An exact penalty function approach for solving the linear bilevel multiobjective programming problem

In this paper, a new penalty function approach is proposed for the linear bilevel multiobjective programming problem. Using the optimality conditions of the lower level problem, we transform the linear bilevel multiobjective programming problem into the corresponding linear multiobjective programming problem with complementary constraint. The complementary constraint is appended to the upper level objectives with a penalty. Then, we give via an exact penalty method an existence theorem of Pareto optimal solutions and propose an algorithm for the linear bilevel multiobjective programming problem. Numerical results showing viability of the penalty function approach are presented.

A Decision-Aid in Supplier Selection for Entrepreneurs, Using Nested-Design, MODM and FAHP

Decision making is an important task for entrepreneurs, and proper performance of purchasing has a direct effect on decreasing costs, increasing profitability, and survival of an entrepreneur. Also, entrepreneurs must follow formal rational decision processes as much as possible with fewer costs. To do so, they can use Design of Experiment techniques in combination with decision-aids. In this paper, the authors develop a fuzzy linear multiobjective model for supplier selection. With this model, the decision maker will be able to identify effective criteria with the Nested-Design technique and their relative importance on supplier selection with FAHP. In this regard, fuzzy linear multiobjective programming will be assigned a share of suppliers for supply and demands in the supply chain. The authors expect that using this combination of techniques will have an impressive effect on reducing supplier selection costs.

PROMOIN: AN INTERACTIVE SYSTEM FOR MULTIOBJECTIVE PROGRAMMING

The interactive system PROMOIN is presented in this paper. This system has been designed in order to work with interactive techniques for Linear Multiobjective Programming problems. The main interactive procedures of the literature have been incorporated into the system, as well as the possibility to change between methods along the solution process, if the user wishes so. This change-of-method option has been developed on a theoretical base devoted to transfer information from one method to the other, so that all this information is not lost when changing to another algorithm. The program has been implemented under Windows environment, with the aim of providing the user with a friendly interface.