Petri Net model of repetitive push manufacturing with Polca to minimise value-added WIP

Abstract

A common simplifying assumption used in the literature is to minimise average Work In Process (WIP), while achieving maximum production rate, which does not consider the fact that the value of WIP increases down the stream of a production process as labour, time, energy and resources are added to it. This paper aims at minimising queues of parts waiting downstream of production process and in turn minimising value-added WIP by constraining more and more inventory of unfinished products at the earlier stages of production. For this reason, generic black token closed loop Petri Net (PN) model of Flexible Flow Shop (FFS) with Paired-cell Overlapping Loops with Card Authorisation (POLCA) is developed. Tokens in the control loops represent Polca cards to control the flow of material from order release till finished products. Marking of PN is done through Mix Integer Linear Programming after the computation of semi-positive P invariants. Simulation is being done to obtain queues of parts, waiting at each station during demand variation. Results were compared with PN model of FFS without Polca. Results showed the constriction of unnecessary WIP towards the initial stage of production instead of at bottlenecks, with proposed model, and in turn minimisation of value-added WIP.