1. A method, comprising: a. mapping each job based on an arrival time, job priority, and service level agreement (SLA) function, to a fixed point in a dual space of linear functions; b. selecting a next job with a highest priority to execute using a line with an angle in the dual space to locate a current job with a highest cost-based scheduling (CBS) score ƒ(t)=∝+βe at , wherein, ξ=e at is applied to get ƒ(ξ)=α+βξ, where ξ is time-dependent variable, ∝ and β are constants with one-to-one mapping between ξ and t, wherein each function ƒ(ξ)=α+βξ is mapped to a point (α, β) in the dual space and determining the CBS score under piecewise linear SLAs with: r ⁡ ( t ) = 1 a ⁢ s 0 + ( j 1 + s 1 - s 0 a ) ⁢ ⅇ - a ⁡ ( t 1 - t ) + ( j 2 + s 2 - s 1 a ) ⁢ ⅇ - a ⁡ ( t 2 - t ) wherein r(t) is prioritized cost based scheduling score, a is parameter in the scheduling algorithm, j 1 , j 2 are the height of the jumps between consecutive segments in the piecewise linear SLA function, s 0 , s 1 , s 2 are the slopes of the segments in the piecewise linear SLA function, t 1 , t 2 are the time when the next segment in the SLA function become effective; and c. prioritizing each job for profit maximization in a service delivery infrastructure with the piecewise linear SLA functions; and d. running the job with the highest CBS score; e. wherein mapping, selecting and running is performed using a processor.