## An integrated approach to product design and process selection free download

**1 Vfc (10) Zj k km < q m Vk,m (11) * > 0;s,, z Jk km,q m e (0, 1) Vz',A;,m (12) Now consider a restricted version of (PSP) with n = ir' The set of customers J„/ who switch to the new product is J T , = {i\Ui Ui > z'} (13) Let P„i = J2iei , Pi represent the total population of the switching customers The restricted problem can be written as RPSP Z(X,7r') = max subject to m€M \m€M k£)C (10), (11), and z Jk km,qm € {0, 1} Vfc,m The first term in the objective is a constant with respect to the problem variables; it can, therefore, be ignored for the purpose of finding the optimal solution The remaining problem has the structure of the uncapacitated facility location problem (UFL) if we treat attribute levels jk as the unit demand points and the processes m as the candidate location sites f m is the fixed cost of opening a facility at location m, and P K iVj k k m is the cost of satisfying the demand at jk from location m Although UFL is NPhard, efficient solution procedures are available for obtaining strong bounds and for solving reasonably large problems within acceptable computation time In our computational study, we use the dual ascent procedure DUALOC developed by Erlenkotter (1978) Let Z'(X,7r') denote the optimal solution to UFL, then Z(X,w') = n'Pi r , £ / t Z'(X,7r') The solution to PSP is given by Z{X) = max^ZiX,*) = Z(X,ir*) Let <§, = U{ — u° The following result indicates that the search for ir* involves considering at most / values of n Proposition! K* E {61,62, , Si} Consequently, at each iteration, we need to solve at most / uncapacitated facility location problems in order to determine the optimal set of processes As shown in the proof of Proposition 1, this step generates the best price and the set of switching customers as well If we impose capacity limitations on individual processes then (11) is replaced by constraints of the form P*>Z] k km < CAP m q m Vfc,m where CAP m is the capacity of process m In this case, the solution approach to PSP essentially requires solving a number of capacitated facility location (CFL) problems, instead of the UFL prob lems considered here While CFL is harder to solve optimally, several heuristic solution methods exist for it so that from an algorithmic standpoint, capacity constraints can be included within the solution approach 33 The AttributeLevel Selection Problem Now consider the problem for determining the optimal set of product attributes given a set of processes M° = {m\q m = 1} Let f(M°)= £ f m , and m€M° v' ]k = min meM o{vj k m} = v ]krn , Clearly, for a given (j,k), Zjk m equals 1 for m = m', and equals for all other m The attributelevel selection problem can now be stated as ASP KM ) Z(M°) = max £ «6I ke>Cj€Jk subject to (2), (3) (4), and s t ,x jk e {0,1} V«,i,* ASP generalizes the model proposed by Kohli and Sukumar (1990) for the seller's return problem to include product price as an extrinsic decision variable We construct a heuristic solution method that extends the KohliSukumar algorithm to incorporate this generalization This procedure uses a dynamic programming like approach in which each attribute is treated as a stage, and individual attribute levels are the states Starting with attribute 1, this method successively performs a local optimization with respect to adjacent attributes that is followed by attribute augmentation Specifically, at step k of the procedure, only attributes k and k + 1 are considered Let J t — \Jt\, t = l,,K For a level j 6 Jk+i, Jk partial product profiles are constructed by associating each r E Jk with j Of these Jk profiles, the profile (r*,j) that maximizes profit is selected, and r* is merged into j The next iterative step involving attributes k + 1 and k + 2 is then solved with respect to these augmented attribute levels for attribute k + 1 Thus the heuristic forms partial product profiles of increasing cardinality in attribute space, with the profile at the end of stage k consisting of the first k + 1 attributes A formal description of the procedure now follows Algorithm BuildProduct Step 1: Initialization: For each customer i, determine the "partial price" of attribute k as 0* = *?U? k /U? where Uf k is the part worth of attribute k to customer i in the product that i buys currently Set fc = l Step 2: Recursion' a Local Optimization: At step k, for each level of attribute k+l, determine the level r* of attribute k that maximizes the overall contribution b Attribute Augmentation : Set v' hk+l = v' hk+l + v r k Step 3: Termination: If k < K — 1, set k = k + 1, and go to step 2 Else, determine the optimal level fa for attribute K Set x 3 k — 1 if J = j^; Xjk = 0, otherwise Do a backward pass; for k = K — 1, , 1, set x T k = 1 if r = r* and x ]t k+\ = 1; x r k — 0, otherwise The major step in this algorithm involves local optimization at each stage For a given level j of attribute k + 1, this problem can be formulated as: Pl(j,*+1) r*j = arg max r€Jk ^ (vi{* ~ v' jM1 v' rk ) /,) s { (14) subject to >ij,k+i + ™** 0
Equation (14) enforces local optimization with respect to attributes k and k + 1, while equations
