Material Requirement Analysis Under Rejection for a Serial Production System Using Simulation Mathapati Shivkumar Digamberrao, and Madhusudanan Pillai V Department of Mechanical Engineering, National Institute of Technology Calicut NIT Campus Post, Calicut, Kerala – 673 601 ABSTRACT: This paper is concerned with the analysis of material requirement for a given quantity of finished goods to produce. The work-part undergoes a sequential production process. During production, the work-part can be rejected at any stage of the production process. This random nature of rejection brings uncertainty in the estimation of raw material requirement. In literature, such production processes are modelled as absorbing Markov Chains. This paper models the above production system using simulation. Arena simulation software is used for this purpose. The material requirement obtained through simulation is agreeing with that given by the analytical model. 1. Introduction An understanding of the performance characteristics of any manufacturing system is essential for making efficient and effective planning and operating decisions. The decision making process become difficult when the decision variable is random in nature. This is true in the case of manufacturing of an item, which undergoes various stages of operation and opportunity for rejection exists at these stages. In literature, such manufacturing processes are modelled as Absorbing Markov chains [1, 2] to determine production system parameters. The present paper models such processes using simulation and the parameter analysed is material requirement. Arena simulation software package is used for this purpose. The material requirement obtained using simulation is compared with that of analytical model. 2. Simulation ‘Simulation involves the modelling of a process or system in such a way that the model mimics the response of the actual system to events that take place over time’ [3]. Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose of understanding the behaviour of the system and/or evaluating various strategies for the operation of the system. In this paper simulation is considered to include both the construction of the model and the experimental use of the model for studying a problem. Thus, simulation modelling is an experimental and applied methodology that seeks to accomplish the following: • Describe the behaviour of systems, • Construct theories or hypotheses that account for the observed behaviour • Use the model to predict future behaviour; that is, the effects produced by changes in the system or in its method of operation. 3. ‘Arena’: a Simulation Tool Arena software enables to bring the power of modelling and simulation to the business. It is designed for analysing the impact of changes involving significant and complex redesigns associated with supply chain, manufacturing, processes, logistics, distribution and warehousing, and service systems [3]. It provides the maximum flexibility and breadth of application coverage to model any desired level of detail and complexity. The Arena software is designed for manufacturing or business process consultants and analysts and industrial or systems engineers. It is typically developed as an enterprise business analysis and productivity tool [4]. 4. Problem Description: Serial Production System The process modelled here consists of a serial production system with three stages. It is a discrete manufacturing system, where a work-part moves through the system and comes out as a finished component. The work-part is a raw material or semi finished part before the start of production operations. At every stage of production the part is subjected to inspection; if it does not conform to specifications, it is either scrapped or reworked. The reworked component undergoes inspection again. It is assumed that nonconforming items are produced randomly at each stage. Figure 1 shows a manufacturing process that requires three operations. Raw Material M1 (Turning) M2 (Drilling) M3 (Milling) Finished Part Figure 1. Manufacturing Stages To analyse the raw material requirement, the scrap rate and rework rate at each stage are required. The hypothetical data related with scrap rate and rework rate at each stage for the above example are given in the Table 1. Table 1 Data from the Production Process Process Incoming material Turning Rework turning Drilling Rework drilling Milling Rework milling Scrap rate in % 0.2 1.0 1.0 2.0 2.0 4.0 3.0 Rework rate in % 1.0 3.0 3.0 Operating rate (Units/hr) 30 20 30 15 10 20 5. Arena Model The create module from the basic process panel of Arena is used to generate parts for production in the manufacturing line. This module is intended as the starting point for entities in the simulation model. Also the entity type is specified in this module. Figure 2. Arena Simulation Model The Arena simulation model of the production system is shown in Figure 2. Record module is used to collect the statistics in the simulation model; here it is used as a counter. The processes module is intended as the main processing method in the simulation. Since the system contains three process stages, three process modules are used. The process time is allocated to the entity. Decide module allows for the decision-making process