Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application

In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved.

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method

In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.

Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

Sustainable Multi-Objective Multi-Reservoir Optimization Considering Environmental Flow

Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.

Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem(FBSP)is about scheduling project activities without exceeding a credit line financing limit.The FBSP is extended to consider different execution modes that result in the multi-mode FBSP(MMFBSP).Unfortunately,researchers have abandoned the development of exact models to solve the FBSP and its extensions.Instead,researchers have heavily relied on the use of heuristics and meta-heuristics,which do not guarantee solution optimality.No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP.CPLEX,which is an exact solver,has witnessed a significant decrease in its computation time.Moreover,its current version,CPLEX 12.9,solves multi-objective optimization problems.This study presents a mixed-integer linear programming model for the multi-objective MMFBSP.Using CPLEX 12.9,we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP.We test our model by solving several problems from the literature.We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases.The small increase in computation time compared with possible cost savings make exact models a must for practitioners.Moreover,the linear programming-relaxation of the model,which takes seconds,can provide an excellent lower bound.

Improving Supply Chain Performance Through Supplier Selection and Order Allocation Problem

Suppliers play the vital role of ensuring the continuous supply of goods to themarket for businesses.If businesses do not maintain a strong bond with their suppliers,they may not be able to secure a steady supply of goods and products for their customers.As a result of failure to deliver products,the production and business activities of the business can be delayed which leads to the loss of customers.Normally,each trading enterprise will have a variety of commodity supply chains withmultiple suppliers.Suppliers play an important role and contribute to the value of the entire supply chain.Should any supplier encounters a problem,the whole supply chain of businesses will be affected and could lead to not guaranteeing the stable supply to the market.Thus,suppliers can be seen as a threat to businesses where they have the ability to increase input prices or decrease the quality of the required products and services they provide.The quantity of the business,and the supply lead time directly affect the operations and reduce the profitability of the business.The paper mainly focuses on the supplier selection problemunder a variety of price level and product families when using a two-phase fuzzy multi-objective linear programming.The objectives of the proposed model are to minimize the total purchasing and ordering cost in order to reduce the quantity of defective materials and the late-delivery components from suppliers.Moreover,the piecewise linear membership function is applied in themodel to determine an optimal solution which is based on the requirement of decision makers under their fuzzy environment.The results of this study can be applied in various business environment and provide a reliable decision tool for choosing potential suppliers relating to these objectives.Based on the results,the company canmake a good decision on supplier selection;therefore,the company can improve the quality and quantity of their final product.This is because,the best supplier can supply raw material using just-in-time application and reduce production risk on the manufacturing process.

Evaluation and advancement of the integrated circular economy model of farming and stock raising

The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity.

Optimization on Water Resource System Operation Policy during Drought

The mixed linear programming model is commonly recognized to be an effective means for searching optimal reservoir operation policy in water resources system. In this paper a multi-objective mixed integer linear programming model is set up to obtain the optimal operation policy of multi-reservoir water supply system during drought, which is able to consider the operation rule of reservoir-group system within longer-term successive drought periods, according to the basic connotation of indexes expressing the water-supply risk of reservoir during drought, that is, reliability, resilience and vulnerability of reservoir water supply, and mathematical programming principles. The model-solving procedures, particularly, the decomposition-adjustment algorithm, are proposed based on characteristics of the model structure. The principle of model-solving technique is to decompose the complex system into several smaller sub-systems on which some ease-solving mathematical models may be established. The objective of this optimization model aims at maximizing the reliability of water supply and minimizing the maximum water-shortage of single time-period within water- supply system during drought. The multi-objective mixed integer linear programming model and proposed solving procedures are applied to a case study of reservoir-group water-supply system in Huanghe-Huaihe River Basin, China. The desired water-shortage distribution within the system operation term and the maximum shortage of single time-period are achieved. The results of case study verifies that the lighter water-shortage distributed evenly among several time-periods can avoid the calamities resulted from severe water shortage concentrated on a few time-periods during drought.

