Expected and Variance for a Single Machine Issue with Linear Decreasing Processing Time Deterioration

Abstract

We consider linear decreasing deteriorating of processing times  of jobs on single machine, i.e., P_(i )=Ƥ_(i )-β_(i ) t_(i ),  〖0<β〗_(i )<1  and 〖t 〗_(i )≥0, where P_(i )  is actual process,  Ƥ_(i )  is a basic process for job i ,  β_(i )  is decreasing rate , t_(i )  is a starting time of job i  with  n- jobs, non- preemptive, no - idle on a single machine. We study some classical criteria as make span, total completion time, total lateness times, total waiting times, maximum lateness times and maximum tardiness times, important conclusion dependent on the decreasing rate of expected of basic process of jobs with respect to its decreasing rate when a basic process is random variable in general case.