Critical decisions in new product introduction and development--a mathematical modeling approach.

ABSTRACT

Choosing products to launch from a set of platform based variants and determining their prices and launch sequences are some of the critical decisions involved in any new product development (NPD) process. In this paper we present mathematical models which facilitate such decision making. The products considered are commercial vehicles, and representative data from a commercial vehicle manufacturer in India have been used for analysis. Our model which determines launch sequence as well as price of the products provides useful insights on the impact of economic conditions like boom or recession on prices, and also cannibalization.

1 INTRODUCTION

In a competitive market firms have to cater to the needs of the customers by offering a variety of products, and at the same time keep the development and manufacturing costs low. Many of the successful firms, particularly in automobile and consumer durable industries, owe their success to developing an effective platform from which they are able to launch a series of derivative products. But the firms need to judiciously balance the conflicting marketing requirements of variety on one hand and complexity of operations and development, and hence, escalating costs on the other. The common trend in automobile industry is to organize design groups on the basis of product platforms. In many of the firms, including the one under study, Vehicle India Ltd. (name disguised for confidentiality), a separate group consisting of personnel drawn from marketing, design, engineering and process planning is responsible for the critical decisions in any development program. We consider the intertwined decisions involved in NPD projects starting from choosing a set of platform-based variants to determining their launch sequence and prices. These decisions are taken after the features of product concepts have been finalized based on market responses and tools like Quality Function Deployment (QFD).

We consider the platform extension problem from the point of view of decision makers evaluating NPD projects, and add to the literature by considering not only development costs but also plant configuration change costs, productionising and technology acquisition costs, complexity costs of maintaining the variants, and labor and material costs in a mixed integer linear programming (MILP) model. The model, instead of evaluating each product development program individually, helps in allocating manpower for each department and choosing the products together subject to the resource and project duration constraints. For the platform extension problem, our endeavor is to determine the platform extensions to be launched for each platform, given that the base models will always be launched. The objective of this simple model is to provide the managers with insights on the binding constraints for each variant and the threshold level of cannibalization that can be allowed. Evaluating new products individually on the basis of net present value as done by Vehicle India Ltd., does not take into account the sharing of resources by the products, and run under the risk of providing a suboptimal solution. The comprehensive MILP model of ours, which is solved using GAMS 21.0, helps in choosing the optimal set of products, considering the relevant costs and satisfying the constraints. Given the available manpower in design and technical support departments, the firm has to satisfy the manhour requirements for design, prototyping, testing and production ramp-up to launch the products on time. Our model helps managers take decisions about the manpower requirements for different departments.

Appropriately pricing the platform based variants and determining their launch sequences are another set of critical decisions faced by the firm. Sometimes the launch dates of new products may be externally enforced as in the case of launch of vehicles satisfying latest emission norms. But the firm can exercise the options of staggering the launch of various products and price them appropriately according to the boom and recessionary conditions in the industry at the time of launch. Several researchers from operations, marketing and economics have studied the problem of determining price and launch sequence. Seminal work [9] helped in choosing between simultaneous and sequential product launches depending on the varying levels of cannibalization. In [7] they made a significant contribution to this class of problem by developing launching sequences for platform-based products. The impact of concurrent technological development on launch sequences for high technology products was studied in [1]. But the impact of economic conditions on launching sequences and prices does not seem to have been considered in the literature before. The motivation of the study stems from the following questions

* Whether there will always be cannibalization if a base model is launched ahead of the platform extension model?

* Can cannibalization of the base model by its extension(s) be allowed? If yes, under what condition this so-called "reverse cannibalization" be allowed?

* What will be the role of "word-of-mouth" effects on the reverse cannibalization?

* Will the prices of the products depend on the economic conditions boom followed by recession or vice-versa) or only on the order of launch?

* What will be the optimum launch sequence for each base and extension model pair?

* What will be the price and optimal launch sequences in a duopolistic market with firms having substitute products?

We develop separate models for boom followed by recession and vice-versa given the sequence of launching the base model or variant first. The boom and recessionary conditions have been captured by varying volumes and the different utilities, which the customers attach to the same product under different economic conditions. The proposed model helps us in understanding the effect of economic conditions on prices and also on the extent of cannibalization that can take place. It provides conditions under which a variant can cannibalize volumes from the base model (reverse cannibalization). We have also been able to analyze the role of "word-of-mouth" effects on the extent of cannibalization.