(15) and (16) insure that customer i will switch to the partial product if and only if it provides a
higher surplus than the surplus offered by the current partial product
To solve Pl(j, k + 1), we first find the optimal price 7r* corresponding to each r £ J7jt The
maximum price that customer i is willing to pay to switch to the partial product defined by levels
r and j for attributes k and k + 1, respectively, is given by
e
%
rj = Wij,k+l + Wirk ~ [U°k+l + U?k ~ 0*k ~ ^i,Jfe+l]
The profit corresponding to a price of e' is given by
Eir =
Y^M
e
n
~ v
'j,k+i
~ v
rj)
l
g]
ged
where Q =
{g\g G J, e
9
r
> e
l
rj } Arguments similar to those used in the proof of Proposition 1 yield
Consequently, the maximal profit corresponding to level r of attribute k is given by
E*j = max ie x{E tT }
Pl(j,k + 1) is then solved by
r*j = arg max r€ j k
{E*j}
At step 3 of BuildProduct, the optimal attribute level is given by
fa
— arg max
je j K
{Ej}, where Ej = E*j
Thus algorithm BasicDesign essentially iterates between the product and the process spaces,
thereby dealing separately with problems of reduced dimensionality While it is difficult to analyze
its convergence properties theoretically, in all our computational experiments, it was found to
converge quite rapidly However, there are instances in which it may converge to a solution that
is only locally optimal In order to overcome this drawback, we imbed this algorithm within a
simulated annealing based approach This enhancement is now described
11
34 Algorithm Refinement Based on Simulated Annealing
Simulated annealing has been successfully employed for solving some difficult problems such as
graph partitioning (Johnson et al 1989), pattern recognition (Geman and Geman 1984), VLSI
design (Kirkpatrick, Gelatt and Vecchi 1983), single machine minimum tardiness schedule (Matsuo,
Suh and Sullivan 1987a), job shop minimum makespan (Matsuo, Suh and Sullivan 1987b) and
operation partitioning ( Ahmadi and Tang 1991 ) We give below a brief description of this approach
For details, the interested reader is referred to Kirkpatrick et al (1983), and Johnson et al (1989)
Consider the following problem:
max h(y), subject to y 6 y
where h(y) is a realvalued function on domain y Each element y 6 y has an associated set of
neighborsM(y) such that any element y' 6 M(y) can be reached from y by a onestep perturbation
A typical ascent algorithm based on neighborhood search moves from a given y to its neighbor y'
if h(y') > h(y) If there is no such neighbor, then the algorithm terminates having returned y as
the best solution If h(y) is not concave, such an algorithm will frequently yield solutions that are
only locally optimal
In contrast, simulated annealing permits occasional downhill moves, and thereby, provides a mech
anism to escape from a local optima Under simulated annealing, the probability that a move will
be made from y to y' is given by
a = exp{{h(y) h(y')}+ /TEMP(g))
where [t]
+
denotes max(0,t), and TEMP(p) is a positive number Thus, a profitable move will
always be accepted; however, there is a nonzero probability of accepting an unprofitable move as
well, a is a function of the difference in the objective function values at y and y', as well as the
temperature TEMP(<7) at a given state g A simulated annealing algorithm goes through several
states of gradually decreasing temperatures A commonlyused sequence of temperatures follows
a geometric series given by TEMP(y) = r * TEMP(<7 — 1) where r is the cooling rate such that
< r < 1 Clearly, the probability of accepting a downhill move decreases with a reduction in
temperature The system is deemed to be frozen if there is virtually no change in the solution value
at successive temperatures Under certain assumptions, it is possible to show ( Anily and Federgruen
1985; Geman and Geman 1984) the existence of certain values of r that guarantee that simulated
12
annealing will obtain the optimal solution in the limiting case Although it is conjectured that
the rate of convergence may be slow, this approach has yielded good solutions for many practical
problems within reasonable computation time
