2014 Volume 8 Issue 5 Pages JAMDSM0070
In this paper, we consider a combinatorial optimization problem in a cyclic production system treating identical jobs. The cyclic production system possesses m machines, and every job consists of n tasks. The n tasks must be processed in a predetermined sequence, and each task must be processed on a predetermined machine. Each machine can process at most one task at a time, and no preemption for task processing is allowed. The job may visit a machine more than once to be completed, i.e., it is a re-entrant one. We focus on a restricted cyclic schedule, saying a periodically segmental schedule, where no task lies over consecutive segments. For a periodically segmental schedule, let s denote the number of jobs being in process during a segment, we also see that the sequence of n tasks of every job is split into s disjoint subsequences of tasks. We define a widget by such a subsequence of tasks. Given a job splitting with the splitting number s, we only have to assign the s widgets on machines in a segment to obtain a periodically segmental schedule. The problem to be discussed here asks to find a job splitting with the minimum splitting number s = s∗ so that for a given τ > 0, the generated s widgets can be assigned on machines in a segment with length τ. We propose a heuristic algorithm utilizing a dynamic programming based linear partition for finding a job splitting. Numerical examples demonstrate the behavior of the proposed heuristic algorithm.