Preliminary results show that the pricing and launch strategies can vary depending on the industry's cycles of boom and recession, and whether they fall on the first or second period of launch. A 'fit for all' pricing and launching sequence can cost the company dearly. It is also found that under certain conditions it will be optimal to launch the base model ahead of the platform extension or variant, which has been widely negated in literature citing the negative impacts of cannibalization. We have also shown that at times, particularly when the launch date matches with the boom period in industry, it will be beneficial to set a price such that the customers of the upgraded variant stick to their product and at the same time, some potential customers of the base model also shift to the variant. The firms can control the costs of providing quality to enable customers of the base model shift to the extension model. Such "reverse cannibalization" becomes easier under the "word-of-mouth" effects from the already established customer base.

The rest of the paper is organized as follows. A review of the relevant literature is presented in the next section which is followed by the description of the problems on platform extension, and pricing and launch sequence determination. Then we study these problems one after the other and analyze the results. Conclusions drawn from the study and their managerial implications are given at the end.

2 REVIEW OF RELEVANT LITERATURE

The typical decisions during a new product introduction stage that we consider here are:

* Product line and platform extension

* Product pricing and launch sequences

2.1 Choice of Product Line and Platform Extension

The four broad classifications of decisions in product development are: concept development, supply chain design, engineering design and production ramp up and launch. Within these, product line design addresses the problem of choosing appropriate levels of differentiating attributes of the product either to maximize profits or maximize the utility to the customers. This class of literature has developed from attribute based conjoint analysis approaches to mathematical modeling considering fixed costs and the use of search techniques like beam search. Our problem domain starts after the product concepts in terms of the different attribute levels have been finalized. Hence we do not cover that literature in details and mention only the relevant papers. In [3] and [4] they have considered the problem of selecting the products to offer from a set of potential products and determining their prices to maximize profit. They also consider fixed and variable costs for the products. In [11] a complex problem is addressed in which a set of products, their prices and processes by which the products are manufactured are chosen. Here, processes are chosen for each attribute level while in real life choice of process may depend on the interaction of multiple attribute levels and may not be traced to a particular attribute level. In [5] they consider a more general problem which accounts for shared and product specific resources. They also consider that products can share resources in an arbitrary way and not just because of common attribute levels. They maximize the difference between the total gross margin and the cost of acquiring the required resources. But in our problem we consider the incremental decision of adding a variant to each platform with the base model being always launched. We consider sharing of resources in design, prototyping and testing and include incremental plant configuration costs and productionizing costs apart from material and conversion costs, and also consider possible cannibalized volume. We address the pricing and sequence launch determination problems separately as our objective is to study the impact of economic conditions and relative launch sequence of the products on prices. A detailed and highly useful review of profit maximizing product line literature can be found in [13].

Evaluations of multiple product line extensions are done in [12]. Introducing new products with shared components has been one of the responses of manufacturers to cater to the diverse customer requirements and exploit manufacturing economies of scale. But this practice of creating line extensions with shared components has two implications: cost interaction among products due to shared costs and revenue interaction between similar products because of cannibalization. The authors have developed a mixed integer linear programming model, which considers both these cost and revenue impacts to identify the subset of line extensions that maximizes profits. They have assumed that a line extension is likely to draw sales only from a limited number of close substitutes either from the firm itself or competitors. These sets of close substitutes are referred to as baseline set [12]. Development costs for the new products and new components are calculated by considering the complexity and newness level of the product/component. The authors have suggested the use of uniqueness and complexity indices in calculating development costs. Separate marketing, operations and cross-functional heuristics were developed and compared. But costs like productionizing costs (which include support costs e.g., for setting up of processes at vendor's end, quality checks, taking pre-launch trials etc.), plant configuration change costs, technology acquisition costs have not been considered. Constraints on design and support manpower as well as timely completion of project are not considered in such platform extension problems although they are critical for product development projects. This particular aspect of the problem is taken care of in the present model.

2.2 Pricing and Launch Sequence determination

The impact of market segmentation, cannibalization on timing of product introduction was studied in [8]. The authors considered durable products, which can be differentiated on some attributes, acknowledged by customers and customer segments which differ in size and in their degree of preference for the differentiated attributes. They defined a cannibalization parameter R= [[n.sub.h]/[n.sub.l]).sup.*](([v.sub.h] - [v.sub.l])/[v.sub.l]), where n and v, respectively, denote the market size and the value for high and low end models. They opined that for sequential introduction, introducing a low end model first aggravates cannibalization as it also becomes attractive for the high end segment. The work in [8] was able to analytically justify the timing of product launches for products catering to two different segments, and also provided a direction to research in this area.