For PDPS, we define the neighborhood of a given solution individually for the process and the
product spaces In the process space, the neighborhood Af\{Q
r
) of a given point
Q
r
= (q[, ,q
T
M )
consists of all points
Q
5
=
(q{ , , q
s
M ) such that
9m
=
Qm
for m = 1, ,Af; m ^ 71, and,
Qn =
1
" Qu
it can be seen that the neighborhood of
Q
r
consists of M points Similarly, the neighborhood
A/2(X
r
) of a point X
r
= (X[,
, A£) in the product space comprises all points X
s
such that
X
a
k
= XI ioik= 1,,A' k^n,
X
U
= x
)n
(or j = l,,J k j ^ g, and,
x
s
= 1 — x
T
It can be seen that the neighborhood of X
r
consists of Ylk=i(Jk
~
1) points For a given pair
(X
r
, Q
s
) of points from the product and the process spaces, the optimum objective function value
Z(Y
rs
) can be obtained as follows For each
(j,
k) such that x
r
jk
= 1, set Zjk m > — 1 where
m' = arg minm^jkmWm = 1} is the machine with the minimum variable cost for producing
attribute k at level j among all the open machines, and set all other Zjkm — 0 Next use the
approach given in §32 to determine the optimal values of s, and 7r It follows, therefore, that a
solution Y to PDPS is completely determined by the selection of the product profile and the set
of open machines
The parameters required for implementing this algorithm are the starting temperature INITTEMP;
the cooling rate r; the termination threshold c; and the maximum values N\ and A
r
2 that the
counters which control the number of neighbors scanned can take A formal statement of the
simulated annealing algorithm is given below The various steps are described in detail subsequently
In the following, Z() represents the optimal objective function corresponding to solution (•), Y
mc
denotes the incumbent solution, and Z
g
is the best solution value obtained until temperature g
13
Algorithm IntegratedDesign
Step 1: Initialization
Set the initial solution Y° = (X°,Q°) to the solution obtained from algorithm BasicDesign
Set the incumbent solution Y
mc
= Y° Also set TEMP(0)=INITTEMP;
m
=
0; g = 0; and
Z = Z(Y°) Go to Step 2
Step 2: Annealing
If ni > Nu go to Step 5 Else, set g =gl; TEMP(#) = r*TEMP(#+l); and n 2
= 0 Go to Step
3
Step 3: Neighborhood Scan
a) Set n 2
< n 2 + 1 If n 2 < N 2 , fix m = 1, and go to Step 3b) Otherwise, set Z
g
= Z(Y
mc
) If
Z
g
< (1 + e)Z
g i, then set n\ *— n\ + 1 Else, set n\ = 0 Go to Step 2
b) If ra > M, go to Step 3a) Else, determine the neighbor
Q
1
of Q° by setting q^ = 1 —
q^
Determine X
1
and Y
1
Go to Step 4
Step 4' Neighbor Selection
If Z(Y
X
) > Z(Y°), set Y° = Y*
nc
= Y
1
, set m < m+ 1, and go to step 3b) Otherwise, compute
a = expHZtY
1
)
Z(Y°)}/TEMP(^)]
Generate a random number a from the uniform distribution [0,1] Set Y° = Y
1
if a > a Set
ra <— ra + 1 Go to step 3b)
Step 5: Reoptimization
Determine the optimal solution Y* corresponding to the incumbent product profile X
mc
The algorithm is initialized with the solution obtained from BasicDesign in Step 1 Computational
experience (see, for example, Johnson et al 1989, and Ahmadi and Tang 1981) indicates that good
starting solutions usually enhance the performance of simulated annealing Step 2 implements the
specified cooling schedule; it also determines whether the frozen state is reached This algorithm
maintains a counter n\ that is incremented by one each time the incumbent solution value obtained
at the end of the neighborhood search at any temperature does not exceed the incumbent solution
14
value at the previous temperature by the threshold c The system is deemed to be frozen if the
counter value equals N\
At each temperature, Step 3 controls the generation of neighbors This is done by considering the
neighborhood of the partial solution Q° through N2 cycles In any cycle, the algorithm generates
each of the M neighbors of Q° in turn For any neighbor
Q
1
, the approach given in §33 is used to
determine the corresponding product profile X
1
Subsequently, Y
1
is determined from Q
1
and X
1
Step 4 in the algorithm executes the logic pertaining to the acceptance of a neighboring solution,
and if necessary, updates the current and the incumbent solutions The solution obtained at the end
of simulated annealing is reoptimized at Step 6 This is done by retaining the incumbent product
profile X
mc
, and solving the process selection problem following the procedure given in §32 to
determine the optimal processes, the optimal price and the optimal set of switching customers
Several parameter values were tested for implementing the simulated annealing phase of algorithm
IntegratedDesign The values actually used in our computational study were r = 090; N\ = 5;
N2 = 10; and INITTEMP= 001 * Zq where Zq is the solution value obtained from BasicDesign
