the determination of the ultimate pit limit (upl) is the first step in the open pit mine planning process. in this stage that parts of the mineral deposit that are economic to mine are determined. there are several mathematical, heuristic and meta-heuristic algorithms to determine upl. the optimization criterion in these algorithms is maximization of the total profit whilst satisfying the...

data envelopment analysis (dea) has been widely studied in the literature since its inception with charnes, cooper and rhodes work in 1978. the methodology behind the classical dea method is to determine how much improvements in the outputs (inputs) dimensions is necessary in order to render them efficient. one of the underlying assumptions of this methodology is that the units consume and prod...

in the process of production, some of the inputs are fixed and cannot easily be changed, such as work hours of workers and hours of administrative or work, these types of inputs are fixed and others are variables. in this paper, by considering some inputs or outputs which are limited, their amounts must be integrated; this concept for integer data is extended. we show the importance of subject ...