226 L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238
identify the relevant breakpoint volume as a function of the primary decision variables y
j k
and s
j t k
.
4. Case study — automotive multiplexing
In this section, we first describe the analysis under- taken by DE and its automotive customer to evaluate
automotive multiplexing as an alternative technology for mechanizing vehicle option content. The approach
outlined is representative of the type of analysis per- formed to evaluate new technologies in the automotive
industry, and is similar in focus to standard finan- cial analyses used for technology adoption decisions
across industries. We, then discuss shortcomings of the standard analysis approach, motivate the need for
a broader context for technology adoption decisions, outline disguised data obtained from DE, and discuss
the relationship between problem structure and the efficiency of the associated solution process.
Cost studies developed by DE for assessment of the multiplexing technology focus on identification of
the level of content complexity where multiplexing is more cost effective than the conventional technology
where again content complexity increases as more features are added to a vehicle. In the study, five lev-
els of vehicle content complexity were identified for costing purposes, as outlined in Table 1. As the level
of content complexity in a vehicle increases from one level to the next, additional LCM hardware is required
for multiplexing; thus, the volume and cost of ad- vanced technology components required for mecha-
nization are greater for higher content levels. Within a level of content complexity, specific subsets of options
OP use the same LCM hardware, but may require a slightly different number of connectors and per-
haps minimal additional wiring, yielding minor cost increases for increasing content within a level.
The study examined both a high-volume and low-volume demand scenario in order to capture the
impact of volume on cost. Consistent with industry estimates, DE engineers assumed an 80 experi-
ence curve for the multiplexing technology, yielding LCM module costs that decrease by 20 each time
production volume doubles. The standard experience curve relationship was applied to compute costs, i.e.
C
v
= C
1
v
− b
, where C
v
represents the cost of the vth unit and b = 0.322, consistent with an 80 experi-
Table 1 Levels of content complexity
Level 1 Power windows
Power locks Courtesy lamps
AMFM cassette Cruise control
Rear window defogger Air conditioning
Level 2 All Level I features
Six-way power seats Power mirrors
Level 3 All Level II features
Express down windows Auto door locks
Illuminated entry
Level 4 All Level III features
Universal theft deterrent UTD Memory eight-way power seats
Adjustable lumbar support Memory power mirrors
Level 5 All Level IV features
Easy close doors Express up windows
Personalized remote keyless entry RK Heated seats
Shoulder belt height adjustment Parking assist mirror adjustment
Dual zone HVAC
ence curve. Based on historical demand data, the cost study further assumed that 60 of the total volume
requires Levels 1 and 2 content complexity, 25 Level 3, and 15 Levels 4 and 5.
Two categories of unit cost elements are relevant for multiplexing, the cost for the LCM hardware and
the cost of the conventional components required to connect LCM modules, and experience effects apply
only to LCM hardware costs. Beyond unit produc- tion costs, the study identified investment costs, e.g.
to modify vehicle designs and to develop the tooling required to produce LCM modules, that must be in-
curred to manufacture multiplexed vehicles. The study also identified significant cost benefits associated with
multiplexing that reflect cost synergies in engineer- ing, increased reliability, reduced warranty costs, and
enhanced diagnostics for service and safety. In order to facilitate unit-cost comparisons with the incumbent
technology, the study aggregated all investment costs and cost benefits over a 3-year planning horizon, and
L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238 227
Table 2 Unit cost comparison results from Delphi cost study
Level Low-volume
High-volume L1
Penalty US 49 Penalty US 21
L2 Penalty US 125
Penalty US 29 L3
Penalty US 173 Penalty US 61
L4 Penalty US 91
Savings US 51 L5
Penalty US 48 Savings US 103
allocated them uniformly across an anticipated vol- ume of vehicles, resulting in a per unit cost penalty
associated with multiplexing for each content level. The focus of the cost study was to determine
whether multiplexing results in a cost penalty or cost savings over the conventional technology for
each level of content complexity. Table 2 presents the results of the unit-cost comparisons generated in
the multiplexing cost study. As indicated in Table 2, the multiplexing technology is cost-justified only for
content Levels 4 and 5 under the high-volume sce- nario. The study concluded that while multiplexing
should become increasingly attractive as the average level of content complexity in vehicles increases, the
new technology should not be adopted at the time of the study. Rather, the study recommended that
an implementation scheme be developed as part of the firm’s strategic planning process, and that the
cost-effectiveness of multiplexing be evaluated for each new electronically controlled feature developed
by the firm.
