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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.

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Tzu li chen ph d assistant professor department of information management

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


Tzu li chen ph d assistant professor department of information management

研究背景與動機

  • TFT-LCD面板產業是由三大生產製程階段所組成,分別為列陣(Array)製程、組立(Cell)製程和模組(Module)製程,每階段製程由多個工廠所組成而形成稱為生產鏈結構(production chain)的生產系統。

  • 由於下列三大趨勢,而使的產能規劃問題變成了TFT-LCD產業日益重要:

    • 多階層、多世代與多廠區共存的生產鏈結構

    • 複雜的產品階層結構而造成了TFT-LCD面板可生產產品種類繁多且廣泛

    • 成長快速與劇烈變動的產品需求

  • 在這些有限產能供給、特殊生產結構與快速成長需求的特性下,TFT-LCD產業必須面臨了因供給與需求不平衡而造成的產能規劃議題

    • 產能分配決策 :決定每個生產廠區的最大化利潤產品族組合以及每個廠區對於每個產品的最適生產數量

    • 產能擴充決策 :決定哪種類型的產能(各廠區總產能或各廠區對各產品族產能)在哪些廠區需要擴充或是要設立新的生產廠區來增加產能、該類型的產能有多少量需要被擴充或增加以及要透過購買多少機台或是附屬資源來擴充產能


Tzu li chen ph d assistant professor department of information management

研究目的

  • 本研究主要針對TFT-LCD產業的產能規劃問題進行探討,本研究的目的整理如下:

    • 定位TFT-LCD產業之產能規劃問題,並從TFT-LCD產業的供給面特性、需求面特性與供給與需求不平衡特性來分析、定義與分類該產能規劃問題。

    • 建構確定性產能規劃問題之數學模式,包含了單階層多廠區產能規劃問題與多階層多廠區產能規劃問題,並提出有效率的陰影價格為基之分解演算法(shadow-price based decomposition;SPBD )來求解該數學模式。

    • 考量需求不確定環境下,建構隨機性產能規劃數學問題之數學模式,包含了單階層多廠區隨機產能規劃與多階層多廠區隨機產能規劃問題,並提出有效率的期望陰影價格為基之分解演算法(expected shadow-price based decomposition;ESPBD )來求解之。


Tzu li chen ph d assistant professor department of information management

Capacity Planning in TFT-LCD Manufacturing


Hierarchical planning levels for tft lcd industry

Hierarchical Planning Levels for TFT-LCD Industry

Module

現場排程

(Module

Operations

Scheduling)

Cell

現場排程

(Cell

Operations

Scheduling)

Array

現場排程

(Array

Operations

Scheduling)

Procurement

Production

Distribution

Sales

需求規劃

(Demand

Planning)

產能規劃

(Capacity Planning)

Product Family

Demand Forecast

Product

Disaggregate

Supply

Network

Plan

關鍵物料規劃

(Critical Material

Planning)

Mid-term

(monthly)

生產鏈規劃

(Supply Network Planning)

Product

Demand Forecast

PUSH

Material

Plan

Time

Disaggregate

Allocation

Plan

Demand

Forecast

Supply Network Plan

Cell

Daily

Schedule

Module

ATP

Array、CF與Cell短期

多廠區日排程

(Array/CF/Cell

Daily Scheduling)

Module短期多廠區最終

日排程(Module Final

Assembly Scheduling)

訂單滿足規劃

(Order

Fulfillment)

Short-term

(daily)

Customer

Order

Cell ATP

Time

Disaggregate

Resource

Disaggregate

PULL

Cell Daily

Schedule

Module Final

Assembly Schedule

Array

Daily

Schedule

Shop floor

(real time)


Planning scenario of capacity planning

Planning Scenario of Capacity Planning

Purchasing Amount

Released Production Quantities (sheet)

Profit (US dollars/piece)

