Timing Successive Product Introductions with Demand Diffusion and Stochastic Technology Improvement

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Timing Successive Product Introductions with
Demand Diffusion and Stochastic Technology
Improvement??????????????????????

• R. Mark Krankel
• Department of Industrial and Operations
  Engineering, University of Michigan,
• Izak Duenyas, Roman Kapuscinski
• Ross School of Business, University of Michigan,
  Ann Arbor, Michigan
• Present by Li Wei

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CONTENTS

• Introduction
• Literature
• Model
• Optimal Policy
• Computational Study and Insights
• Extensions

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Introduction

• Consider an innovative firm that manages the
  development and production of a single, durable
  product.
• Over time, the firms research and development
  (RD) department generates a stochastic stream of
  new product technology, features, and
  enhancements for design into successive product
  generations.

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Introduction

• The firm captures the benefits of such advances
  by introducing a new product generation.
• Due to fixed product-introduction costs, it may
  be unreasonable to immediately release a new
  product generation after each technology
  discovery. Rather, the firm may prefer to delay
  an introduction until sufficient incremental new
  product technology has accumulated in RD.
• The objective of this paper is to characterize
  the firms optimal product-introduction policy

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Introduction

• The total number of product generations is not
  pre-specified rather, it is determined by the
  pace of technology improvement along with the
  firms dynamic decisions on when to introduce.
• Analysis is centered upon two key influences
  affecting the introduction timing decisions
• (1) demand diffusion dynamics, where future
  product demand is a function of past sales
• (2) technology improvement process, specifically
  the concept that delaying introduction to a later
  date may lead to the capture of further
  improvements in product technology.

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Introduction

• Previous literature examining incremental
  technology introduction has focused on either (1)
  or (2), but none have considered both factors
  simultaneously. As a result, the present analysis
  provides new insight into the structure of the
  optimal introduction timing policy for an
  innovative firm.
• Using a proposed decision model that incorporates
  both key influences, we prove the optimality of a
  threshold policy it is optimal for the firm to
  introduce the next product generation when the
  technology of the current generation is below a
  state-dependent threshold, in which the state is
  defined by the firms cumulative sales and the
  technology level in RD.

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Introduction

• Relative papers
• Wilson and Norton (1989) Mahajan and Muller
  (1996)
• These two papers proceed under a demand diffusion
  framework, but do not model the progression of
  product technology.
• Rather, they assume that the next generation
  product to be introduced is available at all
  times starting from Time 0. As a result, they
  respectively conclude the optimality of now or
  never (the new generation product is introduced
  immediately or never) and now or at maturity
  (the new generation product is introduced
  immediately or when the present generation
  product has reached sufficient sales) rules
  governing product introductions.

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Literature

• Two main research areas are directly relevant to
  the current work.
• The first centers on models of demand. Papers in
  this area describe the patterns of demand
  exhibited by single or multiple product
  generations, specifically in relation to new
  innovations. These papers concentrate on system
  dynamics and/or model fit with empirical data.
• The second research area examines decision models
  for technology adoption timing. A subset of this
  group includes papers that model the introduction
  of new products subject to demand diffusion.

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Literature models of demand

• Bass (1969) initiates the stream that examines
  demand diffusion models by formulating a model
  for a single (innovative) product. The Bass model
  specifies a potential adopter population of fixed
  size and identifies two types of consumers within
  that population innovators and imitators.
• Innovators act independently, whereas the rate of
  adoption due to imitators depends on the number
  of those who have already adopted.
• The resulting differential equation for sales
  rate as a function of time describes the
  empirically observed s-shaped pattern of
  cumulative sales exponential growth to a peak
  followed by exponential decay.

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Literature models of demand
Prof Dr. Frank M. Bass (1926-2006) was a leading
academic in the field of marketing research, and
is considered to be among the founders of
Marketing science. He became famous as the
creator of the Bass diffusion model that
describes the adoption of new products and
technologies by first-time buyers. He died on
December 1, 2006.

• Bass, F. M. 1969. A new product growth model for
  consumer durables. Management Sci. 15 215227.

