tzu-li chen, ph.d. assistant professor department of information management
DESCRIPTION
需求不確定下 TFT-LCD 產業隨機產能規劃 Stochastic Capacity Planning for TFT-LCD Manufacturing under Demand Uncertainty. Tzu-Li Chen, Ph.D. Assistant Professor Department of Information Management Fu Jen Catholic University. 研究背景與動機. - PowerPoint PPT PresentationTRANSCRIPT
TFT-LCD (APS)Tzu-Li Chen, Ph.D.
TFT-LCD
*
Array
(Array
Operations
Scheduling)
Cell
Cell
Operations
Scheduling
Module
Module
Operations
Scheduling)
Capacity
Constrained Sales Plan
Cutting Ratio
8
E
8
D
6
A
75,000
75,000
75,000
75,000
75,000
75,000
E
75,000
75,000
75,000
75,000
75,000
75,000
D
75,000
75,000
75,000
75,000
75,000
75,000
A
page *
page *
Capacity of each site
Capacity of each product group in certain site
page *
Deterministic Multi-Site
Capacity Planning
*
Problem definition of multi-site capacity planning
Under the single-stage & multiple-site structure, multiple-product groups and multiple periods environments, each site with the specific generation can produce many different product group and each product group can be produced in many sites with different generation.
Assume demand forecast and sale price of each product group, capacity (supply) and cost information of each site for each product group in the future period are given and deterministic.
Under given foregoing characteristics and constraints, a multi-site capacity planning problem of the TFT-LCD industry consists of two main decisions to maximize total net profit:
Capacity allocation decision
The profitable “product mix” of each site in each period
The best “production quantities” of each product group at each site in each period
Capacity Expansion decision
The “purchasing amounts of the auxiliary tool (Mask)” for each product group at each site in each period
The “capacity expansion quantity” for each product group at each site in each period
*
*
Only consider Array Stage
product hierarchy
Deterministic demand
Product-group-specific
site
- Assumptions
Demand quantities and sale prices of each product group are given and varied by period.
Only consider Array process without Cell and Module processes. Since the Array process is the bottleneck, in a high-investment production environment, today’s capacity planners focus majorly on solving the single-stage and multi-period capacity planning problem.
Variable production cost (including material cost, labor cost and other manufacturing cost) and holding cost depend on average unit cost.
Capacity expansion focuses on purchasing new auxiliary tools without adding new bottleneck machines or building new sites.
The phase-out time of a product group can be estimated.
Calculation methods of capacity expansion cost adopt the “Straight-Line Method” (also called Linear Depreciation Method).
The salvage value of each auxiliary tool is zero.
*
*
- Notation
- Notation
- Objective Function
Total Revenue
- Objective Function
Straight-Line Method
estimated useful life of the auxiliary (Mask)
*
*
- Constraints
*
*
- Constraints
Stochastic Multi-Site Capacity Planning under Demand Uncertainty
*
*
Problem definition of stochastic multi-site capacity planning
Since demand forecasts are usually inaccurate in TFT-LCD industry, traditional deterministic capacity planning model is not reliable and no longer enough to tackle this problem. The stochastic multi-site capacity planning model is developed.
Under the single-stage & multiple-site (f) structure, multiple-product groups (p) and multiple periods (t) environments, each site with the specific generation can produce many different product group and each product group can be produced in many sites with different generation.
We use a scenario tree with discrete demand scenarios to represent the demand uncertainties and each scenario is associated with a given probability. Each scenario specifics demand volumes of each product group over the planning horizon.
Under the given TFT-LCD characteristics and demand uncertainty, the stochastic multi-site capacity planning problem addresses two-stage decisions to maximize the expected total profits.
In the first stage, due to the long procurement lead time of auxiliary tools, the capacity expansion decision (also called here-and-now decision) will determine the robust purchasing quantities of the auxiliary tool for each product group at each site before the actual demand is known.
*
*
TFT-LCD Research_Group©Copyright 2010
*
*
*
*
Modeling Demand Uncertainty and Scenario Generation
*
*
Modeling Demand Uncertainty and Scenario Generation(1)
-Time series forecast model (TFT-LCD case)
*
*
-Demand scenario generation (TFT-LCD case)
*
*
-Demand scenario reduction (TFT-LCD case)
*
*
*
*
Objective Function - maximize expected total net profits
Expected Total Revenue
First-Stage Constraints (non-scenario related)
Second-Stage Constraints (scenario related)
*
*
Without considering capacity expansion decision, our stochastic mixed integer programming model becomes the linear programming-based stochastic multi-site capacity allocation model (SMSCA) below.