The Impact on the Environment and Economy Due to the Introduction of Electric Cars: Based on the Fuzzy Synthetical Evaluation Method

In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are internal combustion engine vehicles, pure electric vehicles and hybrid electric vehicles. Considering the difference of environment, society and economics, we use of three different kinds to define the fuzzy evaluation factor sets. According to the data and calculating results, we finally obtain fuzzy synthetical evaluation matrix. Through comparing and analysis, we draw such conclusion that the widespread using of electric vehicle is benefit for both environment and economics, while has disadvantageous influence for some aspects on society. In Section 3, we establish a model to estimate the influence of widespread use of electric vehicles on energy saving. According to the proportion of coal resources in the whole energies, we use Linear Regression Model to forecast the development situation in the following several years. Contrasting energy consumptions of electric vehicles and internal combustion engine vehicles, we calculate the whole energies saved by widespread use of electric vehicles. In Section 4, we establish a multi-objective programming model to plan the number and type of power station. Considering the thermal power, hydropower, nuclear power and solar power as four ways, combined with the funds of setting up power station, running funds and the cost of dealing with the pollutants, we find the objective function and four constraints, and finally we reach optimal solution using lingo software.

Heuristic Algorithm for Minimizing the Electricity Cost of Smart House

This framework proposes a heuristic algorithm based on LP （linear programming） for optimizing the electricity cost in large residential buildings, in a smart grid environment. Our heuristic tackles large multi-objective energy allocation problem （large number of appliances and high time resolution）. The primary goal is to reduce the electricity bills, and discomfort factor. Also, increase the utilization of domestic renewable energy, and reduce the running time of the optimization algorithm. Our heuristic algorithm uses linear programming relaxation, and two rounding strategies. The first technique, called CR （cumulative rounding）, is designed for thermostatic appliances such as air conditioners and electric heaters, and the second approach, called MCR （minimum cost rounding）, is designed for other interruptible appliances. The results show that the proposed heuristic algorithm can be used to solve large MILP （mixed integer linear programming） problems and gives a decent suboptimal solution in polynomial time.

Predictive simulation and optimal allocation of surface water resources in reservoir basins under climate change

Predicting and allocating surface water resources are becoming increasingly important tasks for addressing the risk of water shortages and challenges of climate change,especially in reservoir basins.However,surface water resource management includes many systematic uncertainties and complexities that are difficult to address.Thus,advanced models must be developed to support predictive simulations and optimal allocations of surface water resources,which are urgently required to ensure regional water supply security and sustainable socioeconomic development.In this study,a soil and water assessment tool-based interval linear multi-objective programming(SWAT-ILMP)model was developed and integrated with climate change scenarios,SWAT,interval parameter programming,and multi-objective programming.The developed model was applied to the Xinfengjiang Reservoir basin in South China and was able to identify optimal allocation schemes for water resources under different climate change scenarios.In the forecast year 2025,the optimal water quantity for power generation would be the highest and account for∼60%of all water resources,the optimal water quantity for water supply would account for∼35%,while the optimal surplus water released from the reservoir would be the lowest at≤5%.In addition,climate change and reservoir initial storage would greatly affect the surplus water quantity but not the power generation or water supply quantity.In general,the SWAT-ILMP model is applicable and effective for water resource prediction and management systems.The results from different scenarios can provide multiple alternatives to support rational water resource allocation in the study area.

TWO INNOVATIVE COALITION FORMATION MODELS FOR DYNAMIC TASK ALLOCATION IN DISASTER RESCUES

This paper addresses the problem of multi-objective coalition formation for task allocation. In disaster rescue, due to the dynamics of environments, heterogeneity and complexity of tasks as well as limited available agents, it is hard for the single-objective and single （task）-to-single （agent） task allocation approaches to handle task allocation in such circumstances. To this end, two multi-objective coalition formation for task allocation models are proposed for disaster rescues in this paper. First, through coalition formation, the proposed models enable agents to cooperatively perform complex tasks that cannot be completed by single agent. In addition, through adjusting the weights of multiple task allocation objectives, the proposed models can employ the linear programming to generate more adaptive task allocation plans, which can satisfy different task allocation requirements in disaster rescue. Finally, through employing the multi-stage task allocation mechanism of the dynamic programming, the proposed models can handle the dynamics of tasks and agents in disaster environments. Experimental results indicate that the proposed models have good performance on coalition formation for task allocation in disaster environments, which can generate suitable task allocation plans according to various objectives of task allocation.

Land use pattern evolution and optimization in the Farming-Pastoral Zone of Northern China

Using information about the land cover of the Farming-Pastoral Zone of Northern China retrieved from multi-temporal NOAA/AVHRR and SPOT VEGETAN images obtained in 1989, 1994 and 1999, the authors analyzed land-use pattern evolution over this 10-year period and built a land-use pattern simulation model, based on which land-use pattern evolution and optimization modeling in this region were studied. Results showed that the proposed model can effectively simulate regional land-use patterns and help improve regional ecological environments.