Sale Quantities (piece)

site

Product Group

7

8

9

10

11

12月

site

Product Group

7

8

9

10

11

12

site

Product Group

7

8

9

10

11

12

site

Product Group

7

8

9

10

11

12

Fab 1

A

19737.534

19737.534

19737.534

19696.095

19696.095

19696.095

Fab1

Fab 1

A

0

0

0

0

0

0

Fab 1

A

18

18

18

15

15

15

Fab 1

A

150100

150100

150100

150100

150100

150100

B

15

15

15

12

12

12

B

0

0

0

0

0

0

B

8575.5366

8575.5366

8575.5366

8571.1353

8571.1353

8571.1353

B

50100

50100

50100

50100

50100

50100

C

7

7

7

7

7

7

C

0

0

1

0

0

0

E

15

15

15

14

14

14

C

12021.072

12021.072

12021.072

12427.438

12427.438

12427.438

C

2161.2858

2161.2858

2161.2858

2224.7472

2224.7472

2224.7472

Fab 2

A

28

28

28

25

25

25

E

0

0

0

0

0

0

Fab2

D

29

29

29

26

26

26

E

175100

175100

175100

175100

175100

175100

E

29839.809

29839.809

29839.809

29839.809

29839.809

29839.809

E

29

29

29

26

26

26

Fab 2

A

0

0

0

0

0

0

. . .

Fab 2

A

217305

205842.51

188592.09

213636.58

187252.72

182909.65

Fab 2

A

37500

35521.935

32545.055

36847.869

32297.202

31548.113

Marginal profit

D

0

0

1

0

0

0

D

261517.3

278370.21

303638.88

267893.07

306447.35

313071.49

D

33945.652

36095.723

39331.462

34654.49

39600.868

40415.095

E

0

0

0

0

0

0

Expansion Upper Bound (sheet)

E

138582.7

121729.79

96461.115

132206.93

93652.646

87028.509

E

17895.493

15719.239

12456.239

17066.887

12089.828

11234.704

site

Product Group

7

8

9

10

11

12

Demand (pieces/month)

Fab 1

A

66,000

66,000

66,000

66,000

66,000

66,000

Product Group

7

8

9

10

11

12

B

66,000

66,000

66,000

66,000

66,000

66,000

Fabn

C

66,000

66,000

66,000

66,000

66,000

66,000

A

150,100

150,10

150,100

150,100

150,100

150,100

E

66,000

66,000

66,000

66,000

66,000

66,000

Fab 2

A

75,000

75,000

75,000

75,000

75,000

75,000

B

50,100

50,100

50,100

50,100

50,100

50,100

D

75,000

75,000

75,000

75,000

75,000

75,000

C

15,100

15,100

15,100

15,100

15,100

15,100

D

175,100

175,10

175,100

175,100

175,100

175,100

E

75,000

75,000

75,000

75,000

75,000

75,000

Capacity of each site at certain site (sheet/month)

E

400,100

400,10

400,100

400,100

400,100

400,100

site

Product Group

Value (pieces/sheet)

site

Product Group

7

8

9

10

11

12

UnconstrainedDemand Plan (forecast)

Fab 1

A

8

Expansion Capability

Fab 1

A

33,000

33,000

33,000

33,000

33,000

33,000

B

6

site

A

B

C

D

E

C

6

Capacity of each site (sheet / month)

B

33,000

33,000

33,000

33,000

33,000

33,000

E

6

Fab 1

1

1

1

0

1

site

7

8

9

10

11

12

Fab 2

A

6

C

33,000

33,000

33,000

33,000

33,000

33,000

D

8

Fab 2

1

0

0

1

1

Fab 1

74,000

76,720

74,240

76,720

74,240

76,720

E

8

E

33,000

33,000

33,000

33,000

33,000

33,000

Fab 2

88,950

88,950

86,050

89,493

86,575

89,493

Fab 2

A

37,500

37,500

37,500

37,500

37,500

37,500

D

75,000

75,000

75,000

75,000

75,000

75,000

E

37,500

37,500

37,500

37,500

37,500

37,500

2

3

Capacity on each site

1

Expansion Upper Bound

Expansion Capability

Cutting Ratio

Capacity

Allocation & Expansion

(Maximum total profit)

Sales department

Capacity of each site at certain site (sheet/month)

Input

4

Output

Constrained Sales Plan

(Sales quantities)

Capacity Allocation Plan

(Release production quantities)

Capacity Expansion Plan

(Purchasing amount of new auxiliary tools)