4 Computational Experience
We conduct two sets of computational experiments The first set addresses the performance of
algorithm IntegratedDesign with respect to the optimal solution, while the second set evaluates
the relative merit of adopting the integrated approach over the sequential approach as a function
of various problem parameters
41 Experimental Details
In order to better focus on the impact of process characteristics, we keep certain customerspecific
parameters fixed across all experiments For example, the part worths Wijk are generated initially
through random sampling from the uniform distribution [60, 340]; the realized values are retained in
all experiments Similarly, in the second set of experiments, the total number of customers / is fixed
at 20 (/ is varied in the first set merely to generate a larger number of problem scenarios) Customer
populations are sampled from the uniform distribution [200, 600] and the resulting values remain
fixed subsequently In all cases, the number of levels is the same for all attributes, ie, \Jk\ = tj, Vfc
Also, the marginal contributions /, = 0, Vz
15
In each problem instance, we generate 1/5 competing products; the active attribute levels for these
products are assigned randomly These products are assigned prices sampled from the uniform
distribution [aU ave , bU aV e], where U ave is a measure of the average utility across all customers and
across all products currently available U aV e — Kw ave , where w ave is the mean realized part worth
given by
_ E, Hk Ej Wjk
Wave —
T T ~
IKt)
and A' and 77 are, respectively, the number of attributes and the number of attribute levels consid
ered in the problem instance The best product and the resulting surplus u® for any customer i are
determined from the profiles of the competing products and their prices, as well as the part worths
Wijk We vary a and b in our experiments to yield various values of the mean price of competing
products TT ave = Uaveio* + b)/2
The problem parameters of interest are i) the number of attributes K, ii) the number of levels
in each attribute 77, iii) the number of processes M, iv) the mean process fixed cost ///, v) the
coefficient of variation of process fixed cost Q, vi) the coefficient of variation of variable cost £„,
vii) the ratio p =
p v /w ave of the mean variable cost to the mean part worth, and viii) the ratio
i?ave/U ave which is a measure of the surplus enjoyed by the customers currently The base values
of these parameters are given in Appendix 2
The actual fixed costs f m used for the various processes are obtained by sampling from a uniform
distribution which has mean /z/, and for which the upper and lower limits are derived from pj and
C/ Similarly, the actual variable costs Vjk m are obtained from a uniform distribution determined
by
n v and
C«
The first experiment considers 27 different scenarios comprising 3 values of the number of segments,
and 9 combinations of the number of attributes and the number of attribute levels as shown in
Table 1 The other problem parameters are retained at their base values indicated in Appendix
2 10 instances of each scenario are generated For a given instance, the optimal solution value
Z opt is obtained by first explicitly enumerating all r/
A
profiles For each of these profiles, the
process selection problem is solved to determine the optimal set of processes and the optimal price
corresponding to that profile, and consequently the profit value as well The optimal solution
for the overall problem is the best profit value across all these product profiles For each problem
instance, we compute the performance ratio PR tn t
= {Z opt
Z tnt )/(Z opt ), where Z, n< is the solution
16
value obtained from IntegratedDesign Table 1 reports the average value of PR in t across all 10
instances; also reported in parentheses is the number of times the optimal solution was obtained in
these 10 instances
For comparison purposes, we also report the corresponding performance ratio PR seq for the se
quential approach, where PR seq = {Z opt
Z seq )/(Z opt ) and Z seq is the sequential solution value
In any problem instance, the sequential solution is obtained by first determining the product profile
using algorithm BuildProduct ignoring the attribute level variable costs Vjk m These costs are
taken into account at the subsequent stage when we solve the process selection problem to yield
the optimal set of processes as well as the optimal price It can be seen that, while the sequential
approach performs limited optimization with respect to the processes and the product price for the
