Modeling and scheduling of cyclic shops with overtaking and time window constraints

Abstract

A cyclic shop is a production system that repetitively produces identical sets of jobs, called minimal part sets (MPSs), in the same loading and processing sequence. Each machine repeats identical work cycles. We investigate two versions of cyclic shops. The first version is a cyclic shop where an operation of an MPS instance can be processed prior to an operation of a previous MPS instance. We call such a shop an overtaking cyclic job shop. The overtaking degree is specified by how many MPS instances the operations of an MPS instance can overtake. More overtaking results in more work-in-progress, but reduces the cycle time, in general. The second version is a cyclic shop where a timing constraint is imposed on an operation. When loading, transferring and unloading jobs are automated by robots or other devices, the space where jobs in progress can reside is very limited. The material handling devices are limited resources that are shared for multiple operations. Therefore, a job that completes processing at a machine may not be able to be immediately unloaded when the next waiting space is full or the material handling devices are busy. The time duration for which a job remains at a machine after processing is called the residency time. In some shops that perform kinds of chemical processes, when the residency time exceeds a specified time limit, the job may be scrapped or reworked due to quality problems. Therefore, the total time for which a job spends at a machine should not exceed the sum of the operation time and the residency time upper bound. The sum is often called a time window. A cyclic shop with time window constraints is called a time-restricted cyclic shop. For each cyclic shop model with a given processing sequence of the operations at each machine or a sequence of robot tasks, we develop the conditions for which the shop has a qualified schedule. The qualified schedule is called a stable earliest starting schedule such that each operation or ea...