Tzu li chen ph d assistant professor department of information management

產能規劃的角色

  • 目的在於依據自於需求規劃(Demand Planning)模組所產生未來12個月未考量產能限制的產品族需求預測(Unconstrained demand forecast),決定未來12個月內各廠區(包括了Array廠區與Cell廠區)中還需購買多少資源(主資源與附屬資源)來擴充產能數量,並決定各廠區的最佳生產產品族組合與各產品族的生產數量

  • 產能規劃輸出結果的意義

    • 提供建議給產能規劃人員來決定要在何時必須下採購單給資源設備廠商來購買擴充資源設備

    • 將產能被分配到生產產品族組合以及考慮產能限制下的可滿足需求預測數量(Constrained demand forecast)提供給需求規劃人員參考是否要重新調整需求預測來應付有限的產能資源

    • 經由產能規劃產生的產能擴充與生產分配資訊將會作為生產鏈規劃(Supply Network Planning)的輸入並驅動生產鏈規劃活動,生產鏈規劃就會依據既有的產能限制(初始產能加上從產能規劃獲得的擴充產能)下,決定Array、Cell與Module各階層每個廠區的6個月投入與產出生產量以及物料需求採購量


Tft lcd

TFT-LCD產能規劃問題特性分析--供給面特性

  • 生產鏈廠區結構特性

    • 多階層生產環境

    • 多世代技術與多廠區之共存

    • 多階層、多世代與多廠區生產鏈結構與關係

    • 多階層生產鏈間不同生產單位轉換

    • 多階層生產鏈的瓶頸漂移現象

  • 生產鏈廠區與產品族關係特性

    • 各世代廠區對不同產品族之經濟切割率

    • 各廠區對不同產品族之生產能力限制

    • 各廠區對不同產品族之潛在產能擴充能力 (potential expansion capability )限制

    • 各廠區對不同產品族之生產良率

      • 各廠區對於生產不同產品族之生產良率為不同的,且每週期同一廠區加工不同產品族種類之良率也會有些微的變動

      • 對於新建立的生產廠區,由於廠區可能在剛設立(ramp up)的階段,正在導入新製程技術以及調整機台設定,公司將會慢慢調升其生產良率,造成每週期的良率呈上升的趨勢

    • 各廠區對不同產品族之生產變動成本


Tft lcd1

TFT-LCD產能規劃問題特性分析--供給面特性

  • 生產鏈廠區供給產能特性

    TFT-LCD產業的廠區供給產能可以分為兩種型態,一種為只考慮以廠為單位的各廠區總產能(Capacity of each site),另一種則必須考量以廠區加上產品族為單位的各廠區對各產品族產能(Capacity of each product group in certain site),此兩種型態的產能分別由不同設備(瓶頸機台或附屬資源)的數量來評定之。

    • 各廠區總產能(Capacity of each site)限制與衡量

    • 各廠區對各產品族產能限制(Capacity of each product group in certain site)與衡量

    • 各廠區擴充產能方式


Tft lcd2

TFT-LCD產能規劃問題特性分析--需求面特性

  • 產品特性

    • 複雜且多階層產品階層架構

  • 產品需求特性

    • 成長快速多期產品需求

    • 劇烈變動的不確定產品需求

  • 產品價格特性

    • 多期產品平均銷售價格(Average Sale Price;ASP)

    • 劇烈變動的不確定產品平均銷售價格

      • TFT-LCD產業不僅具有劇烈變動的不確定產品需求外,也具有劇烈變動的不確定產品平均銷售價格,此也是一項重要的因素影響著產能規劃結果無法準確的得到TFT-LCD穩健產能分配與擴充計劃


Tft lcd3

TFT-LCD產能規劃問題特性分析--供給與需求不平衡特性

  • TFT-LCD產業的產品生命週期短、需求成長快速以及產品價格劇烈波動,在加上新世代製程技術與廠區的建立需要花上長久的前置時間,因此市場常常會出現供過於求或供不應求的狀況(供給與需求不平衡的狀況 )。

  • 產能規劃的目的必須考慮整個規劃時程之供給產能與需求預測資訊,在規劃時程內,因此產能規劃必須平衡此供給與需求不協調的狀況,將資源作最好的分配,使得最後規劃結果達到總利潤最佳化。