selected product profile, it lacks the integrated approach's ability to revise this profile subsequently
The exponential growth in the number of product profiles to be generated explicitly limits the
size of problems that can be considered in the first set of experiments An alternative approach
of evaluating the performance of IntegratedDesign through the use of upper bounds, based on
Lagrangean relaxation, did not yield satisfactory results We found that these bounds were quite
weak even for small problems The major reason for the weakness of these bounds appears to be
the fact that the attributelevel selection problem has very little structure; it is essentially a general
integer program
The second set of experiments examines the impact of eight parameters, which are varied one
at a time while the others are retained at their base values, on the relative performance of the
integrated approach visavis the sequential approach Algorithm IntegratedDesign is used for
generating the integrated solution value while the sequential solution value is determined in the
manner described above Each of M , K and r) are considered at the seven levels of 3, 5, 7, 9, 11, 13,
15 Similarly,
C/
and
Q v are tested at levels of 008, 016, 024, 032, 040, 048 and 056 [Note that
the largest value that the coefficient of variation of a uniformly distributed nonnegative random
variable can take is 058] fi f
is considered at levels $60000, $120000, $180000, $240000, $300000,
$360000, and $420000 Mean fixed cost values higher than $420000 result in many solutions with
zero objective function values; consequently, they are not considered We test p at the seven levels
of 01, 02, 03, 04, 05, 06, and 07 Finally, we generate problems for seven values of the ratio
^avel (Uave)
~ 060, 065, 070, 075, 080, 085 and 090
17
The results of the second set of experiments are shown in Tables 2 through 9 As in the first set,
10 problem instances are generated randomly for each scenario For reporting purposes, we take
the average of the solution values Z seq and Z tnt across these instances under the sequential and
integrated approaches, respectively We use the measures PR = Zi nt /Z aeq and A = Z tnt
Z seq
to evaluate the relative performance of the integrated approach In addition, we also record the
average optimum product prices 7T, n< and 7r se<7 obtained under the two approaches in each problem
scenario
42 Experimental Results
Table 1 indicates that algorithm IntegratedDesign frequently finds the optimal solution Across
the 27 scenarios and the 270 problem instances, it is 1% away from the optimal solution on average
More importantly, its performance does not appear to be datadependent; the worst performance
ratio for the integrated solution is 65% (averaged over 10 problems) It is also seen that, even for
these small problems, the integrated approach yields substantially superior results to the sequential
approach which is on average 16% away from the optimal solution
INSERT TABLE 1 HERE
Tables 2 and 3 deal, respectively, with the impact of the mean variable cost and the mean fixed
cost on solution values As seen in Table 2, while both Z{ n t and Z seq decrease with an increase
in
p (= p v /w ave ), Z int decreases more slowly Consequently, except at very high values of p, AZ
increases leading to an exponential increase in PR Furthermore, 7r, n * is more sensitive to variations
in /> A similar result is obtained for
fj,j
as indicated in Table 3 although in this case, the solution
values as well as PR are less sensitive to changes in ///
INSERT TABLES 2 AND 3 HERE
Tables 4 and 5 deal with the impact of the coefficient of variation in the fixed and the variable costs
Q and £„, respectively In each case, both Z, n< and Z 3eq increase with an increase in the parameter
value Recall that both approaches find the optimal set of processes and the optimal price, albeit for
(possibly) different product profiles As ( v (£/) increases, the probability of finding processes with
lower variable (fixed) costs to manufacture the profile selected by the sequential approach increases;
this, in turn, results in higher profit values The integrated approach is similarly benefitted, so that
18
in Table 4, AZ does not change appreciably with
£ v However, as Tables 5 shows, AZ tends to
decrease with an increase in £/ Also, any change in the value of
( v has a greater impact on the Z
values relative to a similar change in £/
INSERT TABLES 4 AND 5 HERE
Table 6 considers the number of candidate processes M Both Z seq and Z{ nt increase with an
increase in M which is attributable to the fact that as M increases, there is a increasing likelihood
of finding processes with lower cost structures Note that, while both Z seq and Z jn < attenuate with