*
*
Industry Practice and Model Validation
- Numerical Study and Model Robustness
In order to show the robustness of solution generated by two-stage stochastic programming, we conduct detailed numerical study to compare the solution robustness between the two-stage stochastic programming model (SP model) and the deterministic model using expected forecast demands (EV model).
A set of sample data includes two Array sites, five product groups, six months and three demand scenarios (low, medium and high demand) is collected from TFT-LCD industry partners.
Robust auxiliary tool purchasing plan in SP model
Auxiliary tool purchasing plan in EV model
*
*
Industry Practice and Model Validation
- Numerical Study and Model Robustness
To compare the SP model with the current industry practice (EV model), we use a stochastic measure, value of stochastic solution (VSS), to evaluate the performance of each model
According to this result, using the SP model could gain 6.57% more profit than EV model under the given demand scenarios.
SP represents the objective value of two-stage stochastic programming model.
*
*
Industry Practice and Model Validation
- Robust Evaluation by out-of-sample Simulation
To verify the effectiveness of stochastic model under normally distributed demand, we propose the simulation experimental framework to use out-of-sample simulation to study the performance of EV and SP model in 150 randomly generated demand patterns.
*
*
The mean, VaR & CVaR measure of the numerical example
The distribution of the profit for the SP and EV model in the illustrative example
*Improvement gap = (a – b)/b, where a is the value of SP model and b is the value of EV model
The mean value of SP model is larger than EV
model, so the solution of SP model provides
higher expected profits in the face of the
demand uncertainty.
and 90% CVaR, the objective function value of
SP model is also larger than that of the EV
model. That means the worst return profits (VaR)
and worst expected profits (CVaR) using the SP
model are greater than that of EV model under
90% and 95% confidence level.
*
*
4.0751
0.4532
1.4991
1.2060
1.3439
page *
- Robust evaluation by other industrial case studies
The mean, VaR & CVaR of SP and EV model under other industrial case studies
*
*
7.9856
1.3895
0.5028
1.8991
1.1024
10.7028
5.1895
2.5871
4.5465
3.5861
2.0349
0.3203
0.0714
0.4516
0.3188
1.2161
2.3757
3.5475
3.8366
3.3530
0.1919
0.4129
0.2131
0.0001
0.2083
0.1841
0.0280
0.0871
0.3506
0.1613
2.7838
0.2722
0.4264
1.4914
0.5863
7.9856
0.0047
6.5482
1.7996
3.1681
page *
page *
&
purchasepriceofassetsalvagevalue
Depreciation
estimatedusefullifeofasset
Mean demand
14.1”A
Mean demand
20.1”B
Mean demand
22.0”A
Period (month)
Site
Product
Group
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6
P1 8 0 0 0 0 0
P2 3 0 2 0 0 0
P3 0 0 0 0 0 0
P4 0 0 0 0 0 0
A1
A2
4343.474075.77267.70
VSSSPEEV
EV Model
Improvement gap of
Model Mean
Case 1
SP Model 4050.2 3204.0 2996.4 3399.5 3161.0
EV Model 3658.6 3046.0 2920.8 3251.6 3051.5
Case 2
SP Model 2725.6 2324.5 2230.4 2385.6 2301.4
EV Model 2671.3 2317.1 2228.8 2374.9 2294.1
Case 3
SP Model 3068.2 2819.7 2749.5 2908.2 2808.1
EV Model 3031.4 2754.2 2655.3 2800.7 2717.0
Case 4
SP Model 3055.8 2814.9 2690.3 2864.73 2771.6
EV Model 3049.9 2803.3 2684.6 2864.72 2765.9
Case 5
SP Model 2593.1 2236.5 2132.1 2302.4 2210.1
EV Model 2588.4 2235.9 2130.2 2294.4 2206.6
Case 6
SP Model 4297.1 3795.0 3325.5 3917.3 3827.9
EV Model 4180.8 3784.7 3311.4 3859.8 3805.5
Case 7
SP Model 4371.9 3334.3 2967.4 3640.5 3453.5
EV Model 4048.6 3334.1 2785.1 3576.1 3347.5
Case 8
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3000000
4000000
5000000
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123456
(SP)
E
model in the illustrative example
0
5
10
15
20
25
30
35
40
Profit
Frequency
TFT-LCD
*
Array
(Array
Operations
Scheduling)
Cell
Cell
Operations
Scheduling
Module
Module
Operations
Scheduling)
Capacity
Constrained Sales Plan
Cutting Ratio
8
E
8
D
6
A
75,000
75,000
75,000
75,000
75,000
75,000
E
75,000
75,000
75,000
75,000
75,000
75,000
D
75,000
75,000
75,000
75,000
75,000
75,000
A
page *
page *
Capacity of each site
Capacity of each product group in certain site
page *
Deterministic Multi-Site
Capacity Planning
*
Problem definition of multi-site capacity planning
Under the single-stage & multiple-site structure, multiple-product groups and multiple periods environments, each site with the specific generation can produce many different product group and each product group can be produced in many sites with different generation.
