Interactive Solution Approach Research Articles

Environmental supply chain network design using multi-objective fuzzy mathematical programming

The concern about environmental impact of business activities has spurred an interest in designing environmentally conscious supply chains. This paper proposes a multi-objective fuzzy mathematical programming model for designing an environmental supply chain under inherent uncertainty of input data in such problem. The proposed model is able to consider the minimization of multiple environmental impacts beside the traditional cost minimization objective to make a fair balance between them. A life cycle assessment-based (LCA-based) method is applied to assess and quantify the environmental impact of different options for supply chain network configuration. Also, to solve the proposed multi-objective fuzzy optimization model, an interactive fuzzy solution approach is developed. A real industrial case is used to demonstrate the significance and applicability of the developed fuzzy optimization model as well as the usefulness of the proposed solution approach.

A possibilistic programming approach for closed-loop supply chain network design under uncertainty

The design of closed-loop supply chain networks has attracted more attention in recent years according to business and environmental factors. The significance of accounting for uncertainty and risk in such networks spurs an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in closed-loop supply chain network design problems. This paper proposes a bi-objective possibilistic mixed integer programming model to deal with such issues. The proposed model integrates the network design decisions in both forward and reverse supply chain networks, and also incorporates the strategic network design decisions along with tactical material flow ones to avoid the sub-optimalities led from separated design in both parts. To solve the proposed possibilistic optimization model, an interactive fuzzy solution approach is developed by combining a number of efficient solution approaches from the recent literature. Numerical experiments are conducted to demonstrate the significance and applicability of the developed possibilistic model as well as the usefulness of the proposed solution approach.

An interactive solution approach for a bi-objective semi-desirable location problem

In this study, we consider a semi-desirable facility location problem in a continuous planar region considering the interaction between the facility and the existing demand points. A facility can be defined as semi-desirable if it has both undesirable and desirable effects to the people living in the vicinity. Our aim is to maximize the weighted distance of the facility from the closest demand point as well as to minimize the service cost of the facility. The distance between the facility and the demand points is measured with the rectilinear metric. For the solution of the problem, a three-phase interactive geometrical branch and bound algorithm is suggested to find the most preferred efficient solution. In the first two phases, we aim to eliminate the parts of the feasible region the inefficiency of which can be proved. The third phase has been suggested for an interactive search in the remaining regions with the involvement of a decision maker (DM). In the third phase, the DM is given the opportunity to use either an exact or an approximate procedure to carry out the search. The exact procedure is based on the reference point approach and guarantees to find an efficient point as the most preferred solution. On the other hand, in the approximate procedure, a hybrid methodology is used to increase the efficiency of the reference point approach. The approximate procedure can be used when the DM prefers to see locally efficient solutions so as to save computation time. We demonstrate the performance of the proposed method through example problems.

A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach

A supply chain (SC) distribution network design model is developed in this paper. The goal of the model is to select the optimum numbers, locations and capacity levels of plants and warehouses to deliver products to retailers at the least cost while satisfying desired service level to retailers. A maximal covering approach is used in statement of the service level. The model distinguishes itself from other models in this field in the modeling approach used. Because of somewhat imprecise nature of retailers’ demands and decision makers’ (DM) aspiration levels for the goals, a fuzzy modeling approach is used. Additionally, a novel and generic interactive fuzzy goal programming (IFGP)-based solution approach is proposed to determine the preferred compromise solution. To explore the viability of the proposed model and the solution approach, computational experiments are performed on realistic scale case problems.

Interactive Solution Approach to a Multiobjective Optimization Problem in a Paper Machine Headbox Design

A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented.

PETROBRAS STARTS PLATFORM BIDDING

Even though economic dispatch of integrated electricity and natural gas systems using optimization techniques has been widely conducted, a cooperative distributed and multi-objective optimization is still needed for meeting multi-energy demands from both conventional and renewable energy resources. In this study, an original bi-level economic-environmental equilibrium model is proposed to optimize a dispatch strategy for an integrated system, which include combined cooling, heating, and power and power to gas technologies. By optimizing cooperative distributed decisions, the system attempts to provide heat/cooling, power and natural gas loads. An equilibrium consideration of economic energy supply and environmental carbon emission control is achieved using a multi-objective optimization in the model. To reflect interactions of individual system operators in a cooperative distributed manner, a bi-level optimization is applied to address the respective decisions and objective functions. Subsequently, an interactive solution approach based on Non-dominated Sorting Genetic Algorithm-II and genetic algorithm is specifically designed to solve the model by updating individual decisions interactively and iteratively, and the optimality of an integrated solution lies in the capability to coordinate two system operators for a reliable, economic and environmental energy supply. Performance of the dispatch strategy is validated for a case with various system configurations. The obtained results showed that multi-energy needs are met, economic-environmental trade-offs achieved and hierarchical interactions addressed. Proper managerial suggestions are also provided based on comparison analyses. The proposed method is therefore worthy of being popularized in integrated systems.

Group Decision-Making with Multiple Objectives and its Interactive Solution Approach

In this paper, we discuss a group decision-making problem, which involves the decision taken by a committee. The groun decision problem is formulated as follows. There are m decision-makers (members of a committee), n objectives and a set of alternatives. All the members of a committee work together to choose one alternative which is most satisfactory for the group in a sense. Under certain pre-specified behavioural postulates, each member expresses his preference by articulating his aspiration level according to the multiple objectives. An aggregation function can be employed to aggegate aspiration levels. We hereby postulate a system of axioms. Under these conditions, a possibility theorem is proved, which guarantees the existance of an aggregation function. Using the multiobjective optimization technique, such as reference point method, and a computer-assisted system, the group decision problem can be solved in man-machine interactive scheme.

A class of practical interactive branch and bound algorithms for multicriteria integer programming

A practical interactive solution approach to multicriteria integer programming problems is developed. The problem is solved by a branch-and-bound method that employs the Zionts and Wallenius procedure [23] for solving the multicriteria linear programming problem. The development of algorithms for multicriteria decision problems itself is a multicriteria problem, which involves the simultaneous minimization of the number of questions asked of the decision maker and the solution time. Two branch-and-bound algorithms that follow different search strategies to meet different levels of these criteria have been developed. Further, two families of hybrid algorithms that incorporate a combination of the strategies of the two algorithms have also been developed. Strategies for the exploration of the decision-maker's preference structure are discussed. Computational experience with the algorithms is presented. The class of algorithms represents a collection of viable solution strategies applicable to a variety of decision-making styles.