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Literature models of demand

• Norton and Bass (1987) extend the original Bass
  model by incorporating substitution effects to
  describe the growth and decline of sales for
  successive generations of a frequently purchased
  product.
• Jun and Park (1999) examine multiple-generation
  demand diffusion characteristics by combining
  diffusion theory with elements of choice theory.
• Wilson and Norton (1989) propose a
  multiple-generation demand diffusion model based
  on information flow.
• Kumar and Swaminathan (2003) modify the Bass
  model for the case in which a firms capacity
  constraints may limit the firms ability to meet
  all demand.
• Using their revised demand diffusion model, they
  determine conditions under which a capacitated
  firms optimal production/ sales plan is a
  build-up policy, in which the firm builds up an
  initial inventory level before the start of
  product sales and all demand is met thereafter.

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Literaturetechnology adoption timing

• Gjerde et al. (2002) model a firms decisions on
  the level of innovation to incorporate into
  successive product generations. The paper does
  not consider the diffusion dynamics of the
  existing products in the market (product sales
  rates do not depend on cumulative sales).
• Cohen et al. (1996) assume that product can only
  be sold during a fixed window of time. Therefore,
  delaying the product introduction for further
  development will lead to a better product and
  higher revenues but over a shorter time. Cohen et
  al. further assume that the product currently in
  the market or the newly introduced product both
  have sales at a constant rate. Thus, they do not
  consider the diffusion dynamics. They also do not
  consider the stochastic nature of the RD
  Process.

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Literaturetechnology adoption timing

• Balcer and Lippman (1984) conclude that a firm
  will adopt the current best technology if its lag
  in process technology exceeds a certain
  threshold. The threshold is either nonincreasing
  or nondecreasing in time, dependent on
  expectations with respect to potential for
  technology discovery.
• Farzin et al. (1998) considers a similar problem
  under a dynamic programming framework. The paper
  explicitly addresses the option value of delaying
  adoption and compares results to those using
  traditional net present value methods, in which
  technology adoption takes place if the resulting
  discounted net cash flows are positive.
• In each of these works, the technology adoption
  decision does not explicitly consider the effects
  of adoption timing on product-demand dynamics.

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Literaturetechnology adoption timing

• Wilson and Norton (1989) consider the one-time
  introduction decision for a new product
  generation. In their model, product introduction
  has fixed positive effects on market potential
  along with negative effects due to
  cannibalization. They conclude that the optimal
  policy for the firm is given by a now or never
  rule. That is, it will either be optimal to
  introduce the improved product as soon as it is
  available or never at all.
• Mahajan and Muller (1996) conclude that it will
  be optimal to either introduce the improved
  product as soon as it is available or when enough
  sales have been accumulated for the previous
  product generation.(now or at maturity rule)
• Both Wilson and Norton (1989) and Mahajan and
  Muller (1996) implicitly assume that the next
  product generation is available and remains
  unchanged regardless of when it is introduced. In
  contrast, we assume that a firm that delays
  introduction of the next product generation
  expects to capture greater technological advances
  at a later date.

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Model

• Under a discrete-time, infinite-horizon scenario,
  consider a single base product that progresses
  through a series of product generations over
  time.
• The benefits of improved technology are realized
  only through introduction of a new product
  generation that incorporates the latest
  technology available in RD.
• An improvement in the incumbent product
  technology leads to a higher sales potential for
  the new product generation. However, each new
  generation requires a fixed introduction cost.
  The firm seeks an introduction policy that
  maximizes net profits.

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Model

• In each period, the firm has the option to either
  introduce the latest technology or continue
  selling at the current incumbent technology level
  (wait).
• We model the level of technology in RD using a
  single index, and assume that this level improves
  stochastically during each period.
• Our objective is to characterize the firms
  optimal introduction policy given this stochastic
  RD process.

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ModelNotation and Assumptions

• We begin with the following definitions under a
  dynamic-programming framework

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ModelNotation and Assumptions
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ModelNotation and Assumptions

• We consider a durable base product for which
  product technology is additive and introduction
  of a new product generation results in complete
  obsolescence of the previous generation i.e.,
  once a new generation is introduced, sales of the
  previous generation immediately drop to and
  remain at zero. This property is referred to
  later as the complete replacement condition.
• It is assumed that (1) available product
  technology improves in each period according to a
  stochastic process, and (2) sales for any given
  generation follow a demand diffusion process.

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ModelNotation and Assumptions

• Both the technology level and the price of a new
  product are expected to influence the products
  market potential and associated demand diffusion
  dynamics . To understand the effects of
  progressing technology independent of other
  compounding factors, we assume a very specific
  but realistic pricing strategy that maintains
  constant unit profit margins.

