The efficiency of M groups of N machines served by a travelling robot: comparison of two models

This paper solves the problem of calculating the efficiency of M groups of N machines under the care of one operative (robot), whose way of working is to patrol the groups either uni-directionally or bi-directionally, depending on whether they are located on a circle or on a line. Each group of machines is situated on a rotating circular disc (carousel). This work extends the work of Kim and Koenigsberg (1987) as well as the earlier work of Koenigsberg and Mamer (1982) and uses both of the models derived by Bunday and El-Badri (1984) and Bunday et al. (1985) for the uni-directional and the bi-directional patrolling problems. The problem arises in the practical context of a textile winding process and has some other industrial applications. Results are of value in maintaining controls and monitoring the process. A comparison of the two models considered in this paper can be made both numerically and graphically and, as has been shown before by Bunday and El-Badri (1985a, b), higher results for the efficiency, are obtained by patrolling uni-directionally rather than patrolling bi-directionally.