An algorithm based on facial decomposition for finding the efficient set in multiple objective linear programming

We propose a method for finding the efficient set of a multiple objective linear program based on the well-known facial decomposition of the efficient set. The method incorporates a simple linear programming test that identifies efficient faces while employing a top-down search strategy which avoids enumeration of efficient extreme points and locates the maximally efficient faces of the feasible region. We suggest that discrete representations of the efficient faces could be obtained and presented to the Decision Maker. Results of computational experiments are reported

Exact And Representative Algorithms For Multi Objective Optimization

In most real-life problems, the decision alternatives are evaluated with multiple conflicting criteria. The entire set of non-dominated solutions for practical problems is impossible to obtain with reasonable computational effort. Decision maker generally needs only a representative set of solutions from the actual Pareto front. First algorithm we present is for efficiently generating a well dispersed non-dominated solution set representative of the Pareto front which can be used for general multi objective optimization problem. The algorithm first partitions the criteria space into grids to generate reference points and then searches for non-dominated solutions in each grid. This grid-based search utilizes achievement scalarization function and guarantees Pareto optimality. The results of our experimental results demonstrate that the proposed method is very competitive with other algorithms in literature when representativeness quality is considered; and advantageous from the computational efficiency point of view. Although generating the whole Pareto front does not seem very practical for many real life cases, sometimes it is required for verification purposes or where DM wants to run his decision making structures on the full set of Pareto solutions. For this purpose we present another novel algorithm. This algorithm attempts to adapt the standard branch and bound approach to the multi objective context by proposing to branch on solution points on objective space. This algorithm is proposed for multi objective integer optimization type of problems. Various properties of branch and bound concept has been investigated and explained within the multi objective optimization context such as fathoming, node selection, heuristics, as well as some multi objective optimization specific concepts like filtering, non-domination probability, running in parallel. Potential of this approach for being used both as a full Pareto generation or an approximation approach has been shown with experimental studies

Eco-efficient Supply Chains for Electrical and Electronic Products

Hundreds of millions of electrical and electronic appliances are manufactured every year. Furthermore, it is expected that this number will not substantially decrease in the near future. These equipments have a significant impact on the environment, and ceteris paribus, such environmental impact increases with the number of appliances manufactured. Consumers, NGOs and Governments have acknowledged the potential threat posed by these electrical and electronic products. They have systematically demanded companies to reduce the environmental impact caused be their products and services. Companies have responded to these pressures and have engaged in a number of environmentally friendly initiatives. This thesis is motivated by the task of reducing the environmental impact caused by the myriad of electrical and electronic products that make our lives more conformable and enjoyable. More specifically, it addresses the challenge of efficiently and effectively mitigating such impacts. We show that companies will need a mixture of strategies to respond to this challenge. Furthermore, we show that these strategies must consider environmental, technical and marketing aspects of the business of electrical and electronic products. These three aspects need to be considered systemically, and the solutions will vary greatly according to the companies, the products they manufacture, and the ways in which their supply chains are organized