in the system. It is an inspection epoch in this model; the percentage of rework and rejection is given as the inputs. Dispose module is intended for the parts leaving the production system. Separate dispose modules are used for scrapped parts and finished end items. The simulation model is used to determine the quantity of raw material required when the finished parts required is 100 units. One of the parameter of the model is the number of replications, which determined through experimentation. For this experimentation a graph of material required versus number of replication is plotted. This graph is used to determine the steady state condition. It can be seen from the figure 3 that the material requirement is not changing beyond 40 replications. Hence the number of replication can be fixed as greater than 40 and here it is set at 100. Steady State 12 Material Requirement 10 8 6 4 2 0 12 0. 00 10 0. 00 20 .0 0 60 .0 0 1. 00 40 .0 0 80 .0 0 Steady state Analysis No. of Replication Figure 3. Steady State Graph A record module is used to record the items that reach the finished part state. This record module has a user defined variable called finished parts which is a counter type variable. The terminating condition is the specification of expression or condition that is evaluated throughout the simulation run to determine whether or not to stop the simulation [5]. If the condition or expression is true, the simulation run will be terminated. In this simulation model, the terminating condition is the finished parts is equal to 100. The other inputs in the set-up of the simulation model are: 1) Warm-up period: 0 2) Replication length: infinite The useful results of the above simulation model for 100 units of finished parts are: 1) Number of units scrapped after normal operations: 7.80 2) Number of units scrapped after rework: 0.100 3) The material requirement is the sum of number of finished parts and the number of scrapped parts before and after rework and it is equal to 107.9000. This result is compared with the result obtained using the absorbing Markov chain model of the production system. 6. Analytical Method In literature [1, 2] the manufacturing processes of the above type are modelled as absorption Markov chains. Using the properties of absorbing Markov chain, the production system can be analysed [1, 6, 7]. One of the parameters can be analysed is the expected quantity of material that has to be started from state 1 to produce 100 units of finished parts. This analysis is carried out using the method available in Madhusudanan Pillai [1]. For 100 units of finished parts required the material required and scrapped quantity of material are as follows: 1) Material requirement: 107.7935 units 2) Number of units scrapped after normal operations: 7.5886 units 3) Number of units scrapped after rework: 0.2048 units 7. Comparison of simulation results with the analytical method It can be seen that the simulation result is matching with analytical result. A simulation model is often easier to justify to management or customers than some of the analytical models. In addition, simulation might have more credibility because its behaviour has been compared to that of the real system or because it has required fewer simplifying assumptions and hence the simulation model can be considered as the true representation of the real system. Virtually all simulation models are so-called input-output models, that is, they yield the output of the system for a given input. Simulation models are therefore ‘run’ rather than ‘solved.’ They cannot generate an optimal solution on their own as analytical models can; they can only serve as tools for the analysis of system behaviour under specified conditions [4]. 8. Conclusion An Arena simulation model for a serial production system with scrap and rework has been developed. The simulated model has been run for various number of replication and the steady state has been identified. Material requirement for a given quantity of finished part to produce are determined using simulation. Then this result is compared with that of the analytical method. The results obtained through simulation for the material requirement of the above serial production system are agreeing with the material requirement obtained by the analytical method. The simulation model is simple to understand compared to analytical model. References: 1. Madhusudanan Pillai, V., 2005, Stochastic Processes in Cellular Manufacturing Environment. Ph .D thesis, Department of Mechanical Engineering, NIT Calicut. 2. Davis, R. P., and Kennedy Jr., W. J., 1987, Markovian modelling of manufacturing systems. International Journal of Production Research, 25, 337351. 3. Kelton, W. D., Sadowski, R. P., and Strrock, D. T., 2004, Simulation with Arena, Third Edition, (McGraw-Hill). 4. Banks, J., Carson, J. S., Nelson, B. L., Nicol, D. M., 1996, Discrete-Event System Simulation. (Prentice Hall of India Private Limited). 5. Rockwell Software, 2002, User’s Guide - Arena Basic (Doc ID ARENABUM001C-EN-P) 6. Viswanadham, N., and Narahari, Y., 1992, Performance Modelling of Automated Manufacturing Systems (Prentice-Hall of India). 7. Ravindran, A., Philips, D. T., and Solberg, J. J., 1987, Operations Research: Principles and Practice (John Wiley & Sons).