A/, the incremental benefits of increasing the number of candidate processes are greater for the
sequential approach which results in a decrease in both AZ and PR as M increases Nonetheless,
the initial difference in the profits under these two approaches is large enough in that the sequential
approach requires much larger values of M to attain comparable profit levels
INSERT TABLE 6 HERE
As seen in Table 7, the integrated approach is increasingly superior with an increase in the number
of attributes, and the incremental benefit generally appears to be additive Clearly, this approach
is able to make a better use of the cost advantages resulting from higher process flexibility, ie, the
ability of any process to deliver an increasing number of attributes Similarly, Table 8 indicates
that the relative performance of the integrated approach, as measured by AZ, increases with an
increase in the number of attribute levels t] as well
INSERT TABLES 7 AND 8 HERE
In Table 9 we use the ratio of the average price 7r ave to the average utility U ave = (Kw ave ) of
the products currently available as a surrogate to measure the intensity of the prevailing market
competition Lower this ratio, higher is the surplus enjoyed currently by the average customer, and
therefore, less likely (s)he is to switch to the new product As seen from the table, while increased
competition clearly erodes the profits obtained under both approaches, the integrated approach is
more robust especially at low values of x a ve/U ave signifying extensive competition
INSERT TABLE 9 HERE
19
As seen from Tables 2 through 9, a common outcome across all the different scenarios tested in the
second set is that the optimum product price x tnt under the integrated approach is consistently
higher than the price Tr seq under the sequential approach This implies that the utility of the new
product for the average switching customer is higher under the integrated approach
In summary, these experiments reveal that the integrated approach is increasingly preferable as the
problem instance becomes more tightly constrained Such a tightness could be brought about by
the intensity of competition in the market measured by K a ve/U ave , that results in large consumer
surpluses It also results from higher product complexity, expressed in terms of the number of
attributes and the number of attribute levels In regard to the process, this tightness is caused by
high variable and fixed process costs, and from having a limited number of alternative candidate
processes
5 Discussion and Summary
This paper models an integrated framework in which the decision on new product design is made
jointly with the selection of optimal processes required to manufacture the product This problem
is formulated as nonlinear integer program We construct a solution approach that has the concep
tually appealing property of decomposing the problem into the product design and process selection
subproblems that represent the marketing and the manufacturing aspects of this decision, while
providing a mechanism to link these two subproblems together Our emphasis in this paper is on
constructing a basic model for the integrated approach, and using this model to gain useful insights
into productprocess interactions To this extent, we makes certain simplifying assumptions As
discussed elsewhere in this paper, algorithmic extensions within such an approach are certainly
possible; it is also possible, at a cost, to relax some of its assumptions We have chosen not to do
so in order to avoid introducing discontinuities that detract from the insights that we obtain from
our computational experience
The significance of productprocess interactions at the system design level has been emphasized in
the literature on concurrent engineering, simultaneous engineering, and quality functional deploy
ment We believe that this study is one of the earliest attempts at modeling these interactions and
proposing an integrated solution approach Furthermore, our computational experience also iden
tifies conditions that heighten these interactions, and consequently, result in greater benefits from
20
adopting the integrated approach These conditions relate to more intensive market competition,
greater product complexity, low contribution margins, and high fixed process costs
With an increase in market competition, productprocess design integration becomes increasingly
important in order to introduce products that sell well and that are profitable In a niche market
where competition is nonexistent, the need for integrated design may not be paramount On the
