We study a variant of the maximum coverage problem which we label the maximum coverage problem with group budget constraints (MCG). We are given a collection of sets S = {S1, S2, . . . , Sm} where each set Si is a subset of a given ground set X. In the maximum coverage problem the goal is to pick k sets from S to maximize the cardinality of their union. In the MCG problem S is partitioned into ...

Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesth...

In this paper, we analyze a machine repairable system with warm spares and two repairmen. The first repairman never takes vacations. The second repairman leaves for a vacation of random length when the number of the failed units is less than N. At the end of a vacation period, this repairman returns back if there are N or more failed units accumulated in the system. Otherwise this repairman goe...

Multi-unit parallel production systems (MuPPSs) widely exist in many industry areas. A general requirement for the MuPPS is that each system should continuously run and its downtime be as short feasible. For such systems, optimising preventive maintenance (PM) policy crucial so resources number of spare units repairmen can optimally used. On this basis, paper develops an optimal model jointly P...

We consider a machine repair problem with queue-dependent heterogeneous repairmen. The stationary probability distribution of the number of failed machines in the system is derived. A profit model is developed to determine the optimal values of threshold to assign/add one more repairman for increasing the total service rate where the service rate is assumed adjustable. The probabilistic global ...

The present paper deals with profit modelling and comparison between two dissimilar systems under two types of failures based on Markovian Birth-Death process. Type I failure is minor in the sense that the work is in a reduced capacity whereas type II failure is major because it causes the entire system failure. Both systems consist of four subsystems arranged in series-parallel with three poss...

Abstract: In this paper, we study the reliability measures of a repairable system with M operating units, W warm standby units, and R repairmen in which switching failures and reboot delay are considered. It is assumed that there is a significant failure probability q in the switching process. Failure times of an operating unit and of a standby unit are assumed to be exponentially distributed w...

This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacati...