Performance Evaluation and System Design with Simulation Modeling
- 1. MERT YİĞİT EDA ACAR MERVE KILIÇ
- 2. Founded in 1986 and located in Torbalı İzmir Produces plastic materials ; flush tanks, internal mechanisms, toilet seats etc… Eighteen injection machines Five assembly lines
- 4. Work steps Modelling current system Facility layout optimization and design Response surface methodology
- 5. System is simulated over two product as realistic as possible by using Arena software Feasible layout design is obtained by using Flap Optimum number of forklift and transpalet are determined by using RSM
- 6. Before modelling Work flow Bill of material Operation trees Time studies Input analysis Cycle times Break downs Defect rates Size of the boxes and cages
- 8. Defect Rates of Machines
- 11. Product tree
- 12. Time study of Hero Gömme Rezervuar
- 13. Input analysis
- 14. Components are carried ; boxes or cages 228 cages and 1000 blue boxes Capacity of this boxes and cages for each component is identified with a study in stocking area by portable terminals.
- 15. Cage capacity
- 17. Contd’ Distances between each stations both current and layout optimized system Velocity, loading and unloading times of forklift and transpallet Relations between each units
- 19. Simulation model composed of; Lüx Asma Rezervuar
- 20. Hero Gömme Rezervuar
- 21. SIMULATION MODEL
- 27. •Recycling Station and Raw Material are spread along 14 units •Semi Product Warehouse I s spread along 40 units •Finished Good Warehouse is spread along 25 units •Offices are spread along 40units •Assembly Line 1 is spread along 10 units •Assembly Line 2 is spread along 15 units •18 Injection Machines are spread along 72 units •1 machine is spread along 4 units
- 28. FLAP
- 29. FLAP
- 34. Response surface methodology (RSM) is a collection of mathematical and statistical techniques that are useful for the modelling and analyzing problems in which a response of interest is influenced by several variables and the aim is to optimize this response.
- 35. In our case the response is production amount which affected by number of transpallet and forklift. The production amount is response variable of y and independent variables are number of transpallet and forklift The finished goods which quits the injection machines are taken into account when they arrive the warehouse. Hence in simulation model the importance of transportation units is incontrovertible.
- 36. In order to develop first order metamodel… Transpallet Forklift Number of transpallet is Number of forklift is defined defined as 7 as center. as 2 as center. High level of number of High level of number of transpallet is defined as 10. forklift is defined as 3. Low level of number of Low level of number of transpallet is defined as 3. forklift is defined as 1.
- 37. Design Matrix with Structure of Design MatrixCorresponding Replication Results Transpalet(X1) Forklift(X2) R1 R2 R3 R4 R5 10 3 60500 54300 59900 57500 57500 10 1 58400 58700 59800 58400 59100 3 3 60900 59700 60000 57500 61400 3 1 58100 57500 59700 56400 60700 10 2 57500 61100 57500 60300 57500 3 2 60900 56400 57500 50900 50900 7 3 59200 61100 56400 61300 58200 7 1 61900 59500 61000 56000 58300 7 2 60900 59100 60600 59000 61500 Regression metamodel is developed and analyzed by using MINITAB 15.
- 38. First Order Metamodel The regression equation is: Y = 55564 + 448 X1 + 1195 X2 - 170 X1X2 S = 2467,20 R-Sq = 4,4% R-Sq(adj) = 0,0%
- 39. R-Sq = coeffcient of determination R-Sq expresses that the part of the variability of the dependent variable with the variability of the independent variable. R-Sq = 4,4% 4,4 % of the variability on the production amount can be explain by the variability of the number of transportation units.
