used to illustrate the effectiveness of the proposed model. Pareto optimal analysis is conducted to understand the trade-off between economic, environmental, and social aspects of sustainability.

Pareto optimal solution for multiobjective stochastic linear programming problems with partial uncertainty

A study on multiobjective stochastic linear programming (MSLP) problems with partial information on probability distribution is conducted. A method is proposed to utilise the concept of dominated solution for the multiobjective linear programming (MLP) problems, and find a pareto optimal solution (POS) without converting the MLP problem into its unique linear programming (LP) problem. An algorithm is proposed along with a numerical example which illustrated the practicability of the proposed algorithm. Comparison of results with existing methods shows the efficiency of the proposed method based on the analysis of results performed.

Pareto optimal solution for multiobjective stochastic linear programming problems with partial uncertainty

Pareto optimal solution for multiobjective stochastic linear programming problems with partial uncertainty

確率最大化モデルと満足基準最適化モデルを同時に考慮した多目的確率線形計画問題に対する対話型ファジィ意思決定(理論・技術)

確率最大化モデルと満足基準最適化モデルを同時に考慮した多目的確率線形計画問題に対する対話型ファジィ意思決定(理論・技術)

Stochastic optimal scheduling of distributed energy resources with renewables considering economic and environmental aspects

Abstract A distributed energy resource (DER) system is a multi-input and multi-output energy system consisting of small-scale technologies, which provide electricity and thermal energy close to end-users. In recent years, DER systems have attracted much interest as a promising opportunity with substantial economic and environmental benefits. To reduce energy costs and environmental impact of DER systems, daily operation scheduling is crucial, and presents significant challenges even more under energy demand and supply uncertainty in presence of renewables. The contribution of this paper is to provide a stochastic programming model for the optimal operation scheduling of a DER system with multiple energy devices including renewables, considering economic and environmental aspects. To model uncertain parameters of supply and demand side, 24-h scenarios are generated by using roulette wheel mechanism and Monte Carlo simulation method. A stochastic multi-objective linear programming problem is formulated to find the optimized operation strategies of the DER system to reduce the expected energy costs and CO2 emissions, while satisfying the time-varying user demand. By minimizing a weighted sum of the total energy cost and CO2 emissions, the problem is solved by using branch-and-cut. Numerical results show that the Pareto frontier provides good trade-off solutions for DER system operators based on economic and environmental priorities. The total daily energy cost and CO2 emissions under a stochastic approach result to be lower than those under a deterministic one. Moreover, the operation method provided is found to be efficient in reducing significantly energy costs and CO2 emissions of the DER system, as compared with conventional energy supply systems and combined heat and power systems. In addition, a sensitivity analysis is also carried out to investigate the impact of renewables penetration on the economic and environmental performances of the DER system.

Whole blood or apheresis donations? A multi-objective stochastic optimization approach

In the blood supply chain, several alternative technologies are available for collection and processing. These technologies differ in cost and efficiency: for example, collection by apheresis requires very expensive machines but the yield of blood products is considerably greater than whole blood collection. Blood centre managers are faced with the difficult strategic problem of choosing the best combination of technologies, as well as the equally difficult operational problem of assigning donors to collection methods. These decisions are complex since so many factors have to be taken into account, including stochastic demand, blood group compatibilities, donor availability, the proportions of blood types in both donor and recipient populations, fixed and variable costs, and process efficiencies. The use of deterministic demand forecasts is rarely adequate and a robust decision must consider uncertainty and variability in demand as well as trade-offs between several potentially conflicting objectives. This paper presents a multi-objective stochastic integer linear programming model to support such decisions. The model treats demand as stochastic and seeks to optimize two objectives: the total cost and the number of donors required. To solve this problem, we apply a novel combination of Sample Average Approximation and the Augmented Epsilon-Constraint algorithm. This approach is illustrated using real data from Bogota, Colombia.

Impacts of optimal energy storage deployment and network reconfiguration on renewable integration level in distribution systems

Nowadays, there is a wide consensus about integrating more renewable energy sources-RESs to solve a multitude of global concerns such as meeting an increasing demand for electricity, reducing energy security and heavy dependence on fossil fuels for energy production, and reducing the overall carbon footprint of power production. Framed in this context, the coordination of RES integration with energy storage systems (ESSs), along with the network’s switching capability and/or reinforcement, is expected to significantly improve system flexibility, thereby increasing the capability of the system in accommodating large-scale RES power. Hence, this paper presents a novel mechanism to quantify the impacts of network switching and/or reinforcement as well as deployment of ESSs on the level of renewable power integrated in the system. To carry out this analysis, a dynamic and multi-objective stochastic mixed integer linear programming (S-MILP) model is developed, which jointly takes the optimal deployment of RES-based DGs and ESSs into account in coordination with distribution network reinforcement and/or reconfiguration. The IEEE 119-bus test system is used as a case study. Numerical results clearly show the capability of ESS deployment in dramatically increasing the level of renewable DGs integrated in the system. Although case-dependent, the impact of network reconfiguration on RES power integration is not significant.