In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

The assessment of the influence of the work-hardening of material on the optimum die profile and drawing force  in rod drawing process is the main objective of the present paper. The upper bound solution, based on the assumption of perfect plasticity, has been extended to consider the work-hardening of the material during the rod drawing process through curved dies. Analytical results of drawin...

rupture and wrinkling are two prevalent phenomena that happen in hydro-forming process. many efforts have been made to achieve the upper and lower bounds for the pressure related to rupture and wrinkling of sheet, respectively. the aim of this investigation is to improve the upper bound of fluid pressure in hydro-forming process by hemispherical punch. in this article, analytical study of the u...

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

Twist extrusion process is a rather new route to produce highly strained materials. In this process, severe plastic deformation is applied by large shear strains. In current article, required energy for twist extrusion by use of admissible velocity field together with the upper bound technique is predicted. The proposed model is capable of considering the effect of various parameters such as di...

Deformation of the material during cyclic expansion extrusion (CEE) is investigated using upper-bound theorem. The analytical approximation of forming loads agrees very well with the FEM results for different amounts of chamber diameter, friction factor and also for lower die angles. However, the difference between analytical and numerical solution increases at higher die angles which are expla...

In this paper, an upper bound approach is used to analyze the tube extrusion process through rotating conical dies with large mandrel radius. The material under deformation in the die and inside the container is divided to four deformation zones. A velocity field for each deformation zone is developed to evaluate the internal powers and the powers dissipated on all frictional and velocity disco...

Several methods have been proposed for ranking the decision-making units (DMUs) in data envelopment analysis (DEA) with imprecise data. Some methods have only used the upper bound efficiencies to rank DMUs. However, some other methods have considered both of the lower and upper bound efficiencies to rank DMUs. The current paper shows that these methods did not consider the DEA axioms and may be...