Forecasting and Inventory Management of Short Life-Cycle ... · PDF fileForecasting and...
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Forecasting and Inventory Management of Short Life-Cycle Products
A. Kurawarwala and H. MatusoPresented by Guillaume RoelsOperations Research Center
This summary presentation is based on: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Short Life-Cycle Products
(Screenshot of the home page from Dell Inc.: http://www.dell.com – last accessed June 29, 2004.)
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Short Life-Cycles
CausesFast Changing Consumer PreferencesRapid Rate of Innovation
Procurement IssuesForecasting with no historical dataLong lead-timesPerishable Inventory
Introduction Time
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Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
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New Product Introduction
No past sales dataTime-series useless
But multiple-product environmentSome level of predictabilityIndependence (serve different needs)
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Diffusion Theory
“[Innovation] is communicated through certain channels over time among members of a social system”
- Rogers, Everett. Diffusion of Innovations. Simon & Schuster, 1982.
ISBN: 0-02-926650-5.
Marketing application:Mass MediaWord of Mouth
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The Bass ModelNoncumulativeadoption
External Influence
Internal
Influence
time
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The Bass Model: Assumptions
Market potential remains consistent over timeIndependence of other innovationsProduct and Market characteristics do not influence diffusion patterns
Competition?
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The Bass Model: Sales Evolution
( )t tt t
dN Np q m Ndt m
α⎛ ⎞= + −⎜ ⎟⎝ ⎠
Current Sales Remaining market potential
Mass Media Word-of-Mouth Seasonality Coeff.
Many applications at Eastman Kodak, IBM, Sears, AT&T…
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Case-Study: PC Manufacturer
Monopolist (strongly differentiated)Life-cycle: 1-2 yearsPeak sales timing is predictable
Christmas peakTypical seasonal variation in demand
End-of-quarter effectInformation on total life-cycle sales
*T
tα
m
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Numerical Example (M2)Sales Evolution of High-End Computers (M2)
0100200300400500600700800
Apr. Jun
Aug Oct DecFeb Apr Ju
nAug Oct
Time
Sal
es (u
nits
)
- Data source: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Parameters Estimation
Estimation of Nonlinear Least SquaresR-squared above .9
, , , tp q m α
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Numerical Example (M2)Bass Model (M2)
0100200300400500600700800
Apr
.
Jun
Aug Oct
Dec
Feb
Apr
Jun
Aug Oct
M2 sales
Bass Model
- Data source: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
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Procurement Issues
Need to place orders in advanceLong lead-timesCost advantage, timely delivery
Inventory/Backorder costsSchedule the procurement to meet the (random) demand, evolving according to Bass’ Model
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Model Description
State: Cumulative ProcurementControl: Instantaneous ProcurementTransition function
Finite-Horizon OptimizationDiscounted cost at rate
tV
0 0t tV u V= =T
r
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Cost Parameters
Instantaneous trade-off betweenInventory holding costsBackorder costs
Terminal trade-off betweenSalvage inventory lossShortage costs
( )t th V N +−( )t tp N V +−
( )t t tP V N−
( )T Tl V N +−( )T Ts N V +−
( )T T TQ N V−
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Optimal Control Model
Timely delivery of customer orders?What if we do not want to serve all the demand?Why no chance constraints instead?
0
min ( ) ( ) ( ) ( )t T
Trt rT
t t t t t T T T T TuN N
J e P V N N dN dt e Q V N N dNψ ψ− −= − + −∫ ∫ ∫
such that: and 0t t tV u u= ≥
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Hamiltonian function
Define
Hamiltonian
* *( , )t V tJ t Vλ = ∇
( , , ) ( , )tH V u P V u uλ λ= +
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Pontryagin Minimum Principle1. Adjoint Equation
2. Boundary Condition
3. Optimality of Control
* *( , , )t t tt
t
H V uV
λλ ∂= −
∂
( ) ( )T
T T T T T T TT N
d Q N V N dNdV
λ ψ⎡ ⎤
= −⎢ ⎥⎢ ⎥⎣ ⎦∫
* *
0arg min ( , , )t t tu
u H V u λ≥
=
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b sb h s l
≤+ +Case I:
Maintain the same service level
Impulse at the end of horizon
( )t tbV
b hΨ =
+
( )T TsV
s lΨ =
+
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Procurement PolicyCumulative units
Expected Cumulative Demand
Cumulative Inventory
Time
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b sb h s l
>+ +Case II:
For , keep the same service level
For ,Do not purchase anymoreDecrease gradually the service level down to
0 t t≤ ≤ ^
t t T≤ ≤^
( )t tbV
b hΨ =
+
ss l+
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Desired/Effective Service Level
In practice, backorder costs are hard to evaluate…Instead, evaluate the desired SL
Terminal service level: switch the customers to an upgraded model
Loss of goodwillHigher cost
Case II is typical in practiceTerminal SL < Lifetime SL
bb h+
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Procurement PolicyCumulative units
Expected Cumulative Demand
Cumulative Inventory
Phase-Out PeriodV^
t^ Time
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Revised Multiple-Period Implementation
, ,p q mUpdate the estimation ofUnits
Expected Cumulative Demand
Cumulative Procurement
Model Update
Lead-timeTime
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Time-varying costs
Time-varying costsDecreasing purchase costs30% in less than 6 months
Underage CostsBackorder penaltySave the cost decreaseSave from the cost of capital
Decreasing over timeHence, increasing service level
btc
trc−
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Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
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PC Manufacturer: New Product Introduction
1. When should it be launched?May or August?
2. How much and when should we order?Sensitivity Analysis on the Lifetime Service Level
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Parameters Estimation
Randomness summarized inEstimation of the size of the marketEstimation of the peak time
Relation between and Past Product Introductions (M1-M4)
Estimation of the distribution ofSensitivity Analysis on variance
, ,m p qm
*Tp q
q
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Demand Estimation (May)
0
100
200
300
400
500
600
700
May July
Septem
ber
Novem
ber
Janu
ary
March
Demand
- Data source: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Service Levels
Lifetime service level95% vs. 99%?
Terminal service level: 33%
Hence, Case II, i.e.Purchase periodPhase-out period
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Procurement Decisions (May)
Longer Phase-Out with low SLReduce Procurement after peak season
0100200300400500600700800900
1000
May July
Septem
ber
Novem
ber
Janu
ary
March
Demand
95%-Procurement
99%-Procurement
- Data source: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Safety Stock Evolution
Deplete SS in the last quarterAvg SS=5 or 8 weeks of demand
0
200
400
600
800
1000
1200
May July
Septem
ber
Novem
ber
Janu
ary
March
Demand
95%-SafetyStock
99%-SafetyStock
- Data source: Kurawarwala, A., and H. Matsuo. "Forecasting and Inventory Management of Short Life-Cycle Products." Operations Research 44, no.1 (1996).
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Additional Insights
Launching the product early requires less inventoriesWith decreasing costs,
Reduced service levels (but increasing over time); hence, less inventoryDelayed procurement cutoff time
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Conclusions
Application-driven researchAdapt Bass’ ModelOptimal Control
Additional issues:Effectiveness of Bass’ Model?Backorder costs vs. Service Level?Terminal shortage penalty vs. Stopping time?
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Thank you
Questions?