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ModelNotation and Assumptions

• As mentioned above, sales potential is assumed to
  be an increasing function of product technology
  level.
• Moreover, we do not model capacity constraints
  and assume that all demand can be met so that
  sales equals demand.

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Model Formulation
the following assumption is made on the sales
rate curves
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Model Formulation

• (i) ensures that, all else equal, product sales
  rate is nondecreasing in product technology.
• Part (ii) accommodates realistic durable-good
  market scenarios in which the potential market
  size is finite and current period sales do not
  exceed total remaining market potential.
• Condition (iii) limits the rate at which sales
  decrease and in a discrete-time framework
  guarantees that the sales rate from one period to
  the next does not decrease at a faster pace than
  sales accumulated within the period.

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Model Formulation
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Model Formulation

• The optimum introduction policy is computed from
  the optimality equation

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ModelRelationship to Demand Diffusion

• For the scenario considered in this paper, there
  is a natural link between this sales model and
  that of a typical (continuous-time) diffusion
  model. Consider the Bass diffusion model for a
  single innovative product

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ModelRelationship to Demand Diffusion
Mahajan and Muller (1996) present an extension of
the Bass model for the case of multiple product
generations.
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ModelRelationship to Demand Diffusion
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ModelRelationship to Demand Diffusion
where a and b are coefficients of innovation and
imitation, respectively. Because cumulative sales
is tracked as a state variable, the decision
model (1)(3) clearly captures the interaction
between product generations when sales curves are
of the demand diffusion form (6). Moreover, an
examination of (6) shows that the demand
diffusion form satisfies Assumption 1 subject to
a mild restriction on problem parameters.
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Optimal Policy
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Optimal Policy
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Optimal Policy

• The first result states that as the two systems
  progress over time, the cumulative sales level of
  the firm with lower initial cumulative sales will
  never surpass the firm with higher initial
  cumulative sales.

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Optimal Policy
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Optimal Policy

• The result states that all else equal, the
  discounted optimal profit-to-go for a firm with
  lower cumulative sales will not exceed that of a
  firm with higher cumulative sales by more than
  the net value of their cumulative sales
  difference. That is, future benefits cannot make
  up for the current sales deficit.

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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Optimal Policy
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Computational Study and Insights

• The numerical study focuses on the influences of
  a simple technology discovery rate, fixed
  product-introduction costs, and market parameters
  including the diffusion coefficients and a
  parameter describing the sensitivity of product
  market potential to changes in product technology.

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Computational Study and Insights

• for purposes of numerical investigation we begin
  with a simplified baseline scenario. Sales rate
  curves for the baseline scenario are generated
  within a discrete-time framework to approximate a
  demand diffusion process according to the form
  given in (6).
• Technology improvement is assumed to follow a
  simplified stochastic process in which available
  technology in RD increases by one in each period
  with probability p.

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Computational Study and Insights
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Computational Study and Insights
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Computational Study and Insights

• The baseline optimal policy is computed by
  solving the dynamic program (3). In solving (3)
  numerically, we use linear interpolation to
  handle cases in which the current period sales gs
  z is a noninteger multiple of the indexing unit
  used for cumulative sales.

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Computational Study and Insights
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Computational Study and Insights

• Numerical approximation generates the baseline
  set of technology switching curves illustrated in
  Figure 6.

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Computational Study and Insights

• The switching curves in Figure 6 suggest that
  optimal introduction of the next product
  generation may be triggered in one of two ways
• (1) through sufficient product sales at the
  current technology levels,
• (2) through significant advances in available
  product technology.
• (1) implies that, even without further gains in
  RD, a firm that continues to sell the current
  generation long enough may eventually find it
  optimal to introduce the technology on hand even
  though introducing at the same technology level
  was not profitable in the past.
• (2) implies that, regardless of the current
  generations position along its sales curve, it
  may be optimal to introduce a new generation with
  large enough gains in RD technology.

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Computational Study and Insights

• Consider the expected rate of technology
  discovery as measured (for the baseline scenario)
  by the technology discovery probability p.

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Computational Study and Insights

• It is natural that under fixed introduction
  costs, a firm with a higher technology discovery
  rate will introduce new product generations when
  the gain in technology over the previous
  generation is larger.
• Hence, for a given technology lag between the
  product generation in the market and that
  available in RD, an increase in the technology
  discovery probability should increase the
  attractiveness of the decision to wait versus
  introduce.

