Designing Cyclic Schedules for Streaming Repetitive Job-Shop Manufacturing Systems with Blocking and No-Wait Constraints

Abstract

Abstract We consider a problem of designing no-wait cyclic schedules for job-shop manufacturing system with repetitive transportation tasks that are defined by sequences of operations. Each operation is performed in a sector of manufacturing system using its resources, e.g. vehicles, machines, and takes some time for manufacturing and transportation. The sectors and their resources can be shared by several tasks in the exclusive mode. There are no buffers between sectors thus when a transportation car is in a sector it blocks this sector to other cars and cannot leave it until a sector which is required by the following operation in its transportation route is free. The repetitive transportation tasks performed in a manufacturing system are modelled as a system of cyclic processes executing sequences of operations and sharing common resources according to a mutual exclusion protocol. The problem consists in finding no-wait cyclic schedules for which no process (tasks) that started execution will wait for resources (sectors) required to execute its operations and each operation will be started immediately after finishing the previous one. The casade-like structure (C-LS) system of processes is considered. This system is structurally deadlock-free therefore no-buffer (resource blocking) constraint will never lead to deadlock state. The C-LS system of processes can be seen as a composition of subsystems with two cyclic processes sharing a single resource, namely 2-P subsystems. Using our recurrent integer modulus equations model (developed in our previous works) we find for each 2-P subsystem all possible start times of the processes (if exist) that belong to a no-wait schedule and construct all possible no-wait schedules for each component 2-P. Finally, we design cyclic no-wait schedules for the C-LS system by joining the cyclic schedules designed for its component 2-P subsystems.