Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit...
Transcript of Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit...
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SCperf: An inventory management package for R
Marlene [email protected]
Department of Electrical EngineeringPontifical Catholic University of Rio de Janeiro - Brazil.
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Outline
� Inventory
� The basic Economic Order Quantity (EOQ) model� EOQ assumptions� Derivation of the model
� Inventory models
� What is SCperf?
� EOQ() example
� Bullwhip Effect (BE)� Measuring the BE� Measuring the BE for a generalized demand process� SCperf()
� Why did we develop SCperf?
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Inventory
� What is inventory?
Stock of items kept to meet future demand
� Why to hold inventory?
To protect himself against irregular supply and demand
� Inventory Control Decisions
Objective: To minimize total inventory cost
Decisions:
� How much to order?� When to order?
![Page 4: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/4.jpg)
Inventory
� What is inventory?
Stock of items kept to meet future demand
� Why to hold inventory?
To protect himself against irregular supply and demand
� Inventory Control Decisions
Objective: To minimize total inventory cost
Decisions:
� How much to order?� When to order?
![Page 5: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/5.jpg)
Inventory
� What is inventory?
Stock of items kept to meet future demand
� Why to hold inventory?
To protect himself against irregular supply and demand
� Inventory Control Decisions
Objective: To minimize total inventory cost
Decisions:
� How much to order?� When to order?
![Page 6: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/6.jpg)
EOQ assumptions
1. Instantaneous production,
2. immediate delivery,
3. deterministic demand,
4. constant demand,
5. known fixed setup costs,
6. no shortages are allowed,
7. single product.
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EOQ modelNotation:D: demand per time unit,h: holding cost per unit and time unit,c: unit cost for producing orpurchasing each unit.
A: ordering or setup cost,Q: batch quantity,T : cycle time= Q/D
Total cost per cycle = A + cQ +hQ2
2D
Total cost per unit time =A + cQ + hQ2/2D
Q/D=
DA
Q+ cD +
hQ
2h
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EOQ modelNotation:D: demand per time unit,h: holding cost per unit and time unit,c: unit cost for producing orpurchasing each unit.
A: ordering or setup cost,Q: batch quantity,T : cycle time= Q/D
Total cost per cycle = A + cQ +hQ2
2D
Total cost per unit time =A + cQ + hQ2/2D
Q/D=
DA
Q+ cD +
hQ
2h
![Page 9: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/9.jpg)
EOQ modelNotation:D: demand per time unit,h: holding cost per unit and time unit,c: unit cost for producing orpurchasing each unit.
A: ordering or setup cost,Q: batch quantity,T : cycle time= Q/D
Total cost per cycle = A + cQ +hQ2
2D
Total cost per unit time =A + cQ + hQ2/2D
Q/D=
DA
Q+ cD +
hQ
2h
![Page 10: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/10.jpg)
We have that∂TC
∂Q=
D
QA +
Q
2h,
then Qopt =
√2DA
hand Topt =
Qopt
D
Reorder Point: order when the inventory position is equal to zero.
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Modification of the basic model
1. Instantaneous production,
⇐ Finite production rate
2. immediate delivery,
⇐ Lags can be added
3. deterministic demand,
⇐ Stochastic demand
4. constant demand,
⇐ Time-varying demand
5. known fixed setup costs,
⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 12: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/12.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery,
⇐ Lags can be added
3. deterministic demand,
⇐ Stochastic demand
4. constant demand,
⇐ Time-varying demand
5. known fixed setup costs,
⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 13: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/13.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand,
⇐ Stochastic demand
4. constant demand,
⇐ Time-varying demand
5. known fixed setup costs,
⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 14: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/14.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand, ⇐ Stochastic demand
4. constant demand,
⇐ Time-varying demand
5. known fixed setup costs,
⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 15: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/15.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand, ⇐ Stochastic demand
4. constant demand, ⇐ Time-varying demand
5. known fixed setup costs,
⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 16: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/16.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand, ⇐ Stochastic demand
4. constant demand, ⇐ Time-varying demand
5. known fixed setup costs, ⇐ Constraint approach
6. no shortages are allowed,
⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 17: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/17.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand, ⇐ Stochastic demand
4. constant demand, ⇐ Time-varying demand
5. known fixed setup costs, ⇐ Constraint approach
6. no shortages are allowed, ⇐ Shortages are allowed
7. single product.
⇐ Multiple products
![Page 18: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/18.jpg)
Modification of the basic model
1. Instantaneous production, ⇐ Finite production rate
2. immediate delivery, ⇐ Lags can be added
3. deterministic demand, ⇐ Stochastic demand
4. constant demand, ⇐ Time-varying demand
5. known fixed setup costs, ⇐ Constraint approach
6. no shortages are allowed, ⇐ Shortages are allowed
7. single product. ⇐ Multiple products
![Page 19: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/19.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 20: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/20.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 21: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/21.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 22: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/22.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 23: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/23.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 24: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/24.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 25: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/25.jpg)
What is SCperf?
An R package for inventory control.
