Evaluating quality and cost simultaneously Multi-objective stochastic mathematical model and fuzzy programming A solution procedure to implement in real life casting processes Figure A. The framework of the multi-objective blending problemPurpose: In this study we developed a mathematical programming model that aims both cost minimization and quality maximization and a solution procedure for stochastic blending problem in brass casting
Theory and Methods:Quality and cost are connected and challenging issues for production systems. Managers aims to improve the product quality and decrease product cost. However, generally, improvements in a product's design quality level cause an increase in the production cost. In many production systems, it is hard to formulate a product's quality as a function in a model. However, in brass casting blending process, it is possible to model the product quality by using process capability indices thanks to the nature of the blending problem. In this study, a multiobjective stochastic mathematical model has been developed which aims to present to the managers a blend with minimum cost at the highest quality level. The stochastic uncertainty has been converted into a deterministic counterpart by using chance-constrained approach. Therefore, the multi-objective stochastic model has been transformed into a multi-objective deterministic nonlinear mathematical model. The multiobjective model has been handled as a single objective model by using fuzzy programming. In order to implement developed model into real life applications, a solution procedure has been proposed.
Results:The proposed model and the solution procedure have been tested in a numerical example using data supplied from a brass factory. The solution of the numerical example showed that the proposed model and solution procedure can easily select a blend with minimum cost and maximum process capability level.
Conclusion:This study is the first attempt that consider both quality and cost in a model for blending problem. The proposed model and solution approaches can be used in different production processes including a blending problem.