Mixed integer programming (MIP) is a powerful modelling tool for decision-making in the industry and in the public sector. Integer requirements are essential to model a wide variety of situations involving assignment restrictions, logical constraints and yes/no decisions, to name a few. Usually real-life applications result in mixed integer programs that are large in size and that are beyond th...

The ever-increasing concerns of the growth in volume waste tires and new strict government legislations to reduce environmental impact end-of-life (EOL) have increased interest among companies design a sustainable efficient closed-loop supply-chain (CLSC) network. In real world, CLSC network is subject variety uncertainties, such as random fuzzy (epistemic) uncertainties. Designing reliable env...

This paper presents the fuzzy mixed-integer goal programming model for a single machine scheduling problem with bi-objectives consisting of the minimization of the total weighted flow time and total weighted tardiness. This model is solved by a fuzzy goal programming approach to verify and validate the proposed approach for the above problem. Two test problems in small and large sizes are gener...

in this paper, the portfolio selection problem is considered, where fuzziness and randomness appear simultaneously in optimization process. since return and dividend play an important role in such problems, a new model is developed in a mixed environment by incorporating fuzzy random variable as multi-objective nonlinear model. then a novel interactive approach is proposed to determine the pref...