Assume demand forecast and sale price of each product group, capacity (supply) and cost information of each site for each product group in the future period are given and deterministic.
Under given foregoing characteristics and constraints, a multi-site capacity planning problem of the TFT-LCD industry consists of two main decisions to maximize total net profit:
Capacity allocation decision
The profitable “product mix” of each site in each period
The best “production quantities” of each product group at each site in each period
Capacity Expansion decision
The “purchasing amounts of the auxiliary tool (Mask)” for each product group at each site in each period
The “capacity expansion quantity” for each product group at each site in each period
*
*
Only consider Array Stage
product hierarchy
Deterministic demand
Product-group-specific
site
- Assumptions
Demand quantities and sale prices of each product group are given and varied by period.
Only consider Array process without Cell and Module processes. Since the Array process is the bottleneck, in a high-investment production environment, today’s capacity planners focus majorly on solving the single-stage and multi-period capacity planning problem.
Variable production cost (including material cost, labor cost and other manufacturing cost) and holding cost depend on average unit cost.
Capacity expansion focuses on purchasing new auxiliary tools without adding new bottleneck machines or building new sites.
The phase-out time of a product group can be estimated.
Calculation methods of capacity expansion cost adopt the “Straight-Line Method” (also called Linear Depreciation Method).
The salvage value of each auxiliary tool is zero.
*
*
- Notation
- Notation
- Objective Function
Total Revenue
- Objective Function
Straight-Line Method
estimated useful life of the auxiliary (Mask)
*
*
- Constraints
*
*
- Constraints
Stochastic Multi-Site Capacity Planning under Demand Uncertainty
*
*
Problem definition of stochastic multi-site capacity planning
Since demand forecasts are usually inaccurate in TFT-LCD industry, traditional deterministic capacity planning model is not reliable and no longer enough to tackle this problem. The stochastic multi-site capacity planning model is developed.
Under the single-stage & multiple-site (f) structure, multiple-product groups (p) and multiple periods (t) environments, each site with the specific generation can produce many different product group and each product group can be produced in many sites with different generation.
We use a scenario tree with discrete demand scenarios to represent the demand uncertainties and each scenario is associated with a given probability. Each scenario specifics demand volumes of each product group over the planning horizon.
Under the given TFT-LCD characteristics and demand uncertainty, the stochastic multi-site capacity planning problem addresses two-stage decisions to maximize the expected total profits.
In the first stage, due to the long procurement lead time of auxiliary tools, the capacity expansion decision (also called here-and-now decision) will determine the robust purchasing quantities of the auxiliary tool for each product group at each site before the actual demand is known.
*
*
TFT-LCD Research_Group©Copyright 2010
*
*
*
*
Modeling Demand Uncertainty and Scenario Generation
*
*
Modeling Demand Uncertainty and Scenario Generation(1)
-Time series forecast model (TFT-LCD case)
*
*
-Demand scenario generation (TFT-LCD case)
*
*
-Demand scenario reduction (TFT-LCD case)
*
*
*
*
Objective Function - maximize expected total net profits
Expected Total Revenue
First-Stage Constraints (non-scenario related)
Second-Stage Constraints (scenario related)
*
*
Without considering capacity expansion decision, our stochastic mixed integer programming model becomes the linear programming-based stochastic multi-site capacity allocation model (SMSCA) below.