â Inventory models
o Economic Lot Size Models with Constant Demands
Economic Order Quantity, EOQ()Economic Production Quantity, EPQ()
o Economic Lot Size Models with Varying Demands,
Wagner-Whitin algorithm, WW()
o Stochastics Inventory Models
Newsvendor model, Newsvendor()
â Safety Stocks, SS()
â Inventory and Supply Chain Management (SCM)
The bullwhip effect, bullwhip() and SCperf()
![Page 26: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/26.jpg)
EOQ() function
Implements the basic (and with planned shortages) EOQ model
Example:> EOQ(8000,12000,0.3)
Q25298.22
T3.16
TVC7589.47
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The Bullwhip Effect (BE)
Definition: The BE is the increase of the demand variability as onemoves up the supply chain.
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Quantifying the BEA common index used to measure the BE is:
M =Var(qt)
Var(dt)
� M = 1, there is no variance amplification.
� M > 1, the BE is present.
� M < 1, smoothing scenario.
Zhang 2004:
M = 1 +2∑L
i=0
∑Lj=i+1 ψiψj∑∞
j=0 ψ2j
![Page 29: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/29.jpg)
Quantifying the BEA common index used to measure the BE is:
M =Var(qt)
Var(dt)
� M = 1, there is no variance amplification.
� M > 1, the BE is present.
� M < 1, smoothing scenario.
Zhang 2004:
M = 1 +2∑L
i=0
∑Lj=i+1 ψiψj∑∞
j=0 ψ2j
![Page 30: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/30.jpg)
Quantifying the BEA common index used to measure the BE is:
M =Var(qt)
Var(dt)
� M = 1, there is no variance amplification.
� M > 1, the BE is present.
� M < 1, smoothing scenario.
Zhang 2004:
M = 1 +2∑L
i=0
∑Lj=i+1 ψiψj∑∞
j=0 ψ2j
![Page 31: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/31.jpg)
Quantifying the BEA common index used to measure the BE is:
M =Var(qt)
Var(dt)
� M = 1, there is no variance amplification.
� M > 1, the BE is present.
� M < 1, smoothing scenario.
Zhang 2004:
M = 1 +2∑L
i=0
∑Lj=i+1 ψiψj∑∞
j=0 ψ2j
![Page 32: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/32.jpg)
Quantifying the BEA common index used to measure the BE is:
M =Var(qt)
Var(dt)
� M = 1, there is no variance amplification.
� M > 1, the BE is present.
� M < 1, smoothing scenario.
Zhang 2004:
M = 1 +2∑L
i=0
∑Lj=i+1 ψiψj∑∞
j=0 ψ2j
![Page 33: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/33.jpg)
The modelInventory model
� Two stage supply chain
� Single item with no fixed cost
� OUT replenishment policy
� MMSE as forecast method
Define:
dt : demandL: lead timeyt = D̂L
t + z σ̂Ltz : Φ−1(α)SSLT = z σ̂Lt
qt : order quantityα: the desired SLD̂Lt =
∑Lτ=1 d̂t+τ
σ̂Lt =√
Var(DLt − D̂L
t )
SS = zσd√L
qt = yt − (yt−1 − dt) = (D̂Lt − D̂L
t−1) + z(σ̂Lt − σ̂Lt−1) + dt
![Page 34: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/34.jpg)
SCperf()
Computes the BE and other SC performance variables.
Usage: SCperf(ar, ma, L, SL)
Arguments:
� ar : a vector of AR parameters,
� ma: a vector of MA parameters,
� L: is the LT plus the review period which is equal to one,
� SL: service level, 0.95 by default.
Example:
> SCperf(0.95, 0.1, 2, 0.99)
bullwhip1.5029
VarD12.3077
VarLT5.2025
SS11.5419
SSLT5.3062
z2.3264
![Page 35: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/35.jpg)
Why did we develop SCperf?
� Educational purposes:to offer to useRs, teachers, researchers and managers a free,open-source, package for inventory control
� Managerial purposes:might be used as an alternative (or complement) to otherSCM commercial packages.
� The long-term goal of SCperf is to implement the lastresearch in inventory control theory as well as all thestate-of-the-art capabilities that are currently available incommercial packages.
![Page 36: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/36.jpg)
Why did we develop SCperf?
� Educational purposes:to offer to useRs, teachers, researchers and managers a free,open-source, package for inventory control
� Managerial purposes:might be used as an alternative (or complement) to otherSCM commercial packages.
� The long-term goal of SCperf is to implement the lastresearch in inventory control theory as well as all thestate-of-the-art capabilities that are currently available incommercial packages.
![Page 37: Marlene Marchena marchenamarlene@gmail€¦ · D: demand per time unit, h: holding cost per unit and time unit, c: unit cost for producing or purchasing each unit. A: ordering or](https://reader035.fdocuments.net/reader035/viewer/2022071410/6105244f8b4afd4beb77a214/html5/thumbnails/37.jpg)
Why did we develop SCperf?
� Educational purposes:to offer to useRs, teachers, researchers and managers a free,open-source, package for inventory control
� Managerial purposes:might be used as an alternative (or complement) to otherSCM commercial packages.
� The long-term goal of SCperf is to implement the lastresearch in inventory control theory as well as all thestate-of-the-art capabilities that are currently available incommercial packages.