other hand, intensive competition is forcing the major automobile manufacturers to integrate their
design and manufacturing activities Chrysler, for example, has built a billion dollar center in order
to locate experts from different functional areas in the same facility (Woodruff and Lasly 1992)
Similarly, Nissan claims that simultaneous engineering and close interaction between the design
and manufacturing personnel played critically important roles in introducing Quest in the crowded
minivan market (Narita 1991)
In regard to product complexity, the computational study suggests that the integrated approach
is more desirable for products with more attributes and/or more attribute levels As these two
parameter values increase, product and process decisions become more interrelated, and techniques
that consider the overall decision in totality become more useful The results of this study also show
that the integrated approach is able to deliver a product with higher utility and is consequently
able to charge a higher price as well
The results also suggest that when variable costs are high, there is a greater need to carefully select
the attribute levels A number of new products with novel, wellconceived attributes have failed
during the growth stage of their life cycles primarily because the firms have underestimated the
costs associated with providing these attributes A case in point is that of Ultrasofts Diapers (Swasy
1990) While the firm touted its design features such as the superabsorbent pulp material used
in these diapers to keep babies dry, they underestimated the associated processing costs and the
manufacturing problems that these features might entail Consequently, in spite of strong customer
acceptance, this product flopped The difference in the values of ir int and ir seq indicates that, by
explicitly accounting for the manufacturing costs, the integrated approach provides a more realistic
assessment of the optimal price
Similarly, adopting the integrated approach becomes more important for larger investments result
ing in high fixed costs Again, there is empirical evidence to suggest that firms that have carefully
evaluated both product design and process selection alternatives before making major investments
21
have been successful For example, before introducing its Sensor line of razors and blades, Gillette
spent considerable time and effort in insuring that the stateoftheart technology in laser weld
ing could indeed meet the required output rates without adversely affecting blade hardness and
sharpness (Ingrassia 1992) The success of Sensor (43% of the nondisposable razor market in less
than 3 years) and the higher price that it commands in the market testify to the wisdom of having
considered the product design and the manufacturing decisions simultaneously
In highlighting the above conditions, we do not mean to suggest that the benefits of adopting
the integrated approach is limited to these conditions only Rather, under these conditions, the
integrated approach is so significantly superior that its adoption is critical for achieving any measure
of competitiveness
Acknowledgements
The authors thank Don Erlenkotter for providing the DUALOC code, and Marilyn Lucas for the
extensive computational support This research was partly supported by a grant from the Research
Board at the University of Illinois
22
References
1 Ahmadi, R H and C S Tang (1991), "An Operation Partitioning Problem for Automated
Assembly System Design," Operations Research, Vol 39, 824835
2 Albers, S (1976), "A Mixed Integer Nonlinear Programming Procedure for Simultaneously
Locating Multiple Products in Attribute Space," in Methods of Operations Research, edited
by R Henn et al, Proceedings of the First Symposium on Operational Research, Univ of
Heidelberg, Germany, 899909
3 Brazier, D and M Leonard (1990), "Concurrent Engineering: Participating in Better De
signs," Mechanical Engineering, January, 5253
4 Corneujols, G, G L Nemhauser and L A Wolsey (1990), "The Uncapacitated Plant Lo
cation Problem," in Discrete Location Theory, edited by R L Francis and P Mirchandani,
John Wiley and Sons, New York, NY
5 Dobson, G and S Kalish (1988), "Positioning and Pricing a Product Line," Marketing Sci
ence, Vol 7, 107125
6 Eliashberg, J and A K Manrai (1989), "Optimal Positioning of New Products: Some Analyt
ical Implications and New Results," Working Paper No 89003, Wharton School, University
of Pennsylvania, Philadelphia, PA,
7 Erlenkotter, D (1974), "A DualBased Procedure for Uncapacitated Facility Location "Operations
Research, Vol 26, 9921109
8 Evans, B (1988), "Simultaneous Engineering," Mechanical Engineering, February, 3842
