Chance-Constrained Approaches for Multiobjective Stochastic Linear Programming Problems

Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.

Reconstruction of geological surfaces using chance-constrained programming

Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.

Chance-constrained programming (CCP)abatement of SO_2 emission for acid deposition control in Liuzhou City

A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.

Goal programming approach for sustainable forest management(case study in Iranian Caspian forests)

We used a goal programming technique to determine the optimal harvest volume for the Iranian Caspian forest. We collected data including volume, growth, wood price at forest roadside, and variable harvesting costs. The allometric method was used to quantify seques- trated carbon. Regression analysis was used to derive growth models. Expected mean price was estimated using wood price and variable harvesting costs. Questionnaire was used to determine the constraints and the equation coefficients of the goal programming model. The optimal volume was determined using the goal programming method according to multipurpose forest management. LINGO software was used for analysis. Results indicated that the optimum volumes of species were 250.25 m3.ha-1 for beech, 59 m3.ha-1 for hornbeam, 73 m3.ha-1 for oak, 41 m3.ha-1 for alder, and 32 m3.ha-1 for other species. The total optimum volume is 455.25 m3.ha-1.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

Optimum blending of iron ore from Choghart stockpiles by using goal programming

Iron and steel industry is an important sector of Iran's economy.Choghart iron ore mine is an important iron ore producer of Iran steel industry.Phosphorous contained in the iron ore concentrates of Choghart mine has a detrimental effect on the steel making process,whereby this causes cracks to form in the refractory lining of blast furnaces.In the past,about 1.43 Mt of low-grade and 4.53 Mt of high-phosphorous materials had been transported to low grade and high phosphorous stockpiles,respectively,for future beneficiation.As a result of the progressive depletion of high-grade ore and establishment of beneficiation plant in Choghart,exploitation of these two stockpiles in this mine became an important issue.In this work,a linear goal programming(GP) model was developed in order to determine the optimum iron ore blend in terms of quality from low grade and high phosphorous stockpiles of Choghart mine.The model was solved by the SOLVER V.9 program.Results show that feeding with acceptable quality(w(Fe)≥50% and w(P)≤1.2%,mass fraction) materials can be blended from stockpiles that satisfy the needs of the Choghart processing line.

HEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMS

At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive evaluation the advanced operation research techniques can be used in continuous production systems in developing countries very widely, because of initial inadequate plant layout, stage by stage development of production lines, the purchase of second hand machineries from various countries, plurality of customers. A case of production system planning is proposed for a chemical company in which the above mentioned conditions are almost presented. The goals and constraints in this issue are as follows： （1） Minimizing deviation of customer＇s requirements. （2） Maximizing the profit. （3） Minimizing the frequencies of changes in formula production. （4） Minimizing the inventory of final products. （5） Balancing the production sections with regard to rate in production. （6） Limitation in inventory of raw material. The present situation is in such a way that various techniques such as goal programming, linear programming and dynamic programming can be used. But dynamic production programming issues are divided into two categories, at first one with limitation in production capacity and another with unlimited production capacity. For the first category, a systematic and acceptable solution has not been presented yet. Therefore an innovative method is used to convert the dynamic situation to a zero- one model. At last this issue is changed to a goal programming model with non-linear limitations with the use of GRG algorithm and that＇s how it is solved.

A Glorious Literature on Linear Goal Programming Algorithms

In the last several years, there has been a marked improvement in the development of new algorithms for solving Linear Goal programming (LGP). This paper presents a survey of current methods for LGP.

Optimizing the Asset and Liability Management of Telecommunication Company using Goal Programming Model

Since the telecommunications companies experience great competition,high churn rate,data traffic issues during the Covid-19 pandemic and the upgrade to 5G connectivity,the finance management of a telecommunications company should be analyzed to study the volatility and returns in the sector.This paper aims to develop a goal programming model to examine the asset and liability management of a telecommunication company,namely Telekom Malaysia Berhad(TM)in Malaysia.The result of this study shows that TM has achieved all the goals in maximizing assets,equities,profits,earnings and optimum management item while minimizing liabilities over the period of study from 2015 to 2019.Potential improvements on these goals have also been identified through this study.This paper has also contributed to the studies in financial management since past studies have not been done on asset and liability management in telecommunications companies which is rapidly growing and expanding even while the world is suffering from economy crisis during this pandemic.

STOCHASTIC GENERALIZED GOAL PROGRAMMING

This thesis presents the combination of the stochastic programming and generalized goal programming. We puts forward several generalized goal programming models with stochastic parameter--stochastic generalized goal programming. Furthermore, we probe into the theory. and algorithm of these models. At last, this method was applied to an example of an industrial problem.

Goal Programming for Investment Portfolio and Its Application

To solve the problem of investment portfolio with single goal of maximal NPV, a 0- 1 programming model was proposed and proved effective; and to solve that concerning more elements of a project such as risk level and social benefit, a goal programming model is then introduced. The latter is a linear programming model adopting slack variable called deviation variable to turn inequation constraint into equation constraint, introducing a priority factor to denote different importance of the goals. A case study has demonstrated that this goal programming model can give different results according to different priority requirement of each objective.

