This paper addresses the energy minimization problem in job scheduling, particularly for portable and battery-operated systems. The authors propose a model where jobs must be executed between their arrival and deadline times by a single processor with variable speed, assuming that energy consumption is a convex function of the processor speed. They present an offline algorithm to compute a minimum-energy schedule and analyze several online heuristics, focusing on the Average Rate (AVR) heuristic. The AVR heuristic sets the processor speed based on the average rate requirement of jobs and schedules them using the earliest-deadline-first policy. The analysis shows that the AVR heuristic has a constant competitive ratio for the power function \( P(s) = s^2 \), with the ratio lying between 4 and 8. For more general power functions \( P(s) = s^p \) where \( p \geq 2 \), the competitive ratio is shown to be between \( p^p \) and \( 2^{p-1} p^p \). The paper also discusses simulation results and open problems, highlighting the importance of energy conservation in portable computing devices.This paper addresses the energy minimization problem in job scheduling, particularly for portable and battery-operated systems. The authors propose a model where jobs must be executed between their arrival and deadline times by a single processor with variable speed, assuming that energy consumption is a convex function of the processor speed. They present an offline algorithm to compute a minimum-energy schedule and analyze several online heuristics, focusing on the Average Rate (AVR) heuristic. The AVR heuristic sets the processor speed based on the average rate requirement of jobs and schedules them using the earliest-deadline-first policy. The analysis shows that the AVR heuristic has a constant competitive ratio for the power function \( P(s) = s^2 \), with the ratio lying between 4 and 8. For more general power functions \( P(s) = s^p \) where \( p \geq 2 \), the competitive ratio is shown to be between \( p^p \) and \( 2^{p-1} p^p \). The paper also discusses simulation results and open problems, highlighting the importance of energy conservation in portable computing devices.