  • 需求預測大於供給可用產能(供不應求)

    • 產能分配(Capacity Allocation)

      • 決定每個生產廠區的最大化利潤產品族組合以及每個廠區對於每個產品的最適生產數量

    • 產能擴充(Capacity Expansion)

      • 決定哪種類型的產能(各廠區總產能或各廠區對各產品族產能)在哪些廠區需要擴充或是要設立新的生產廠區來增加產能,以及該類型的產能有多少量需要被擴充或增加

      • 產能擴充決策上,由於本研究所考慮的是透過購買某產品族副屬資源的方式來擴充各廠區對各產品族產能,並且還必須考量未滿足需求之產品族所剩餘之生命週期以及需求趨勢

      • 透過產能決策決定哪些產品族將要移轉到(migration)哪些新的廠區進行生產

  • 需求預測小於供給可用產能 (供過於求)

    • 產能分配(Capacity Allocation)

      • 決定每個生產廠區的最大化利潤以及最小化總成本的產品族組合以及每個廠區對於每個產品的最適生產數量。


Tft lcd4

TFT-LCD產能規劃問題分類


Tzu li chen ph d assistant professor department of information management

Deterministic Multi-Site

Capacity Planning

Tzu-Li Chen, James T. Lin and Shu-Cherng Fang, “A Shadow-Price Based Heuristic for Capacity Planning of TFT-LCD Manufacturing”, Journal of Industrial and Management Optimization, Vol. 6, No.1, pp.209-239, 2010.


Problem definition of 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

Through outcomes of capacity expansion, a new product transfer plan that improves the flexibility configurations of multi-site structures is simultaneously identified.


Specific characteristics of multi site capacity planning

Specific characteristics of multi-site capacity planning

  • Only consider Array Stage

  • Single-Stage & Multi-Site

  • Structure

  • Release and output production

  • balance constraint according to

  • economic cutting ratio

  • Product group level of the

  • product hierarchy

  • Deterministic demand

  • and vary by periods

  • Deterministic price

  • and vary by periods

  • Aggregated demand

  • forecast and sale price

  • Global capacity of each site

  • Product-group-specific

  • capacity at a certain site

  • Only focus on purchasing the

  • “mask” to expand capacity of

  • each product group in certain

  • site

  • Capacity consumption rate

  • Potential expansion capability

  • constraint

  • Capacity expansion upper

  • constraint

  • Limited flexibility configuration

  • Production capability

  • constraint between each site

  • and each product group

  • Different yield rate of each

  • product group in each site


Multi site capacity planning problem assumptions

Multi-Site Capacity Planning Problem - 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.


Multi site capacity planning milp model notation

Multi-Site Capacity Planning MILP Model - Notation


Multi site capacity planning milp model notation1

Multi-Site Capacity Planning MILP Model - Notation


Multi site capacity planning milp model objective function

Multi-Site Capacity Planning MILP Model - Objective Function

Objective Function - maximize the total net profit

Total Revenue

Total Variable Production Cost

Total Inventory Holding Cost

Total Capacity Loss Cost

Total Expansion Cost


Multi site capacity planning milp model objective function1

Multi-Site Capacity Planning MILP Model - Objective Function

Straight-Line Method

Adopt Straight-Line Method to calculate the capacity expansion cost.

using the number of time periods until the period T

estimated useful life of the auxiliary (Mask)


Multi site capacity planning milp model constraints

Multi-Site Capacity Planning MILP Model - Constraints

Connector between capacity allocation and expansion problems!!!


Multi site capacity planning milp model constraints1

Multi-Site Capacity Planning MILP Model - Constraints


Tzu li chen ph d assistant professor department of information management

Stochastic Multi-Site Capacity Planning under Demand Uncertainty

Lin, J. T., Wu, C. H., Chen, T. L. and Shih, S. H., “A Stochastic Programming Model for Strategic Capacity Planning in Thin Film Transistor – Liquid Crystal Display (TFT-LCD) Industry”, Computers and Operations Research, accepted.


Problem definition of stochastic multi site capacity planning

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.

In the second stage, when a specific demand scenario is realized, capacity allocation decision (also called wait-and-see decision) will then generate a profitable product mix and production quantities for each site for each scenario.


