The Deviation Issue and Total Completion Time on a Single Machine Scale Subject to Decreasing and Growing Linear Deterioration are Theoretically Addressed

We addressed in this research the schedule of activities that are subject to the condition of linear degradation in declining and growing rate states, respectively, with the goal of guaranteeing that the primary process's duration would be fixed (ρ) and that its implementation would take place in a single machine. The objective was to find the optimal schedule for calculating the total completion time ∑_(ḭ=1)^ń▒C_ḭ , and the optimal schedule for the deviation problem (sum of squares of the difference between the tasks' total required time and the previously established due date time. where the objective is to minimize the squared deviation of job completion times from a due date), two theories that state as the Λ-shaped scheduling theory with increasing rate ƛ_ḭ of jobs and the v-shaped scheduling theory with decreasing rate đ_ḭ of jobs satisfy the conditions 0<đ_ḭ<1 ańd đ_ḭ<1/(ń-1), have been demonstrated in situations where the base is implemented at a constant basic processing time .