Firouzabad Institute of Higher EducationAnnals of Optimization Theory and Practice2588-36664220210731On discounted discrete scheduled replacement model698213360510.22121/aotp.2021.283204.1065ENTijjani AWaziriSchool of Continuing Education, Bayero University Kano, Nigeriahttps://orcid.org/00Journal Article20210425An operating unit sometimes cannot be replaced at the exact optimum replacement time for some reasons. The unit may be rather replaced at idle times, such as a day, a week, a month, a year and so on. So to address such problem of replacing a unit at idle times, this paper come up with a discounted discrete scheduled replacement model for a unit. It is assumed that the replacement is at scheduled times NT(N=1,2,3,…) for a fixed T>0, such that the model constructed involves minimal repair and discounting rate (∝ >0). The unit considered in this paper is subjected to three categories of failures, which are Category I, Category II and Category III failures. Category I failure is an un-repairable one, which occurs suddenly. While Category II and Category III failures are both repairable, which occurs due to time and usage, and the two failures are minimally repaired. A numerical example is provided, so as to investigate the characteristics of the model presented and determine the optimal discrete replacement time (N^*) of the unit.http://aotp.fabad-ihe.ac.ir/article_133605_e5d0423ea94c196c8d26e8d72aad1730.pdf