This paper deals with the problem of sequencing robot activities for a robot-centered parallel-processor workcell where n jobs and m identical processors exist in the cell, and a robot is responsible for both loading and unloading activities. The objective of this paper is to determine the sequence of robot activities for minimizing the sum of completion times. A modified shortest processing time procedure based on the traditional shortest processing time sequencing rule in order to determine an upper bound has been proposed. A branch and bound algorithm to find an optimal sequence of robot activities has then been presented. A numerical example is illustrated and the computational results have been given.