Cyclic Scheduling of Identical Parts in a Robotic Cell

Abstract

We consider a robotic owshop in which one type of product is to be repeatedly produced, and where transportation of the parts between the machines is performed by the robot. The identical parts cyclic scheduling problem is then to nd a shortest cyclic schedule for the robot, i.e. a sequence of robot moves that can berepeated in nitely many times and has minimum cycle time. This problem has beensolved by Sethi et al. 1992] when m 3. In this paper, we considerably generalize their results by proving that the identical parts cyclic scheduling problem can besolved in time polynomial in m, where m denotes the numberof machines in the shop. In particular, we present a dynamic programming approach that allows to solve the problem in O(m 3 ) time. Our analysis heavily relies on the concept of pyramidal permutation, a concept previously investigated in connection with the traveling salesman problem.

Bicriteria robotic cell scheduling

“…On the other hand, feasible robot move cycles are defined by Crama and Van de Klundert (1997) as the cycles in which the robot does not load an already loaded machine and does not unload an already empty machine. For example, in a two-machine robotic cell there are two feasible 1-unit cycles, namely, S 2 1 and S 2 2 where S m i represents the ith robot move cycle in an m-machine robotic cell.…”

“…In order to define the robot move sequence performed under each cycle we will make use of the following definition which is borrowed from Crama and Van de Klundert (1997).…”

“…Considering only the 1-unit cycles, Crama and Van de Klundert (1997) proved that the set of pyramidal permutations necessarily contains an optimal solution of the problem. Let A 0 , A i 1 , .…”

“…, A i m denote the activity sequence of a 1-unit cycle in an m-machine cell. Then Crama and Van de Klundert (1997) defines this cycle to be pyrami-…”

“…However, Brauner and Finke (1999) showed that 1-unit cycles need not be optimal for m ≥ 4. Crama and Van de Klundert (1997) described a polynomial time dynamic programming algorithm for minimizing the cycle time over all 1-unit cycles in an m-machine cell producing identical parts. considered a robotic cell with two identical CNC machines which possess operational and process flexibilities.…”