A Weighted Goal Programming Model for the DASH Diet Problem: Comparison with the Linear Programming DASH Diet Model

A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.

An Evolutionary Firefly Algorithm, Goal Programming Optimization Approach for Setting the Osmotic Dehydration Parameters of Papaya

An evolutionary nature-inspired Firefly Algorithm (FA) is employed to set the optimal osmotic dehydration parameters in a case study of papaya. In the case, the functional form of the dehydration model is established via a response surface technique with the resulting optimization formulation being a non-linear goal programming model. For optimization, a computationally efficient, FA-driven method is employed and the resulting solution is shown to be superior to those from previous approaches for determining the osmotic process parameters. The final component of this study provides a computational experimentation performed on the FA to illustrate the relative sensitivity of this evolutionary metaheuristic approach over a range of the two key parameters that most influence its running time-the number of iterations and the number of fireflies. This sensitivity analysis revealed that for intermediate-to-high values of either of these two key parameters, the FA would always determine overall optimal solutions, while lower values of either parameter would generate greater variability in solution quality. Since the running time complexity of the FA is polynomial in the number of fireflies but linear in the number of iterations, this experimentation shows that it is more computationally practical to run the FA using a “reasonably small” number of fireflies together with a relatively larger number of iterations than the converse.

SURFACE MINE PLANNING OPTIMIZATION BY GOAL PROGRAMMING

This paper introduced an approach to surface mine planning optimization-Goal Programming.The multiobjective[0-1] model has been built and the software has been developed.The method has been applied to a huge surface coal mine,the result of which shows that it is effective and feasible.

Reformative Financial Risk Management Approach： A Multistage Decision Support System with the Assistance of Fuzzy Goal Programming and Expertons Method

The potential demand on financial risk management has being increased considerably by the reason of Basel 11 regulations and instabilities in economy. In recent years, financial institutions and companies have been struggled for building up intensive financial risk management tools due to Basel II guidance on establishing financial self-assessment systems. In this respect, decision support system has a significant role on effectuating intensive financial risk management roadmap. In this study, a reformative financial risk management system is presented with the combination of determining financial risks with their importance, calculating risk scores and making suggestions based on detected risk scores by applying corrective actions. First, financial risk factors and indicators of these risk variables are selected and weights of these variables are specified by using fuzzy goal programming. After that, total risk scores are calculated and amendatory financial activities are appeared by means of expertons method which also provides possibilities of the alternative decisions. To illustrate the performance of integrated and multistage decision support system, a survey is applied on the end users.

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

In this paper, a fish farm was modeled using the Lexicographic linear goal programming approach due to incommensurability in objectives. The study considered the fish farming plan with two sizes of catfish from stocking to harvesting at four-month intervals. The multi-objective goals developed are required raw materials feed, water, light (resource utilization), sales revenue, profit realized, labor utilization, production costs, and pond utilization. The developed model was tested using related data collected from the farm records with the use of TORA 2007 software. The compromised solution from the results showed that the developed model is an efficient tool for decision-making process in the fish farm business organization.

A Note on Standard Goal Programming with Fuzzy Hierarchies: A Sequential Approach

In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it has been assumed that the normalized deviations should lie between zero and one. In some cases, this assumption may not be valid. Therefore, additional constraints must be incorporated into the model to ensure that the normalized deviations should not exceed one. This modification is illustrated by the given numerical example.

Estimation of CARA Preferences and Positive Mathematical Programming

The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.

Adaptive sampling immune algorithm solving joint chance-constrained programming

This work investigates one immune optimization algorithm in uncertain environments, solving linear or nonlinear joint chance-constrained programming with a general distribution of the random vector. In this algorithm, an a priori lower bound estimate is developed to deal with one joint chance constraint, while the scheme of adaptive sampling is designed to make empirically better antibodies in the current population acquire larger sample sizes in terms of our sample-allocation rule. Relying upon several simplified immune metaphors in the immune system, we design two immune operators of dynamic proliferation and adaptive mutation. The first picks up those diverse antibodies to achieve proliferation according to a dynamical suppression radius index, which can ensure empirically potential antibodies more clones, and reduce noisy influence to the optimized quality, and the second is a module of genetic diversity, which exploits those valuable regions and finds those diverse and excellent antibodies. Theoretically, the proposed approach is demonstrated to be convergent. Experimentally, the statistical results show that the approach can obtain satisfactory performances including the optimized quality, noisy suppression and efficiency.

From Mutual Creation to Mutual Benefit:China’s National Teacher Training Program between Higher Teacher Education and K-12 Teachers

Sustainable Development Goal(SDG 4)lays solid theoretical foundation for the development of higher teacher education in improving the quality of teaching faculty nationwide.Sustainable teacher training paves a way for teacher professional development in the long run.China’s“National Teacher Training Program”serves a connection between higher teacher education and K-12 teachers in multiple perspectives when exploring K-12 teachers’improvement of the essence by upgrading the initiative of the program with the assistance of educational technology and modern educational philosophy from mutual creation to mutual benefit.Direction orientation strategic design based on demand for teaching faculty,curriculum setting in modules,and characteristics creation have been carried out to upgrade the training of teacher colleges and National Teacher Training Program in the future for achieving a win-win situation between higher teacher education and K-12 education.