Material Handling Tools for a Discrete Manufacturing System: A Comparison of Optimization and Simulation Frank Werner Fakultät für Mathematik OvGU Magdeburg, Germany (Joint work with Yanting Ni, Chengdu University, China) 1
Overview of the Talk • Introduction • Literature Review • Markov Decision Process Model • Dynamic Programming Algorithm • Numerical Experiments • Conclusion 2
Introduction Background: • A material handling tool (MHT) is one of the essential components in a manufacturing system. • MHTs are responsible for the transitions of the lots between the stations. • The strategy of MHTs will impact the delivery rate, cycle time and WIP level. 3
Introduction • A Markov decision process (MDP) will be applied to model the MHT system. • A dynamic programming algorithm will be used to solve this problem. 4
Introduction Two contributions are discussed in this paper: • A systematic management method of MHTs under a discrete manufacturing will be developed using a Markov decision process. The quantified relationships between MHTs and WIP will be discussed within the constant WIP (CONWIP) methodology and constant demand. • The dynamic MHT replenishment method of MHTs will be discussed within the theory of Little’s law. 5
Literature Review • Many approaches for analyzing the performance of MHTs have been proposed, etc.: • Huang et al. (2011) study the vehicle allocation problem in a typical 300 mm wafer fabrication. They formulate it as a simulation-optimization problem and propose a conceptual framework to handle the problem. • Chang et al. (2014) study the vehicle fleet sizing problem in semiconductor manufacturing and propose a formulation and a solution method to facilitate the determination of the optimal vehicle fleet size that minimizes the vehicle cost while satisfying time constraints.
Literature Review • To overcome the shortcomings of simulation, some mathematical models are developed to quantify the parameters of a material handling system (MHS), such as a queuing theory model, queuing network model and a Markov chain model. • Nazzal and McGinnis (2008) model a multi-vehicle material handling system as a closed-loop queuing network with finite buffers and general service times. • Zhang et al. (2015) propose a modi fied Markov chain model to analyze and evaluate the performance of a closed-loop automated material handling system .
MDP Model System Analysis • In a discrete manufacturing factory, there exist many types of MHTs to carry the working lots between different stages. • There might exist only two possible scenarios for each individual workstation - an MHT change or no change. 8
MDP Model System Analysis 1.MHT no Change – Single Cycle Machine M i Lot ….... Lot Lot ….... Lot Upload Processing Load Lot Processing Lot MHT X (Y) MHT X (Y) MHT X (Y) MHT X (Y) MHT X MHT X BUFFER BUFFER 2.MHT Change – Two-Loop Cycle Machine M i Lot Lot ….... Lot Lot ….... Lot Lot Upload Processing Load Processing MHT X MHT Y MHT X MHT Y Figure 1: MHT Cycle Classification MHT X MHT Y MHT X MHT Y Empty MHT Empty MHT Empty MHT Empty MHT BUFFER BUFFER BUFFER BUFFER 9
MDP Model Some basic notations : 10
MDP Model Assumptions : (1) The processing time at each station is constant, and production meets an M/G/1 queuing system. (2) A lot arrives according to an exponential distribution λ with the associated parameter . (3) Each MHT transports the lots based on the FIFO (first- in-first-out) rule. (4) The loading time, the unloading time and the running speed of the vehicles have a deterministic value, and both acceleration and deceleration of vehicles are ignored. 11
MDP Model Assumptions (cont’d) : (5) The WIP quantity meets the CONWIP scenario * and the desired WIP level is . w (6) The route of the MHT at a specific work station for one specific product is fixed within the product design period. (7) The delivery quantity is aligned with the demand of the master production schedule (MPS). (8) Only one product is considered in this paper. 12