9 Garey, M R and D S Johnson (1979), Computers and Intractability: A Guide to the Theory
of NPCompleteness, W H Freeman and Company, New York, NY
10 Gavish, B, D Horsky and K N Srikanth (1983), "An Approach to Optimal Positioning of
a New Product," Management Science, Vol 29, 12771297
11 Geman, S and D Geman (1984), "Stochastic Relaxation, Gibbs Distribution, and the Bayesian
Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence,
Vol 6, 721741
23
12 Green, P E and A M Kreiger (1985), "Models and Heuristics for Product Line Selection,"
Marketing Science, Vol 4, 119
13 Green, P E, J D Carroll and S M Goldberg (1987), "A General Approach to Product
Design Optimization via Conjoint Analysis," Journal of Marketing, Vol 45, 1737
14 Hauser, J R and P Simmie (1981), "Profit Maximizing Perpetual Positions: An Integrated
Theory for the Selection of Product Features and Price," Management Science, Vol 27,
3356
15 Hauser, J R and D Clausing (1988), "The House of Quality," Harvard Business Review,
MayJune, 6373
16 Ingrassia, L (1992), "The Cutting Edge," Wall Street Journal, April 6
17 Johnson, R M (1974), "Tradeoff Analysis of Consumer Values," Journal of Marketing Re
search, Vol 11, 121127
18 Johnson, D S, C R Aragon, L A McGeoch and C Schevon (1989), "Optimization by
Simulated Annealing: An Experimental Evaluation, Part I, Graph partitioning," Operations
Research, Vol 37, 865892
19 Kirkpatrick, S, C D Gelatt, Jr and M P Vecchi (1983), "Optimization by Simulated
Annealing," Science, Vol 220, 671680
20 Kohli, R and R Krishnamurthi (1987), "A Heuristic Approach to Product Design," Man
agement Science, Vol 33, 11231133
21 Kohli, R and R Sukumar (1990), "Heuristics for Product Line Design," Management Sci
ence, Vol 36, 14641478
22 Matsuo H, C J Suh and R S Sullivan (1987a), "A Controlled Search Simulated Annealing
Method for the Single Machine Weighted Tardiness Problem," Working Paper #87122,
Graduate School of Business, Univ of Texas, Austin, TX
23 Matsuo H, C J Suh and R S Sullivan (1987b), "A Controlled Search Simulated Annealing
Method for General Job Shop Scheduling Problem," Working Paper, Graduate School of
Business, Univ of Texas, Austin, TX
24
24 McBride, R D and F S Zufreyden (1988), "An Integer Programming Approach to the
Optimal Product Line Selection Problem," Marketing Science, Vol 7, 126140
25 Narita, R (1991), "Designing Cars with "You" in Mind: The Hidden Source of Customer
Satisfaction," presented at the University of Michigan Automotive Management Briefing Sem
inar, Traverse City, MI, August 8
26 Shocker, A D and V Srinivasan (1974), "A Consumer Based Methodology for the Identifi
cation of New Product Ideas," Management Science, Vol 20, 921937
27 Sudharshan, D, J H May and A D Shocker (1987), "A Simulation Comparison of Methods
for New Product Location," Marketing Science, Vol 6, 182201
28 Sudharshan, D, J H May and T S Gruca (1988), "DIFFSTRAT: An Analytical Procedure
for Generating New Product Concepts for a DifferentiatedType Strategy," European Journal
of Operational Research, Vol 36, 5065
29 Swasy, A (1990), "Unexpected Woes Can Kill New Products," Wall Street Journal, October
9
30 Woodruff, D and E Lasly (1992), "Surge at Chrysler," Business Week, November 9, 8896
31 Zufreyden, F S (1977), "A Conjoint Measurement Based Approach for Optimal New Product
Design and Product Positioning," in Analytical Approaches to Product and Market Planning,
edited by A D Shocker, Marketing Science Institute, Cambridge, MA
32 Zufreyden, F S (1979), "ZIPMAPA ZeroOne Integer Programming Model for Market Seg
mentation and Product Positioning," Journal of the Operational Research Society, Vol 30,
6376
25
Appendix 1
Proofs
Remark 1 PDPS is NPhard in the strong sense
Proof: The result is proved by restriction: we show that a special case of PDPS is NPhard in the
strong sense Consider the case in which / = 1, l\ — 0, p, = 1, ttj = 0, Jk = 1, and tom = 1, Vfc
Clearly, in an optimal solution, ir = K, and s\ = 1 PDPS then reduces to
Z = max K
^ f m qm
]T] Vikm^lkm
subject to
^Um < 9m VA:,m
zikm,q m € (0, 1) Vfc,m
This problem has the structure of the uncapacitated facility location (UFL) problem [see, for
example, Erlenkotter 1974] The result follows from the observation that the vertex cover problem
that is known to be NPhard in the strong sense (see, for example, Garey and Johnson 1979) can
be transformed to UFL (Cornuejols, Nemhauser and Wolsey 1990)
Proposition 1 x* £ {^i,#2> • • >^/}
Proof: Order <$, such that 6^ <
6[ 2 ]
< • • < <$[/], and let 6[ ]
= 0 When tt =
fy],
it follows from
(13) that Sj = 1 for j £ {[*]>[* + 1], • • , [/]}, and s
:
= for all other j s
3
remains unchanged for
any value of tt in the interval (