A scenario tree with discrete demand scenarios for representing the demand uncertainties

A scenario tree with discrete demand scenarios for representing the demand uncertainties


Problem definition of stochastic multi site capacity planning1

Problem definition of stochastic multi-site capacity planning


Modeling demand uncertainty and scenario generation

Modeling Demand Uncertainty and Scenario Generation

In order to build the representative scenario tree with several discrete demand scenarios, a methodology that combines the forecast techniques and scenario generation methods is proposed to approximate the stochastic demand process.


Modeling demand uncertainty and scenario generation 1 time series forecast model tft lcd case

Modeling Demand Uncertainty and Scenario Generation(1)-Time series forecast model (TFT-LCD case)

Historical and predicted demand date of all products in the TFT-LCD manufacturing

The mean demand, standard deviation and 95% confidence intervals of three products in each period


Modeling demand uncertainty and scenario generation 2 demand scenario generation tft lcd case

Modeling Demand Uncertainty and Scenario Generation(2)-Demand scenario generation(TFT-LCD case)

100 simulation scenarios (sample paths) of all products by the monte carlo sampling


Modeling demand uncertainty and scenario generation 3 demand scenario reduction tft lcd case

Modeling Demand Uncertainty and Scenario Generation(3)-Demand scenario reduction(TFT-LCD case)

Different demand scenario sizes of all products by the scenario reduction


Two stage stochastic programming model of multi site capacity planning notation

Two-Stage Stochastic Programming Model of Multi-Site Capacity Planning- Notation


Two stage stochastic programming model of multi site capacity planning objective function

Two-Stage Stochastic Programming Model of Multi-Site Capacity Planning- Objective Function

Objective Function - maximize expected total net profits

Total Expansion Cost

First-Stage

Objective

Expected Total Revenue

Expected Total Production Cost

Second-Stage

Objective

Expected Total Inventory Cost


Two stage stochastic programming model of multi site capacity planning constraints

Two-Stage Stochastic Programming Model of Multi-Site Capacity Planning- Constraints

First-Stage Constraints (non-scenario related)


Two stage stochastic programming model of multi site capacity planning constraints1

Two-Stage Stochastic Programming Model of Multi-Site Capacity Planning- Constraints

Second-Stage Constraints (scenario related)

Connector between capacity allocation and expansion problems!!!


Expected shadow price based decomposition scenario dependent capacity allocation phase

Expected Shadow-Price based Decomposition- Scenario-dependent capacity allocation phase

Without considering capacity expansion decision, our stochastic mixed integer programming model becomes the linear programming-based stochastic multi-site capacity allocation model (SMSCA) below.

Since the stochastic multi-site capacity allocation problem is a large-scale linear programming model with the huge number of demand scenarios, we can decompose this whole model into a number of capacity allocation sub-models with individual demand scenario.


Industry practice and model validation numerical study and model robustness

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 robustness1

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.

SPrepresents the objective value of two-stage stochastic programming model.

EEV represents the expected results of using solution of the expected-value deterministic model.


Industry practice and model validation robust evaluation by out of sample simulation

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 total profit of each out-of-sample scenario under the fixed capacity expansion solutions of SP model and EV model is calculated and the profit distribution from the collection of the profit values of all out-of-sample scenarios is formed.


Industry practice and model validation robust evaluation by out of sample simulation1

Industry Practice and Model Validation- Robust Evaluation by out-of-sample Simulation

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.

  • In terms of 95% VaR, 90% VaR, 95% CVaR

  • 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.


Industry practice and model validation robust evaluation by other industrial case studies

Industry Practice and Model Validation- Robust evaluation by other industrial case studies

The mean, VaR & CVaR of SP and EV model under other industrial case studies

It can be seen that the mean profit and financial risk measures (VaR and CVaR value) of SP model are always greater than that of EV model in all eight cases.


Future research

Future Research

  • Stochastic Risk Programming with Risk Measure

  • Stochastic Dynamic Programming (Multi-Stage Stochastic Programming)

  • Robust Optimization with unknown Demand Distribution


Thank you for your attention welcome your comments and questions

Thank you for your attention!& Welcome your comments and questions!


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