Long-term Optimal Scheduling of Cascade Hydropower Stations Using Fuzzy Multi-objective Dynamic Programming Approach

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

The vendor selection and order quantity allocation problem with fuzzy demand and price discount is formulated as a multi-objective mixed-integer fuzzy programming model. The proposed model has the following characteristics: deterministic and fuzz constraints, and the assumption of fuzzy demand and price discount are expressed by using constraint equations. According to the special features of the model, appropriate solution strategy is proposed. It involves three steps: (1) membership function for every fuzzy objective and constraint is set up; (2) by means of max-min operator, the multi-objective mixed-integer fuzzy programming model is converted into several equivalent single-objective linear programming model; (3) the optimal solution for order quantity allocation problem is derived based on two-phase approach. An application example was also given for testing the feasibility and effectiveness of the proposed method

In pragmatic project management cases, many complex resources and large-scale related activities are involved. Moreover, when situations are under the conflict and incommensurate of time and cost, it becomes more difficult for managers to make their decisions. Hence, we construct fuzzy multi-objective programming model from CPM technique. Through emphasizing the selectable flexibility among the feasible projects, we describe the decision problem brought from uncertainty and complex in project. In our research, taking the conflict and incommensurate of time and cost as two major factors, we measure weight and priority to denote the importance degree between the objectives. Adopting Tiwari et al., we also develop the result when trading off the decision vs. the vague environment of time and cost and the past' single objective' method has become the exceptional case of multi-objective models. Secondly, we broaden the consumed time and cost of activity events when assumptions are certain to merge the practical situation. We applied fuzzy number to express estimate time and cost. It based on Lee and Li method to solve this problem. Finally, we employ numerical example to explain it with LINGO package to calculate.

This paper deals with a fuzzy goal programming methodology for solving multiobjective linear fractional chance constrained programming problems containing fuzzy numbers and exponentially distributed fuzzy random variables associated with the system constraints. In model formulation process, the problem is converted into an equivalent fuzzy programming model by applying chance constrained programming technique in a fuzzily defined probabilistic decision making situation. Then using the concept of α-cut for fuzzy numbers and by considering the tolerance level of fuzzy numbers the problem reduces to an equivalent sub problem with interval coefficients. In this method the convex combination of each interval is used and the problem is reduced to a nonlinear programming problem. Finally the model is solved by converting nonlinear model into its equivalent multiobjective linear programming model by using Taylor series; and a priority based fuzzy goal programming method is used for achievement of the highest membership degree. To demonstrate the efficiency of the proposed technique an illustrative example, studied previously, is solved and the solution is compared with the existing methodology.

Automobile service enterprise location determination is an interesting and important issue in the logistic research field. To deal with this uncertainty, some researchers addressed the fuzzy time and cost issues for locating an automobile service enterprise. However, a decision maker hopes to minimize the travel time of customers meanwhile minimizing their costs when locating a facility. They prefer arriving at the destination within the specific time period and cost. To handle this issue in a more practical manner, by taking the vehicle inspection station as a typical automobile service enterprise example, the authors proposed a fuzzy change-constrained multi-objective optimization approach to handle it. Moreover, some region-wide constraints can greatly influence FLA and travel time is also has indeterminate due to the influence of some unpredictable factors. To handle them, they developed a fuzzy chance-constrained multi-objective programming model to determine its location with regional constraints, fuzzy inspection demands and varying velocities. A hybrid algorithm integrating fuzzy simulation, neural networks (NN), and genetic algorithms (GA), namely a random weight based multi-objective NN-GA, is proposed to solve the proposed models. A numerical example is provided to illustrate the effectiveness of the proposed model and the proposed algorithm.

A multi-objective fuzzy linear programming model for optimization of natural gas supply chain through a greenhouse gas reduction approach

Reservoir management is a highly complex problem, which includes the uncertainty in the inflows as well as in the objectives. Stochastic dynamic programming (SDP) has been widely used to develop the optimal operating policies of multipurpose reservoirs. In the recent years, fuzzy optimization has been used to incorporate the uncertainty caused due to the imprecise nature of objectives. In the present study, a comparison is made between a conventional SDP model and fuzzy dynamic programming models for optimal operation of a multipurpose reservoir. The two models are developed for Hirakud Reservoir on River Mahanadi in the State of Orissa in India. The performance of the reservoir is evaluated under the operating policies derived from these models through simulation. The results indicate that the fuzzy dynamic programming model performs better in achieving the flood control objective and thus in the overall performan1ce of reservoir.

