Stochastic simulation of assembly line for optimal sequence using Petri Nets (PN)

Abstract

The assembly of any product or machine is highly complex. The order of sequence affects the make span time of assembly and thus the throughput. Which part should come in what order and what tasks will be performed together, how many work stations are required etc. are very crucial in obtaining the optimal line. The number of work stations, what task constitute the work station, which precede and what is in succession will affect the time to accomplish the task and also the utilization of resources i.e. manpower and machines both. There may be many solutions available to assembly line but it has to be validated. It is therefore argued to simulate the proposed solutions. The solution based on average data will not represent the actual plant performance. It is inevitable to have a promising technique to arrive at pragmatic result and brings down the assumptions to minimal. The stochastic nature of setup times, no operation times will affect the performance of the plant. The stochastic task timings are being used to represent real conditions and compare the performance of different alternative sequences of assembly. The assembly of finished product is the outcome of work break down (WBD), their sequence of assembly based on multiple precedence relationships. It is a highly challenging job for engineers to find the optimal sequence so that the utilization of machines and throughput are maintained high. The possible sequences of assemblies are tested and the sequence that yields maximum output must be selected. Hence one has to find the solution based on dynamic conditions. This paper is an attempt to first get solution using optimization techniques using linear programming problem (LPP) or heuristics. Then simulate those sets on Petri Nets. The Petri Net is an interactive, simple and yet very powerful technique to represent the problem graphically and coding the same using general purpose programming language for validating the same for intended result. Real time patterns using best fit, statistical interferences, probability density functions (pdf), discrete distributed systems(DDS), or stochastic modeling can be used to simulate problem to measure performance of assembly line.