Analysis of decisions on sequential product introduction for high technology products under conditions of network externality is shown in [10]. The impact of exogenous technological improvements on sequence of launches was studied in [1] and it was shown that for a range of circumstances it will be optimal to launch products in an increasing order of performance. For the introduction strategy of new products, a diffusion model considering both positive and negative 'word of mouth' effects was proposed in [8]. Their contribution lies in analyzing the impact of word of mouth effects on optimal advertising policies. Though we do not consider optimal advertising policies, but their approach has given us useful insights on how to incorporate "word-of-mouth" effects and network externality in our pricing and launch sequence determination problem.

3 PROBLEM DESCRIPTION AND ANALYSES 3.1 Platform Extension Problem

Currently, Vehicle India Ltd. has base models for all the given platforms. New emission norms have to be reinforced. Enforcement year/quarter is known and strict. The company has in its stables an engine, capable of meeting emission norms, which will give rise to a new set of base models. Apart from these base models with new engine, each platform can be renewed with substantial changes in sub-systems like engine (a more powerful one), gearbox and axles etc. These decisions have been taken based on inputs from marketing in terms of customer preferences for attribute levels and tools like QFD to convert customer requirements into engineering design but profitability, development costs and manufacturing costs have not been considered. But the company feels all costs need to be considered and all projects evaluated together before it finalizes the launch decisions. It will anyway develop the new base models with in-house technology. But some of the platform extensions will involve acquiring advanced technology and will also lead to major changes in some other sub-systems apart from those required for the new base models.

Now the company faces a decision such as which of the platform extension models need to be introduced? There are resource constraints in design and technical support departments as well as on the total time available to these departments so that the overall project is not delayed. We also need to take into account the cannibalization effect between these models. Baseline set is given--usually within the platform only.

Our objective function is similar to that in [12] i.e. maximizing (incremental revenue--development costsmaterial costs--labor costs). Productionising costs incurred by support departments like planning, vendor development, quality assurance and tool engineering are also considered. We have also added incremental fixed costs of plant configuration change for the particular model, field trial and certification costs and complexity costs of maintaining the variant which are captured by cost of maintaining product data bases, cost of carrying inventory of unique parts and cost of carrying finished products in supply float. The plant configuration change cost will be calculated for a plant, which is best capable of producing the model on the basis of managerial judgment because here our objective is to find out whether the model should be produced or not. Specific product to plant allocation issues will be considered later.

Apart from determining which products to launch and the manpower to be allocated for design and development of the products, we are also interested in finding out the impact of cannibalization and the possible threshold levels of cannibalization. So we have experimented with three cases: one, in which no cannibalization is allowed; two, where cannibalization is by base model only; and three, where cannibalization is by extension model only. We then tried to analyze the results.

We have considered ten platforms of commercial vehicles with one base model and one platform extension per platform. The platforms include 15 tonne bus, 16 tonne truck, multi axles, tractor trailers, CNG buses, rear engine buses, intra city light commercial vehicles with tonnages of 4 tonnes, tippers, used for construction work etc. Our model can be modified to include multiple extensions per platform with the addition of another variable "platform introduction indicator", which will be associated with costs to be shared by all the models for the platform. The platform extensions are: 15ttc, 16ttc, maxleex, ttrailerex, 4tttyre, 7t44, cngbusex, 25ttipptc, 40ttruckac, and rebusatr. The base models consist of 15tbus, 16ttruck, maxle, ttrailer, 4ttruck, 7ttruck, cngbus, 25ttipper, 40ttruck, and rebus. (All profits are in thousands of Indian Rupee (Rs.)).

Observations

Impact of the constraint on reduced revenue due to cannibalization

* By tightening the constraint on cannibalization such that reduced revenue due to cannibalization is made to be less than 1% of revenue of j model due to expansion and cannibalization, 7tttyre is not allowed to cannibalize and profit reduced to Rs.79588138. Extending the limiting percentage to 2%, increases profit to Rs.83554138.72 as 15tbus, 16ttruck, maxle also start cannibalizing from their respective variants. Profits further increase to Rs.86162507.7860 with constraint at 10%, allowing cannibalization for 25tipper and rebus and reducing corresponding volume from k models for 25tipptc and rebusatr.

Impacts of cannibalization

* Without any kind of cannibalization profit reduces drastically to Rs.15716475.38 but the same products get launched. Thus allowing cannibalization or not does not change the product line though it adversely affects profits. Launching of products is governed more by the duration and manpower constraints.

* Allowing only 'j' model to cannibalize with the cannibalized volumes same as the base case scenario increased profit to Rs.20289201.77. Thus even allowing the base model to cannibalize is better than no cannibalization. This happens as the savings in costs due to the costlier model not getting produced dominates the loss in revenue due to cannibalization.