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Computational Study and Insights
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Computational Study and Insights

• It is evident that although the technology
  introduction thresholds are increasing in the
  discovery probability (as shown in Figure 7), the
  expected rate, both in terms of time and sales,
  at which the firm will introduce new generations
  is also increasing i.e., firms with a higher
  expected technology discovery rate are expected
  to introduce new product generations more
  frequently and with larger technology gains
  between generations.

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Computational Study and Insights

• Next, we examine the influence of the firms cost
  structure on the optimal policy. As illustrated
  in Figure 8, a decrease in the fixed introduction
  cost K decreases the optimal introduction
  threshold at any given cumulative sales level.

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Computational Study and Insights

• Let us turn to the parameters that describe the
  product market. The modeled product sales
  dynamics will be affected by the diffusion
  coefficients a and b in (6) as well as the market
  potential parameter m, that determines the
  product market potential for a specific
  technology level.

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Computational Study and Insights

• Market Potential Parameter
• An increase in m translates to larger gains in
  market potential per unit gain in technology. In
  turn, the sales rate at a given level of
  cumulative sales is more sensitive to increases
  in product technology when m is higher.

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Computational Study and Insights

• Demand Diffusion Coefficients
• A product with a higher coefficient of innovation
  a would exhibit a sales rate curve that starts
  with higher one-period sales, peaks earlier, and
  lies completely above that of a product with
  lower a. Figure 10 illustrates how the
  coefficient of innovation influences the product
  sales rate curves.

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Computational Study and Insights

• Demand Diffusion Coefficients
• We find that a product with higher coefficient of
  innovation is associated with more-frequent
  product introductions.

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Computational Study and Insights

• Demand Diffusion Coefficients
• Similar to the effect of a, a higher coefficient
  of imitation b translates to a sales rate curve
  that lies completely above that for lower b.

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Computational Study and Insights

• Demand Diffusion Coefficients
• As with a, the introduction thresholds are
  decreasing in the products coefficient of
  imitation b. Thus, a firm should introduce new
  product generations more frequently given a base
  technology that diffuses through its potential
  adopter population faster.

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Computational Study and Insights
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Computational Study and Insights

• Uncertain Demand
• Here, we describe two possible scenarios for
  uncertain demand along with the revised
  decision-model formulations.

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Computational Study and Insights
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Computational Study and Insights

• The decision model (1)(3) is reformulated as
  follows to accommodate this single-period demand
  uncertainty

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Computational Study and Insights
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Computational Study and Insights

• A firm may also wish to capture the uncertainty
  in overall market acceptance of a new product
  generation while taking into account potential
  correlation between the market success of two
  sequential generations. For the demand diffusion
  case, the estimation of a new generations market
  potential N(z) is a key source of such
  uncertainty.

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Computational Study and Insights

• The present model framework can capture the
  market success uncertainty for a new generation
  using a Markov modulated demand formulation. A
  possible implementation is presented here for
  illustration.

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Computational Study and Insights
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Computational Study and Insights

• The decision model (12)(13) implements this
  Markov modulated demand framework for
  accommodating uncertainty in product success.

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Extensions

• A limitation of our analysis is that the model
  does not consider the effects of introduction
  timing on consumers purchase strategies and
  resulting demand patterns. Significant increase
  in the firms pace of product introductions may
  cause consumers to postpone purchase decisions in
  anticipation of forthcoming product improvements
  (e.g., Dhebar 1994, Kornish 2001).

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Extensions

• The model does not however capture the
  time-to-market concerns that may arise in a
  competitive market setting. As described in
  Hendricks and Singhal (1997) the cost of delay
  (and hence value of earlier introduction) in such
  environments can be significant.
• One possible direction for future research is to
  consider a game theoretic model with multiple
  firms.
• An alternative approach may be to follow Cohen et
  al. (1996) and impose a fixed window of time for
  new product introduction. Such a constraint
  implicitly captures time-to-market concerns.

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Extensions

• Generalize the framework to incorporate upgrade
  purchases or to permit simultaneous sale of
  multiple product generations with substitution
  effects.
• Allow product price to fluctuate over time and
  differ between product generations.
• Incorporate a decision variable for the expected
  pace of product innovation (e.g., as measured by
  RD investment) would enable a more-complete
  analysis of firm policies.

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THANKS!