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?