Threshold levels of cannibalization and insights

* With all base models cannibalizing 70% or more of the volumes from the variants profits drastically reduce to Rs.9064294.98. So only limited cannibalization is useful. An interesting finding can be to find out that threshold level of cannibalization.

* We observe from the results that with no cannibalization by the variants but the base models cannibalizing to the extent of 60% of the expansion volume of the variants, profits increase but at 70% of such cannibalization, profits reduce. Thus the threshold level of cannibalization by base model occurs between 60 and 70%. But in reality all products will not be cannibalized by the same percentage. Still the learning from this exercise is that moderate level of cannibalization is actually beneficial and increases profits and only beyond a certain level does it start diminishing profits rapidly.

* We find from the results that with no cannibalization by the base models but only by the variants profits increase continuously from the no cannibalization case as cannibalization percentage by variants increase from 60 to 70 and then 80.

* With 100% cannibalization of the base model by the variant profit becomes even higher at Rs.544308862.758. But interestingly it is lesser than only 60% cannibalization of the variants by base models (profit = Rs.66110503.24) and also lesser than the base case when both the base and variants are cannibalizing from each other (profit = Rs.80748138.71)

* Thus even allowing the variants to cannibalize all of the base models may not be beneficial.

* Allowing 100 % cannibalization by variant and 60% by base model produces profit of Rs.563190334.68. This again shows 100% cannibalization of variant will also not give the best results.

Impact of manpower availability

* Reducing manpower by 10% in each of design, testing and workshop leads to reduction of profit to Rs.78447929.37, as cngbusex could not be launched. Reducing the duration also by 10% has exactly the same effect.

3.2 Pricing and launch sequence determination problem

The platform extensions which need to be launched (as indicated in the output of the previous model both with and without cannibalization benefits) is reviewed along with the base models to determine whether they will be launched simultaneously or sequentially and their order of launch if they are to be launched sequentially. We take these decisions by formulating separate models for boom time and recession time in the economy. Different economic conditions at the time of launch needs to be considered, as predetermined launch dates due to emission norms or some other regulations, like withdrawal of diesel buses, can be either in the boom time or recession time in commercial vehicle industry. The firm will have to determine the sequence of launches of its base and platform extension models and set prices suitably. The result of these models gives us insights into the influence of "network externalities" which can be different during boom time and recession time. During recession time sales will be sluggish while in boom time a positive feedback about some vehicles by fleet operators can very well influence purchase decisions of others and thus network externality will be comparatively higher.

We have separate models for simultaneous and sequential introduction both for boom and recession times and we compare the likely profits to be accrued under such conditions. The models although draw from those in [9] but are different due to the incorporation of different prices depending on the state of the economy and also the "word-of-mouth" effects. Later, we make the problem more realistic by considering multiple attributes for each product. For illustration we take up the case when the launch time is a boom period for the industry and determine which of the base ('j') and platform extension ('k') type of products can be launched in the first period. Similar analysis is done for recession, and recession followed by boom conditions.

Allowing base models to be launched ahead of platform extensions have not been considered earlier in literature except under the influence of availability of technology. It is argued that such a launch sequence will lead to cannibalization of the 'k' type of products and will also result in delayed revenues for the firm. But justification of such a launch sequence will depend on whether the launch period is a boom time or a recession time for the industry and how the customers value them, apart from the availability of technology which was studied by [1]. Launching the economy base product ahead of the extension product can very well be justified if the launch time is a recessionary phase for the industry. In [10] they mention about offering different qualities to customers for firms with low and higher network externalities but the context of their problem is different from ours.

Model description for Sequential Introduction

As an illustration we consider the situation wherein the first period matches with a boom time in the industry and in the second period recessionary conditions prevail. Our objective will be to find out the conditions for the launch of 'k' model ahead of 'j' and vice-versa as well as the conditions for their cannibalization. Thus one of the products will be offered to the market in both the periods while the other one will be available in the second period only. This is a departure from the approach in [9], in which 'k' products are available in the first period and 'j' products in the second period. We do not explicitly consider platform related costs in these launch sequence models, as done in [7] because they are considered in choosing the product line. Our objective will be to maximize the difference between the price and the marginal cost of providing quality to the customers and choose the set of products, which on being launched in the first period achieves this objective.

y = {1 if j is launched in the 1st (boom) period and is joined by k in the 2nd (recession) period

{0 if k is launched in the 1st (boom) period and is joined by j in the 2nd (recession) period

The variable 'y' is defined here to incorporate both the launching of 'k' first and 'j' first in the same model. But we carry out the analysis keeping 'y' fixed.

