Motivation

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Capacity Planning in a General Supply Chain with

Multiple Contract Types

Stephen C. Graves and Xin Huang

May 2008

Copyright Stephen C. Graves 2008All Rights Reserved

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Motivation• Prior research has developed algorithms

and software for modeling and optimizing the inventory across a supply chain – “strategic inventory placement model”

• Impetus for current research – develop and deploy a tactical model to provide decision support for determining capacity levels across a supply chain


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Intent

• Develop a framework to support capacity planning decisions in a supply chain with−Multiple products−Each product requires multiple processes (or

components)−Each resource provides capacity for one or more

processes

• Need to determine the right level and type of capacity investments

• Need to account for network interrelationships, demand uncertainty, multiple time periods, & different capacity contracts.


4

Work to Date• Developed framework for structuring

models

• Developed and tested algorithms for determining the amount, type and timing of capacity investments across a complex multi-product supply chain

• Implementation of user-friendly software is underway


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Model assumptions• Given demand forecast and contract

prices, we first make capacity decisions: −For each resource how much capacity to

reserve and with what type of contract• Then we learn what the actual demand is

and decide how to allocate capacity to meet demand as best as possible

• Objective is to maximize revenue net of capacity costs


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Example 1

Laptop A

Chip Set A

Foundry 1

Display A A & T

Foundry 3 CM 1


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Example 1: Sample Input Data

Laptop A

Mean 2200

STD 200

Sales price $700

Table 1: Table of Product Information

Fixed Unit Price

Unit Reservation Price

Unit Exercise Price

Foundry 1 90 85 10

Foundry 3 200 160 50

CM 1 115 25 100Table 2: Table of Resource Price Inputs


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Example 1: Model Outputs

Fixed-price Capacity

Option Capacity

Total

Foundry 1 2211 0 2211

Foundry 3 2040 171 2211

CM 1 1954 257 2211

The Expected Total Profit: $ 601,623

Mean – Laptop A: 2200


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Example 1: Performance Statistics

Fixed-price Capacity Utilization

Option Capacity Utilization

Foundry 1 2131/2211 = 96.4% --

Foundry 3 2018/2040 = 98.9% 112/171 = 65.5%

CM 1 1945/1954 = 99.5% 185/257 = 72.0%

Units sold Lost sales

Average # of 2130 75


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Example 3

Laptop A Laptop B

Chip Set A

Foundry 1

Display A A & T Chip Set B Display B A & T

Foundry 3 Foundry 3Foundry 4CM 1 CM 2

Foundry 3

CM 1Foundry 2


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Example 3: Sample Input Data Laptop A Laptop B

Mean 2200 1000

STD 200 100

Sales price $700 $1000Table 5: Table of Product Information

Fixed Unit Price

Unit Reservation

Price

Unit Exercise Price

Foundry 1

CS -A 90 85 10

Foundry 2

CS A/B 100 80 30

Foundry 3

Display 200 160 50

Foundry 4

CS - B 98 78 28

CM 1 A&T – A/B

115 25 100

CM 2 A&T - B 110 30 90

Table 6: Table of Resource Price Inputs


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Questions of Interest• Which suppliers should the manufacturer

choose?

• What types of contract should we use for each supplier? Only fixed-price contract? Only option contract? Or Both.

• How much capacity should we buy?


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Option Capacity

Total

Foundry 1 CS -A 2009 0 2009

Foundry 2 CS A/B 365 0 365

Foundry 4 CS - B 728 110 838

Foundry 3 Display 3023 189 3212

CM 1 A&T – A/B 2121 252 2373

CM 2 A&T - B 800 38 838

The Expected Total Profit: $ 1,183,981

Mean – Laptop A: 2200Mean – Laptop B: 1000


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Example 4

1

1 2a

• Compare the following four strategies

1. Plan the capacity as given in the figure without option capacity

2. Use a common process to replace process 2a and 2b

3. Add option capacity to process 2a and 2b

4. Combine strategy S2 and S3

1 2a

2

2b 3

2b 3

S11

1

1

2

2 3

2 3

S21

1 2a

1 2a

2

2b 3

2b 3

S3

1

1

1

2

2 3

2 3

S4


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Example 4: Data• Both products have the same price: changes

from 66 to 150• Demand information:

− E[D_1] = 500, STD(D_1) = 100, E[D_2] = 500, STD(D_2) = 100

• Fixed price contracts: − [p_1, p_2a, p_2b, p_3] = [10, 50, 50, 10]

• Option contracts:− Reservation Price = 5, Exercise Price = 50


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Example 4

Profit Margin

ExtraProfit (%)

S2/S1

S3/S1

(S2+S3)/S1S4/S1


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Example 5: Multi-period Planning• A Supply Chain Network

− 2 Products, 3 Processes, and 12 Periods.• Each process has 4 different types of contract

− 1 period, 3 periods, 6 periods, and 12 periods• Each contract has 4 terms

− Duration, Fixed-price, Option reservation price, and Option exercise price

1

1

1

2

3 2

3 2


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Sample Demands

1 2 3 4 5 6 7 8 9 10 11 12

70100

180

210

240

240

230

180

100

70 60 50

240

230

180

100

70 60 50 70100

180

210

240

0

50

100

150

200

250

300

350

400

1 2 3 4 5 6 7 8 9 10 11 12

Product 1

Product 2

Sum

E [D1]

E [D2]


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Sample Prices• Prices:

− Product 1: 65; Product 2: 65.

• Costs:− All processes have the same price structure.

Duration 1 3 6 12

Fixed Price 10 9.5 9 8.5

Reservation Price

8 7.5 7.25 6.75

Exercise Price

3 2.5 2.25 2.25


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Results

1 2 3 4 5 6 7 8 9 10 11 12

Process 1 69 99 247 247 247 247 247 247 105 72 72 72

Process 2 242 236 166 115 74 74 74 83 110 199 217 248

Process 3 325 325 325 325 325 325 325 325 325 325 325 325

0

50

100

150

200

250

300

350

400

1 2 3 4 5 6 7 8 9 10 11 12

Product 1

Product 2

Sum


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Results (cont.)

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Option

Committed

P1 Demand

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12

Option

Committed

P2 Demand

Process 1

Process 2

0

50

100

150

200

250

300

350

400

1 2 3 4 5 6 7 8 9 10 11 12

Option

Committed

Sum of Demand

Process 3


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Summary• Have developed a framework to

support capacity planning decisions for supply chain

• Have developed solution algorithms for single period and multi-period problems

• To do − develop a case study to test and

validate approach−finalize prototype software with user

friendly interface


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Collaboration Opportunities• Need a test case(s) to validate and

refine framework −Are we looking at problem in right way?−Does the data exist to test model?−Can our algorithms result in better

decisions?−What’s critical/non-critical in how we are

viewing problem?

• Interest in internships for LFM or SDM students for “beta testing”

• Contact Steve Graves ([email protected]) or Xin Huang ([email protected])

mailto:[email protected]


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Example 2

Laptop B

Chip Set B

Foundry 4

Display B A & T

Foundry 3 CM 2


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Example 2: Sample Input Data

Laptop A

Mean 1000

STD 100

Sales price $1000

Table 3: Table of Product Information

Fixed Unit Price

Unit Reservation Price

Unit Exercise Price

Foundry 4 98 78 28

Foundry 3 200 160 50

CM 2 110 30 90Table 4: Table of Resource Price Inputs


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Option Capacity

Total

Foundry 4 937 104 1041

Foundry 3 910 131 1041

CM 2 870 171 1041

The Expected Total Profit: $ 556,320

Mean – Laptop B: 1000


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Example 2: Performance Statistics

Fixed-price Capacity Utilization

Option Capacity Utilization

Foundry 4 920/937 = 98.2% 55/104 = 52.9%

Foundry 3 900/910 = 98.9% 75/131 = 57.3%

CM 2 866/870 = 99.5% 109/171 = 63.7%

Units sold Lost sales

Average # of 975 23

Motivation

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