Fuzzy multi-objective decision model for calibration supplier selection problem

Electric vehicles are the future trend of our transportation. The problem is how we do it considering environmental, social, economic, and health impacts. In this paper, we build a Multi-objective Dynamic Programming model that simulates the reforming process from gasoline vehicles to electric vehicles. The result and the methods can be used as a reference for government electric vehicles replacing strategy. The model will show how the vehicles reform will be carried out. The replacing process will be divided into four stages. And in the end of our 40 years process, most gasoline vehicles are replaced. The advantages and problems faced while replacing will also be discussed in the paper.

Designing sustainable supply chain networks under uncertain environments: Fuzzy multi-objective programming

This paper investigates a multi-objective supplier selection and order allocation problem under quantity discounts in a fuzzy environment. Prior research on supplier selection and order allocation with quantity discounts mainly considered partial fuzziness of the decision problem; a situation where both the objectives of the decision maker and the constraints are fuzzy has not been studied up to now. This paper closes this gap by integrating both aspects into a single model. First, a combination of fuzzy preference programming and interval-based TOPSIS is proposed for evaluating suppliers. Secondly, based on the scores obtained in the first step, a fuzzy multi-objective linear programming model is developed. Subsequently, a new solution procedure for solving the fuzzy multi-objective linear programming model is presented. The procedure first transforms fuzzy constraints and coefficients into deterministic coefficients, and then three different fuzzy programming approaches, namely interactive fuzzy multi-objective linear programming, and the weighted additive as well as the weighted max-min method are implemented. Finally, the performance of each method is evaluated by computing the distance between each solution and the preferred solution.

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.

In this paper, we integrated the forward logistics and the reuse reverse logistics to set up a closed-loop integrated logistics system under a random fuzzy environment. A random fuzzy multi-objective programming model was established which can describe the integrated logistics as a cycle of production, distribution, consumption, collection, transportation, recycling, disposal, reuse and redistribution. We then used the expected value operator and the chance-constrained operator to handle the random fuzzy objective functions and the random fuzzy constraints. The solution scheme was pursued by a genetic algorithm based on random fuzzy simulation and compromise approach. And an application to a Chinese beer company was given as an illustration.

In the initial stage of emergency rescue for major railway emergencies, there may be insufficient emergency resources. In order to ensure that all the emergency demand points can be effectively and fairly rescued, considering the fuzzy properties of the parameters, such as the resource demand quantity, the dispatching time and the satisfaction degree, the railway emergency resources dispatching optimization model is studied, with multi- demand point, multi-depot, and multi-resource. Based on railway rescue features, it was proposed that the couple number of relief point - emergency point is the key to affect railway rescue cost and efficiency. Under the premise of the maximum satisfaction degree of quantity demanded at all emergency points, a multi-objective programming model is established by maximizing the satisfaction degree of dispatching time and the satisfaction degree of the couple number of relief point - emergency point. Combined with the ideal point method, a restrictive parameter interval method for optimal solution was designed, which can realize the quick seek of Pareto optimal solution. Furthermore, an example is given to verify the feasibility and effectiveness of the method.

The increasing use of water and the decrease in average rainfall along with climate change have caused the reduction of water resources in arid and semi-arid regions. In addition, despite the consumption of more than half of these resources in the agricultural sector, a rate between 0 and 15% of the price of the products has always been received from the farmers. Considering the concept of virtual water and the water content of products in the form of green water, blue water and gray water, the present research has calculated the economic value of virtual water of agricultural products with the approach of maximizing water use efficiency. The investigated sample includes eight cities (counties) of Sanmenxia, Jiaozuo, Nanyang, Shangqiu, Puyang, Luohe, Luoyang and Kaifeng and six agricultural products (wheat, barley, potato, rapeseed, tomato and corn). A fuzzy dynamic programming model has been used to evaluate the objective function. The results showed that the maximum and minimum economic value of water content (sum of surface and groundwater) of the products were estimated for Kaifeng and Shangqiu regions equal to 1.16 and 0.86 Yuan/m3, respectively.