[P.sub.kb]--Price of 'k' in boom

[P.sub.kr]--Price of 'k' in recession

[P.sub.jb]--price of 'j' in boom

[P.sub.jr]--price of 'j' in recession

[c.sub.k]--cost of providing per unit of quality [q.sub.k]

[c.sub.j]--cost of providing per unit of quality [q.sub.j]

[v.sub.k]--value which a customer of 'k' attaches to per unit quality

[v.sub.j]--value which a customer of 'j' attaches to per unit quality

[n.sub.kb]--volume of 'k' in boom

[n.sub.jb]--volume of 'j' in boom

[n.sub.kr]--volume of 'k' in recession

[n.sub.jr]--volume of 'j' in recession

a--fraction of volume of 'j' cannibalized by 'k'

b--fraction of volume of 'k' cannibalized by 'j'

[BR.sub.k]--buyer's risk corresponding to late introduction of model 'k'.

[BR.sub.j]--buyer's risk corresponding to late introduction of model 'j'.

[SR.sub.k]--seller's risk from introducing model 'k' late

[SR.sub.j]--seller's risk from introducing model 'j' late

(The formulation of the model is given in the Appendix).

Assumptions:

When we choose the launch sequence of the base and the platform extension models, we assume that both the products are ready to be launched and design, testing and pre-launch activities would be completed before the launch date, which can be the date for enforcement of emission norms. Quality, q, is defined as the ratio of power and fuel economy, when we want to capture the utility of a product like commercial vehicles through a single attribute. Later, we consider a more realistic scenario with multiple attributes. For same power, if fuel economy is higher, 'q' will be less (characteristics of 'j' models) but its value to customers can be higher. Here it is used to distinguish the base model and the extension model. It may so happen that both the base as well as the extension models has the same numerical value of 'q' (120 hp and 6 Km/litre fuel economy and 100 hp and 5Km/litre fuel economy), but the value the customers attach to them per unit quality are different, and thus it may help in distinguishing the product to the customers. Thus [v.sub.k] can be less than, equal to or greater than [v.sub.j]. It is assumed that value and quality are linearly related to make the analysis simpler. This is widely followed in literature e.g., in [9],[7],[1]. Also, it would have been realistic to distinguish between [v.sub.kk] (how a potential customer of 'k' values 'k') and [v.sub.kj] (how a potential customer of 'k' values 'j') instead of the same [v.sub.k] in both cases. So later we define the values accordingly. Finally, when we take up the multi-attribute case we need not have to worry about the linear relationship between 'v' and 'q'. Also, we distinguish between [c.sub.k] and [c.sub.j] as the costs for providing per unit quality for the base and the extension models will be different (unlike in Moorthy and Png, who assume the same cost of providing per unit quality for both kinds of products). These differences arise as quality is represented in our problem by two attributes (i e. power and fuel economy) or later as a bundle of attributes and not by a single attribute. Prices are calculated as marginal prices, required to satisfy the constraints, as follows.

Thus [P.sub.jr] = [v.sub.j][q.sub.j]. Putting this value in constraint (ii), we get [P.sub.kb] = [v.sub.k]* [q.sub.k] - [(BR).sub.j] *([v.sub.k]-[v.sub.j])*[q.sub.j].

[P.sub.kr], when 'k' is launched in the 2nd period (recession) is found out from constraint (vi)

[P.sub.kr] = [v.sub.k]*[q.sub.k] - ([v.sub.k]-[v.sub.j])*[q.sub.j]/[(BR).sub.k]

[P.sub.kr], when 'k' is launched in the 1st period (boom) is found out from constraint (v)

[P.sub.kr] = [v.sub.k]*[q.sub.k]-([v.sub.k]-[v.sub.j])*[q.sub.j]

[P.sub.jb] is obtained from constraint (i) by using value of [P.sub.kr], when 'k' is launched in 2nd period.

Thus [P.sub.jb] = [v.sub.j]*[q.sub.j]+([v.sub.j]-[v.sub.k])*([q.sub.j]-B[R.sub.k]*[q.sub.k])

From the cannibalization conditions we see that the variant can cannibalize from the base model if [q.sub.k]=[q.sub.j] and [v.sub.k] = [v.sub.j]. So for this kind of "reverse cannibalization" to occur, [q.sub.k*]=[q.sub.j*]. This gives [v.sub.k]/([2.sup.*][c.sub.k]) = [v.sub.j]/([2*[c.sub.j])*(1+R') in which [v.sub.k]=[v.sub.j] where R'= [l+{[n.sub.kr] = (([v.sub.k]/[v.sub.j])- l)*([n.sub.kb] + a*[n.sub.jb])*[(BR).sub.j]}/([n.sub.jb]*(1-a)*S[R.sub.j] + [n.sub.jr]}].

