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).
Short Life-Cycle Products
(Screenshot of the home page from Dell Inc.: http://www.dell.com – last accessed June 29, 2004.)
Short Life-Cycles
CausesFast Changing Consumer PreferencesRapid Rate of Innovation
Procurement IssuesForecasting with no historical dataLong lead-timesPerishable Inventory
Introduction Time
Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
New Product Introduction
No past sales dataTime-series useless
But multiple-product environmentSome level of predictabilityIndependence (serve different needs)
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
The Bass ModelNoncumulativeadoption
External Influence
Internal
Influence
time
The Bass Model: Assumptions
Market potential remains consistent over timeIndependence of other innovationsProduct and Market characteristics do not influence diffusion patterns
Competition?
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…
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
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).
Parameters Estimation
Estimation of Nonlinear Least SquaresR-squared above .9
, , , tp q m α
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).
Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
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
Model Description
State: Cumulative ProcurementControl: Instantaneous ProcurementTransition function
Finite-Horizon OptimizationDiscounted cost at rate
tV
0 0t tV u V= =T
r
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−
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= ≥
Hamiltonian function
Define
Hamiltonian
* *( , )t V tJ t Vλ = ∇
( , , ) ( , )tH V u P V u uλ λ= +
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≥
=
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 =
+
Procurement PolicyCumulative units
Expected Cumulative Demand
Cumulative Inventory
Time
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+
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+
Procurement PolicyCumulative units
Expected Cumulative Demand
Cumulative Inventory
Phase-Out PeriodV^
t^ Time
Revised Multiple-Period Implementation
, ,p q mUpdate the estimation ofUnits
Expected Cumulative Demand
Cumulative Procurement
Model Update
Lead-timeTime
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−
Outline
Forecasting new product introductionProcurement issues
Model FormulationOptimal Control SolutionDiscussion
Case Study
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
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
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).
Service Levels
Lifetime service level95% vs. 99%?
Terminal service level: 33%
Hence, Case II, i.e.Purchase periodPhase-out period
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).
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).
Additional Insights
Launching the product early requires less inventoriesWith decreasing costs,
Reduced service levels (but increasing over time); hence, less inventoryDelayed procurement cutoff time
Conclusions
Application-driven researchAdapt Bass’ ModelOptimal Control
Additional issues:Effectiveness of Bass’ Model?Backorder costs vs. Service Level?Terminal shortage penalty vs. Stopping time?
Thank you
Questions?