Abstract:

This paper surveys several replacement policies for parallel systems, where three newly proposed notions in our research are considered: (i) Random number of units, (ii) excess and shortage costs, and (iii) approach of “whichever occurs last”. First, we take up replacement policies for a parallel system when its number of units could be constantly predetermined and randomly estimated. Next, we introduce excess and shortage costs used in scheduling problems into models and derive optimal replacement times, where the case of random number of units is also considered. Third, when a parallel system is operating for successive jobs with a random working time, we plan two kinds of policies of replacement first and replacement last that are formulated by using two respective approaches of “whichever occurs first” and “whichever occurs last”. All discussions are given analytically and optimal replacement polices are computed numerically.