- 40. Transpalet(X1) Forklift(X2) R1 R2 R3 R4 R5 10 3 60500 54300 59900 57500 57500 10 1 58400 58700 59800 58400 59100 3 3 60900 59700 60000 57500 61400 3 1 58100 57500 59700 56400 60700 10 2 57500 61100 57500 60300 57500 3 2 60900 56400 57500 50900 50900 7 3 59200 61100 56400 61300 58200 7 1 61900 59500 61000 56000 58300 7 2 60900 59100 60600 59000 61500 • Some changes on the number of transpallet and forklift seems do not affect the production amounts seriously. • Besides, sometimes it is observed that more production amounts in the system in which less transporter units are used.
- 41. • If the product is carried with box, the choice of transporter (transpallet or forklift) is depends on the decision of the operator. • The criterion of the selection is determined in terms of probability because the exact criterion of that decision is not certain. • This decision is based on the assumption that if the product is carried with box it should be transferred by transpallet with % 50 probability and transferred by forklift with % 50 probability. • Since transpallet and forklift have different carrying capacities for boxes, process times are entered to the system as distribution, not constant. • Hence, variety in production amount is acceptable. If we look at only amounts of products which are transported with cages we can see the direct proportion between number of transporters and production quantity.
- 43. • Assumptions of Regression – Normality of the error terms: Error terms must be normally distributed. – Constant variance: The variance of distribution of the error terms must be constant. – Independency of the error terms: Error terms must be statistically independent.
- 44. Normality of the Error Terms Analysis of Linearity Residual Analysis for Constant Variance (Homoscedasticity) Residual Analysis for Independency
- 45. The regression equation is: Y = 54749 + 1880 X1 - 2232 X2 - 112 X1^2 + 857 X2^2 - 170 X1X2 S = 2398,98 R-Sq = 14,1% R-Sq(adj) = 3,0%
- 46. • Since increase on R-Sq and R-Sq(adj) is observed and p value is decreased, it is decided to continue the RSM process from this second order model
- 47. Canonical form The regression equation is Y = 57012 + 1540 X1 - 3363 X2 - 112 X1^2 + 857 X2^2 S = 2406,00 R-Sq = 11,3% R-Sq(adj) = 2,5%
- 48. Canonical analysis is implemented considering the stationary points.
- 49. • Number of forklift and transpallet should be integer. Hence:
- 50. • are known as eigenvalues or characteristic roots of the matrix B. • If the all are negative, is a point of maximum response, • If the all are positive, is a point of minimum response, • If the have different signs, is a saddle point.
- 51. However in our model is a point of maximum response. Transpalet (X1) Forklift (X2) R1 R2 R3 R4 R5 Average 10 3 60500 54300 59900 57500 57500 57940 10 1 58400 58700 59800 58400 59100 58880 3 3 60900 59700 60000 57500 61400 59900 3 1 58100 57500 59700 56400 60700 58480 10 2 57500 61100 57500 60300 57500 58780 3 2 60900 56400 57500 50900 50900 55320 7 3 59200 61100 56400 61300 58200 59240 7 1 61900 59500 61000 56000 58300 59340 7 2 60900 59100 60600 59000 61500 60220 7 transpallets and 2 forklifts provide the highest amounts of production units.
- 52. Design table Transpalet(X1) Forklift(X2) R1 R2 R3 R4 R5 10 3 59600 62400 62700 60400 60200 10 1 58600 59300 61000 62500 60200 3 3 60700 57800 61500 55800 62200 3 1 62900 54600 60800 62200 62200 10 2 60100 61900 62700 62500 60200 3 2 62900 57800 61500 61300 62200 7 3 61300 62900 60200 63000 63000 7 1 59500 62200 60200 62100 63900 7 2 62100 61900 60200 61700 63000 First order metamodel Y = 62008 - 157 X1 - 772 X2 + 123 X1X2
- 53. S = 1946,67 R-Sq = 4,2% R-Sq(adj) = 0,0%
- 54. Facility layout optimization and design implemented model has the same situation of the model which has no implementation of the facility layout. Because of the system is already optimized the R-Sq and R-Sq(adj) are very low. However we continue with the Second order metamodel: The regression equation is Y = 57019 + 1005 X1 + 1642 X2 - 90,5 X1^2 - 603 X2^2 + 123 X1X2
- 55. • S = 1894,81 R-Sq = 13,7% R-Sq(adj) = 2,6%
- 56. Canonical form The regression equation is Y = 55376 + 1251 X1 + 2463 X2 - 90,5 X1^2 - 603 X2^2 S = 1895,84 R-Sq = 11,4% R-Sq(adj) = 2,5%
- 57. • Canonical analysis is implemented considering the stationary points.
