The modelling and solution approaches based on possibility and probability theory for blending problems in casting industry

In this thesis, the blending problem in brass casting industry is studied as single-blend and multi-blend models which are used in operational and tactical levels, respectively. The raw materials used in process are classified whether the ingredients? ratios are deterministic or uncertain for each model considering their objectives. The uncertainties in raw materials are modeled by using probability and possibility distributions in the single-blend model. Three new approaches, first of which transforms the probabilistic uncertainties into the possibilistic ones, second of which transforms possibilistic uncertainties into the probabilistic ones and without any transformation are developed for solving single-blend which includes probabilistic and possibilistic parameters. In the multi-blend, each ingredient?s uncertainty, demands and unit purchasing costs are modeled by using possibility theory. The multi-blend problem is considered as an aggregate production plan and then struggled to model and solve by using Lai and Hwang?s approach [78, 79]. However, it is shown in thesis that this modeling and solution approach has some insufficiencies to model and solve the problem considered. Therefore, a more comprehensive mathematical model that uses ?either or? constraints and a novel algorithm are developed to solve the problem.