Thus we get [c.sub.j]/[c.sub.k] = 1+ [n.sub.kr]/{[n.sub.jb]*(1-a)*S[R.sub.j] + njr}. As 'a' which is the fraction of 'j's volume cannibalized by 'k' increases, the firm has to reduce the cost of providing [q.sub.k] i.e. [c.sub.k] with respect to the cost of providing [q.sub.j]. This is intuitive as to get more customers of base model to buy the extension model, the firm needs to reduce the cost of the extension model. But for the base model to cannibalize from the variant we find that if [v.sub.j] = [v.sub.k], the condition reduces to [q.sub.j] [less than or equal to] [q.sub.k], which is always true as per the assumption. Thus in that case cannibalization will always occur. But if [q.sub.k]=[q.sub.j]/B[R.sub.k] and [v.sub.j] > [v.sub.k], the cannibalization condition reduces to [v.sub.j] [less than or equal to] [v.sub.k]/B[R.sub.k] which may not be always true. So a common belief that a base model will always cannibalize from its variant will be true only when some specific conditions are satisfied (and not always).

The additional parameters when "word-of-mouth" effects are incorporated are as follows.

Let [k.sub.1]and [k.sub.5] be the contact rates of positive word of mouth from the already installed customer base for 'k' cannibalizing from 'j', and vice-versa, respectively. Also, [k.sub.2] and [k.sub.6] are fractions of the already installed base who actually will spread positive word of mouth for 'k' cannibalizing from 'j', and vice-versa, respectively. 'a' in our original formulation may be interpreted as [k.sub.1]*[k.sub.2], [k.sub.3] is the fraction of the potential volume of the cannibalized model about which the customers are 'aware' but have not yet bought them. (1-[k.sub.3]) is the fraction of the potential volume of the cannibalized model about which the customers are 'unaware'. [k.sub.4] is the advertising reach. The additional term ([k.sub.1]*[k.sub.2]*[n.sub.kb]) in the launching and cannibalization conditions can be interpreted as the increase in utility to customers because of a positive "word-of-mouth". Similar analysis done for recession followed by boom condition shows that the prices depend on the period of launch and not on the economic conditions provided the values ([v.sub.k] and [v.sub.j]) that the customers attach to quality do not change with boom or recession. On the other hand, prices will also change with boom and recession if the values of [v.sub.k] and [v.sub.j] change with the economic conditions.

Now we extend the problem to include multi-attribute products. Commercial vehicles are complex products and buying decision of fleet operators are very involved and depend on various product attributes. Typical attributes for commercial vehicles chosen by M/s Vehicle India Ltd. are fuel economy, power-to-weight ratio, payload, maximum cruising speed, gradability and price.

Let 'i' be the index for attributes and 'n' the number of attributes. Let price be the nth attribute. Product 'k' is distinguished by attributes with level 'p' and product 'j' with the same attributes but with levels p'

We define the parameters differently as shown below

[v.sub.kip]--the utility a potential customer of 'k' attaches to attribute i of level p [v.sub.kip']--the utility a potential customer of 'k' attaches to attribute i of level p' [v.sub.jip]--the utility a potential customer of 'j' attaches to attribute i of level p [v.sub.jip]--the utility a potential customer of 'j' attaches to attribute i of level p' [q.sub.ip]--attribute i of level p

For value additional subscript of 'b' (boom) or 'r' (recession) will be added

Prices for multiple attributes will be as follows:

(i) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

The above expression for price shows that as the utility customers attach to the attributes 'i' of level 'p' increases, [P.sub.kb] will increase. As [[summation].sub.i] [v.sub.kip'r]*[q.sub.ip'] increases i.e. prospective customers of 'k' start valuing another product more, [P.sub.kb] reduces. As [SIGMA] [v.sub.jip'r]*[q.sub.ip], increases i.e customer for the base product start valuing their own product more, [P.sub.kb] has to increase to separate k from product j.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], when 'k' is launched in the first period

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], when 'k' is launched in the second period

Launching and cannibalization conditions can be found out as before. The term [n-1.summation over (i=1)] v * q is the sum of the

utilities for each product summed over all attributes except price. But price will be taken as one of the attributes in the conjoint analysis. Respondents will be asked to rate each product concept in both boom and recession. Thus the utility of the products will be obtained. Using the respondent group's utility function for price, we will find out the monetary value of price. The monetary value of the utility or the reservation price of the product can be found out by the method suggested in [6]. But as mentioned earlier, our contribution lies in incorporating economic conditions over different time periods for pricing a product instead of determining the reservation price based on consumer utilities for a particular time period.