- 58. • Number of forklift and transpallet should be integer. Hence
- 59. • are known as eigenvalues or characteristic roots of the matrix B. • If the all are negative, is a point of maximum response, • If the all are positive, is a point of minimum response, • If the have different signs, is a saddle point.
- 60. • It is proven that the 7 transpallets and 3 forklifts are efficient to increase production amount by running the simulation model with upgrading number of forklift and transpallet. Transpalet(X1) Forklift(X2) R1 R2 R3 R4 R5 Average 10 3 59600 62400 62700 60400 60200 61060 10 1 58600 59300 61000 62500 60200 60320 3 3 60700 57800 61500 55800 62200 59600 3 1 62900 54600 60800 62200 62200 60540 10 2 60100 61900 62700 62500 60200 61480 3 2 62900 57800 61500 61300 62200 61140 7 3 61300 62900 60200 63000 63000 62080 7 1 59500 62200 60200 62100 63900 61580 7 2 62100 61900 60200 61700 63000 61780
- 62. Current System • Alternative System 2 LAYOUT NOT OPTIMIZED LAYOUT NOT OPTIMIZED RESPONSE SURFACE METHODOLOGY NOT APPLIED RESPONSE SURFACE METHODOLOGY APPLIED NUMBER OF FORKLIFT 1 NUMBER OF FORKLIFT 2 NUMBER OF TRANSPALLET 6 NUMBER OF TRANSPALLET 7 TOTAL: 60000 TOTAL: 61500 Utilization of Forklift 85.412 Utilization of Forklift 45.635 Utilization of Transpallet 59.680 Utilization of Transpallet 59.768 • Alternative System 1 • Alternative System 3 LAYOUT OPTIMIZED LAYOUT OPTIMIZED RESPONSE SURFACE METHODOLOGY NOT APPLIED RESPONSE SURFACE METHODOLOGY APPLIED NUMBER OF FORKLIFT 1 NUMBER OF FORKLIFT 3 NUMBER OF TRANSPALLET 6 NUMBER OF TRANSPALLET 7 TOTAL: 62900 TOTAL: 63000 Utilization of Forklift 97.325 Utilization of Forklift 37.325 Utilization of Transpallet 59.505 Utilization of Transpallet 59.505
- 64. Firstly works are begining modeling the current system as realistic as possible with Simulation software Arena. After determining the most produced product of the factory, All the data which are related to production such as time studies , bill of materials, downtimes, defect rates, cycle times are taken. The second step of the work is adding second product which is Hero Gömme Reservoir in simulation model.
- 65. While doing this works in addition to the first step of the work Transportation times and distances informations are added to the model. According to product type cage and box capacities are determined. Relationship chart is constructed and Facility Layout Optimization and Design is applied by using Flap. Response Surface Methodology are used to determine the optimum number of transpalet and forklift in factory.
- 67. Work orders can be created according to customer orders by this way WIP can be decreased and facility becomes appropriate for Lean philosophy. In this system injection machines work independently and work orders are constant. Schedule decision criteria can be added to simulation model. There is no scheduling method for assignment of work orders to the machines.
- 68. There are two more lines in the real system. These can be added. We added two assembly lines If simulation model decides which product will be produced by checking demands and arranges which product is going to be produced, how much, etc… Modelcan be replicated monthly so, it can be analyzed in long-term Instead of daily