*
*
Industry Practice and Model Validation
- Numerical Study and Model Robustness
In order to show the robustness of solution generated by two-stage stochastic programming, we conduct detailed numerical study to compare the solution robustness between the two-stage stochastic programming model (SP model) and the deterministic model using expected forecast demands (EV model).
A set of sample data includes two Array sites, five product groups, six months and three demand scenarios (low, medium and high demand) is collected from TFT-LCD industry partners.
Robust auxiliary tool purchasing plan in SP model
Auxiliary tool purchasing plan in EV model
*
*
Industry Practice and Model Validation
- Numerical Study and Model Robustness
To compare the SP model with the current industry practice (EV model), we use a stochastic measure, value of stochastic solution (VSS), to evaluate the performance of each model
According to this result, using the SP model could gain 6.57% more profit than EV model under the given demand scenarios.
SP represents the objective value of two-stage stochastic programming model.
*
*
Industry Practice and Model Validation
- Robust Evaluation by out-of-sample Simulation
To verify the effectiveness of stochastic model under normally distributed demand, we propose the simulation experimental framework to use out-of-sample simulation to study the performance of EV and SP model in 150 randomly generated demand patterns.
*
*
The mean, VaR & CVaR measure of the numerical example
The distribution of the profit for the SP and EV model in the illustrative example
*Improvement gap = (a – b)/b, where a is the value of SP model and b is the value of EV model
The mean value of SP model is larger than EV
model, so the solution of SP model provides
higher expected profits in the face of the
demand uncertainty.
and 90% CVaR, the objective function value of
SP model is also larger than that of the EV
model. That means the worst return profits (VaR)
and worst expected profits (CVaR) using the SP
model are greater than that of EV model under
90% and 95% confidence level.
*
*
4.0751
0.4532
1.4991
1.2060
1.3439
page *
- Robust evaluation by other industrial case studies
The mean, VaR & CVaR of SP and EV model under other industrial case studies
*
*
7.9856
1.3895
0.5028
1.8991
1.1024
10.7028
5.1895
2.5871
4.5465
3.5861
2.0349
0.3203
0.0714
0.4516
0.3188
1.2161
2.3757
3.5475
3.8366
3.3530
0.1919
0.4129
0.2131
0.0001
0.2083
0.1841
0.0280
0.0871
0.3506
0.1613
2.7838
0.2722
0.4264
1.4914
0.5863
7.9856
0.0047
6.5482
1.7996
3.1681
page *
page *
&
purchasepriceofassetsalvagevalue
Depreciation
estimatedusefullifeofasset
Mean demand
14.1”A
Mean demand
20.1”B
Mean demand
22.0”A
Period (month)
Site
Product
Group
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6
P1 8 0 0 0 0 0
P2 3 0 2 0 0 0
P3 0 0 0 0 0 0
P4 0 0 0 0 0 0
A1
A2
4343.474075.77267.70
VSSSPEEV
EV Model
Improvement gap of
Model Mean
Case 1
SP Model 4050.2 3204.0 2996.4 3399.5 3161.0
EV Model 3658.6 3046.0 2920.8 3251.6 3051.5
Case 2
SP Model 2725.6 2324.5 2230.4 2385.6 2301.4
EV Model 2671.3 2317.1 2228.8 2374.9 2294.1
Case 3
SP Model 3068.2 2819.7 2749.5 2908.2 2808.1
EV Model 3031.4 2754.2 2655.3 2800.7 2717.0
Case 4
SP Model 3055.8 2814.9 2690.3 2864.73 2771.6
EV Model 3049.9 2803.3 2684.6 2864.72 2765.9
Case 5
SP Model 2593.1 2236.5 2132.1 2302.4 2210.1
EV Model 2588.4 2235.9 2130.2 2294.4 2206.6
Case 6
SP Model 4297.1 3795.0 3325.5 3917.3 3827.9
EV Model 4180.8 3784.7 3311.4 3859.8 3805.5
Case 7
SP Model 4371.9 3334.3 2967.4 3640.5 3453.5
EV Model 4048.6 3334.1 2785.1 3576.1 3347.5
Case 8
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