S T MDP Model 13
MDP Model Decision times T Lots of production tasks will be released based on the numbers of available vehicles and the { } ∈ ∈Ν recycle status at each time, t T = 0,1,2,..., L L + where is the length of the defined production L cycle. 14
MDP Model Definition of the set of states S 15
MDP Model Definition of the set of actions A 16
MDP Model Definition of the set of actions A 17
P trans MDP Model State transition probabilities P trans 18
P trans MDP Model State transition probabilities P trans 19
P trans MDP Model State transition probabilities P trans 20
= × × ' a b c P P ( s s ) P P P trans trans i i i i i MDP Model State transition probabilities P trans The state will change when new lots arrive, tasks are cancelled or a machine has a breakdown. These three events can separately occur and so the state transition probability is: ( ) = × × ' a b c P s s a k l m , , , , P ( ) k P l ( ) P ( ) m trans i i i i i i 21
MDP Model Reward Function v(SA) The purpose of the vehicle management is to minimize the penalties for late deliveries of each product and to control the WIP level in the whole line within certain lower and upper limits. We can formulate the following optimization function as: 22
γ − = D ( , ) R s a e t t i i MDP Model Maximize the Reward Function v(SA) s.t. 23
γ − = D ( , ) R s a e t t i i MDP Model (cont’d) 24
Dynamic Programming Algorithm • The whole set of stages are grouped into 3 parts: a bottleneck group, a front group and a backend group. • The CONWIP methodology is used for the front group and the FIFO rule is used for backend group . 25
Dynamic Programming Algorithm 26
Dynamic Programming Algorithm 27
Dynamic Programming Algorithm 28
Dynamic Programming Algorithm 29
Dynamic Programming Algorithm 30
Dynamic Programming Algorithm 31
Dynamic Programming Algorithm 32
Dynamic Programming Algorithm Station 1 Station 2 Station k-1 Station k Station k+1 Station n-1 Station n CONWIP for front stations = v SA ( ) L n ∑∑ First: Stage k MaxE [ R s a ( , )] t i i * ( = = f s ) FIFO for backend stations t 0 i 1 k k Stage2 to Stage k-1 Stage(k+1): * * f ( s ) to f ( s ) Stage1: − − 2 2 k 1 k 1 * f ( s ) Stage(k+2) to Stage(n-1) * f ( ) s k +1 k +1 1 1 * * f ( s ) to f ( s ) Stage n + + − − 2 2 1 1 k k n n * ( f s ) n n = t * * * * * * * * * * * * * SA ( s a s , ( ), s a s , ( ),..., s , a ( s ), s , a ( s ),..., s ) + + + 1 1 1 2 2 2 k k k k 1 k 1 k 1 n 0 1 t L ( SA SA , ,..., SA ,..., SA ) Figure 2: Sequence graph for dynamic programming 33
Experiments We implemented our approach in a 300 mm semiconductor assembly and test factory and collected the required data for performing the experiments. a b c c Wafer Store ST1: SCAM ST2: EPOXY ST3: CURE ST4: BA Vehicle X Vehicle Y a a a d ST8: Finish ST7: Test ST6: CTL ST5: BI Warehouse Figure 3: Workstation flow in the case factory 34
λ 1 Experiments λ • Experiment 1: =3.64 lots/hour 1 35
λ 1 Experiments λ • Experiment 1: =3.64 lots/hour 1 ku Quantity of WIP comparison (Stdev) ku 9.5000 Quantity of WIP comparison (Mean) 87.0000 9.0000 86.0000 8.5000 85.0000 84.0000 8.0000 83.0000 7.5000 82.0000 81.0000 7.0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 MDP+DP Simulation MDP+DP Simulation Day Cycle time Comparison (Mean) Day Cycle time Comparison (Stdev) 7 1.25 6.9 1.2 6.8 1.15 6.7 1.1 6.6 1.05 6.5 1 6.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 MDP+DP Simulation MDP+DP Simulation Vehicle mean utilization rate (Stdev) Vehicle mean utilization rate (Mean) 0.14 0.9 0.12 0.85 0.1 0.8 0.08 0.75 0.06 0.7 0.04 0.65 0.02 0.6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 MDP+DP Simulation MDP+DP Simulation 36
λ 1 Experiments λ • Experiment 2: =4.42 lots/hour 2 37
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