4 CONCLUSIONS AND MANAGERIAL IMPLICATIONS

The platform extension and manpower planning model helps the firm in choosing the products to launch based on all relevant costs. It also aids in allocating scarce manpower in design and development for the various product development projects. The results also give us useful insights on the threshold levels of cannibalization that can be allowed. We find moderate levels of cannibalization can be allowed, provided the firms try to estimate the possible cannibalization volumes into their planning procedure. Thus while forecasting volumes of new products; managers should also try to estimate potential cannibalization volumes, which can be done by studying the changes in market share of some products because of the launch of new products, through a choice simulator. Estimates of the cannibalized volumes used in decision making for choosing the products to be launched will give a more realistic picture.

The analysis using data from Vehicle India Ltd shows that moderate levels of cannibalization (within 30% of expansion volume) by both base model and platform extension can be allowed. So the managers should have enough incentive to estimate possible cannibalization volumes and incorporate those in their decision-making.

The pricing and launch sequence determination problem estimates prices, based on customer's utilities for the products and their launch sequences. It also provides us with launching and cannibalization conditions for both the base and platform extensions. Thus we have been able to show that a base model can be launched ahead of the variant without getting fully cannibalized. Managers should also try to control the costs of the variant and give positive "word-of-mouth" information to prospective customers to enable the variant to cannibalize from the base model. Considering the products with multiple attributes from the real life case of Vehicle India makes the problem more realistic. It is also found that the target price obtained from conjoint analysis and the final price tag of the products are usually different as managers use their judgment about economic conditions and competition to arrive on the final price figure. Our approach which uses conjoint inputs and also takes into account the effect of boom and recessionary conditions in the industry, and the difference due to staggered launches will enable managers to arrive at a price figure that is more objective.

We plan to extend the work by considering competition under a duopolistic framework. In India, the commercial vehicle market is shared by two major players. An adaptation of Bertrand's model for differentiated products can be used for this purpose. We also plan to consider the problem of product to plant allocation and capacity augmentation in multiple plants. The model and some preliminary results are shown in [2].

APPENDIX BOOM FOLLOWED BY RECESSION WITH VALUES OF [V.sub.K] AND [V.sub.J] REMAINING SAME IN BOOM AND RECESSION

Maximize [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

such that

[(BR).sub.k]*([v.sub.j]*[q.sub.k]-[P.sub.kr]) +M*y [less than or equal
   to] ([v.sub.j]*[q.sub.j]-[P.sub.jb]) +M [Ensuring customers of 'j'
   to stick to j' in 1st period
(boom)]

[(BR).sub.j]*([v.sub.k]*[q.sub.j]-[P.sub.jr]) -M*y [less than or equal
   to] ([v.sub.k]*[q.sub.k]-[P.sub.kb]) [ensuring customers of 'k' to
   stick to 'k' in 1st
period(boom)]
([v.sub.j]*[q.sub.k]-[P.sub.kr]) +M*y [less than or equal to]
   ([v.sub.j]*[q.sub.j]-[P.sub.jr]) +M [ensuring customers of 'j' to
   stick to 'j' in 2nd period (recession)
   when 'j' is launched first]

([v.sub.j]*[q.sub.k]-[P.sub.kr]) -M*y [less than or equal to]
   [(BR).sub.j]*([v.sub.j]*[q.sub.j]-[P.sub.jr]) [ensuring customers
   of 'j' to stick to 'j' in 2nd period (recession)
   when 'k' is launched first]

[v.sub.k]*[q.sub.j]-[P.sub.jr])-M*y [less than or equal to] ([v.sub.j]*
   [q.sub.j]-[P.sub.jr]) [ensuring customers of 'k' to stick to 'k' in
   2nd period (recession) when 'k' is launched
first]

([v.sub.k]*[q.sub.j]-[P.sub.jr])+M*y [less than or equal to]
   [(BR).sub.k]*[v.sub.k]*[q.sub.k]-[P.sub.kr] [ensuring customers of
   'k' to stick to 'k' in 2nd period (recession) when 'k' is launched
first]

[P.sub.kb] [less than or equal to] [v.sub.k]*[q.sub.k], [P.sub.jb]
   [less than or equal to] [v.sub.j]*[q.sub.j], [P.sub.k]r [less than
   or equal to] [v.sub.k]*[q.sub.k], [P.sub.jr] [less than or equal to
   [v.sub.j]*[q.sub.j]
x)

TABLE 1: SUMMARY OF RESULTS

Serial No.  Scenario            Products launched     Objective fn.
                                                     Value in Rupees
                                                          '000)

1a          Allowing            15ttc, 16ttc,       80748138.71
(base       cannibalization     maxleex,
case)                           ttrailerex,4ttyre,

                                7t44,cngbusex,
                                25tipptc

                                15ttc,16ttc,        20289201.76
                                maxleex,

1b          Allowing only 'j'   ttrailerex,4ttyre,
            products to         7t44,cngbusex,
            cannibalize         25tipptc
            (volumes same       same as above       78981412.33
            as base case)

1c)         Allowing only the
            variant to
            cannibalize
            (volumes same
            as base case)

2           Without             15ttc,16ttc,        15716475.38
            cannibalization     maxleex,
                                ttrailerex,4ttyre,
                                7t44,cngbusex,
                                25tipptc

3           With varying        Products launched
            levels of           remain same as
            cannibalization by  above.
            base model and no
            cannibalization by
            variant

a)          50%                                     31451035.32
b)          60%                                     66110503.24
c)          70%                                     37003859.29

4           With varying
            levels of
            cannibalization
            by variant and no
            cannibalization
            by base model

a)          70%                                     385731146.54
b)          80%                                     438590385.28
c)          100%                                    544308862.75
d)          100% by variant                         563190334.68
            and 60% by base
            model

TABLE 2: LAUNCHING AND CANNIBALIZATION CONDITIONS

                 Launching condition

Boom             'k' before 'j'              'j' before 'k'
Followed
by               [v.sub.j] [less than or     ([v.sub.j]-[v.sub.k]) *
recession        equal to] [v.sub.k] and     ([q.sub.k]-[q.sub.j]/
without          [q.sub/j] [less than or     B[R.sub.k]) = 0
word of          equal to] [q.sub.k]
mouth                                        either [v.sub.j]=[v.sub.k]
effects                                      Or [q.sub.k]=[q.sub.j]/
and [v.sub.j],                               B[R.sub.k] or both
[v.sub.k]

Boom             1 [less than or equal to]   1 [less than or equal to]
followed         [q.sub.k]/[q.sub.j] [less   [q.sub.k]/[q.sub.j] [less
by               than or equal to]           than or equal to]
recession        ([v.sub.jjr] -              ([v.sub.jjr] -
with word        [v.sub.kjr])/([v.sub.jkr]-  [v.sub.kjr])/{B[R.sub.k]*
of mouth         [v.sub.kkr]) and            ([v.sub.jkr]-[v.sub.kkr]))
effects          [q.sub.k]/[q.sub.j] [less   and
and [v.sub.kj],  than or equal to]           (k5*k6*[n.sub.'jb] -
[v.sub.jk],      B[R.sub.j]*([v.sub.kjr]-    [v.sub.kjr]
[v.sub.jj],      [v.sub.jjr])/k1*k2*         + [v.sub.jjr])/
[v.sub.kk]       [n.sub.'kb]                 {B[R.sub.k]*([v.sub.jkr]-
                                             [v.sub.kkr])) [less than
                                             or equal to] [q.sub.k]/
                                             [q.sub.j]

                 Cannibalization condition

Boom             'k' to cannibalize          'j' to cannibalize
Followed         from 'j'                    from 'k'
by
recession        [q.sub.k]=[q.sub.j]         [v.sub.j]/[v.sub.k] [less
without          and [v.sub.k]=[v.sub.j]     than or equal to]
word of                                      (1+[q.sub.j]/[q.sub.k] -
mouth                                        B[R.sub.k])/
effects                                      (2*[q.sub.j]/[q.sub.k] -
and [v.sub.j],                               B[R.sub.k])
[v.sub.k]

Boom             1 [less than or equal to]   [q.sub.j]/[q.sub.k]
followed         [q.sub.k]/[q.sub.j] [less   [less than or equal to]
by               than or equal to] {vjjr+    {[v.sub.kkr]+B[R.sub.k]*
recession        B[R.sub.j]*([v.sub.kjr]-    ([v.sub.jkr]-
with word        [v.sub.jjr])}/([v.sub.kkb]  [v.sub.kkr])}/
of mouth         +kl*k2*[n.sub.'kb])         ([v.sub.jjb]+k5*k6*
effects                                      [n.sub.'jb]-[v.sub.kjr]
and [v.sub.kj],                              +[v.sub.jjr]) [less than
[v.sub.jk],                                  or equal to] 1
[v.sub.jj],
[v.sub.kk]

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Atanu Chaudhuri, Indian Institute of Management, Lucknow, India

Kashi N. Singh Indian Institute of Management, Lucknow, India