Our discussions with management indicated that new technologies such as multiplexing are tradition-
ally adopted in an incremental fashion to hedge the risks of large-scale investments in retooling without
volume commitments. The incremental adoption ap- proach is consistent with the traditional unit cost-based
focus of technology adoption cost studies in the indus- try, but has significant limitations that act to conceal
the true profit implications of alternative technology adoption decisions. Frey 1991 provides excellent ex-
amples of incremental adoptions of features in auto- mobiles based on his experiences with Ford Motor
company, and discusses the need for product champi- ons to get new features and technologies into automo-
biles. The model developed in this research provides a framework for developing the required support for
promising new technologies. Several factors motivate a more thorough analysis
of automotive multiplexing. First, given the experience curve rates assumed relevant for technologies like mul-
tiplexing in the automobile industry, the cost of mul- tiplexing depends significantly on the total amount of
LCM hardware used for content mechanization across all levels of content complexity. In turn, the cumula-
tive production volume of LCM hardware is a func- tion of both the mix of OP offered by the firm across
all levels of content, and the demand for those OP. In addition, hybrid policies that allow any combination
of content levels to use multiplexing e.g. a selected mix of moderate- and high-content vehicles, should
be evaluated to more accurately determine the poten- tial impact of adopting the advanced technology on
the firm’s overall costs and profits. Finally, efforts by automobile manufacturers to restructure their vehicle
divisions to eliminate duplication of effort and facil- itate coordination across similar vehicles Wall Street
Journal, 1994, 1996b, c potentially increase the rel- evant volumes of LCM hardware, further decreasing
the marginal cost of multiplexing.
As discussed in Section 3, one factor important in the evaluation of new technologies is the experi-
ence effect. While traditional analysis often includes explicit consideration of experience as, e.g. in the
DE cost study, the lack of coordination with product mix decisions and the focus on incremental adoption
i.e. failure to consider the implications of coordinated adoption across content levels prevent identification
of the true cost and profit implications of alternative adoption decisions. In fact, because of the significant
experience effect governing LCM hardware cost, the profit maximizing assignment of mechanization tech-
nology k = 1 or k = 2 to a particular option package is strongly influenced by the degree to which other se-
lected OP use the multiplexing technology, as shown below.
4.1. Implications of volume-related experience benefits for multiplexing
The cost studies summarized in Section 3 indicate that multiplexing costs less than conventional mecha-
nization for the highest content vehicles only when a sufficient volume of those high-content, multiplexed
vehicles are produced and sold. The cost of using multiplexing for lower content vehicles is shown to
228 L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238
Table 3 Option packages by content complexity L1–L5
Level Option packages
Economy vehicle Luxury vehicle
Level 1 L1-I
Courtesy lamps, AC, AMFM cassette OP1
– L1-II
L1-I plus: rear window defogger, cruise control OP2
– L1-III
L1-I plus: power windows, power locks OP3
– L1-IV
All Level 1 options OP4
– Level 2
L2-I L1-IV plus: power mirrors
OP5 –
L2-II L2-I plus: six-way power seats
OP6 –
Level 3 L3-I
L2-II plus: auto door locks OP7
OP1 L3-II
L3-I plus: illuminated entry OP8
OP2 L3-III
L3-II plus: express down windows OP9
OP3 Level 4
L4-I L3-III plus: memory power mirrors
– OP4
L4-II L4-I plus: eight-way power seats, adjusstment lumbar support
– OP5
L4-III L4-I plus: universal theft deterrent UTD
– OP6
L4-IV All Level 4 options
– OP7
Level 5 L5-I
L4-IV plus: dual zone HVAC, heated seats –
OP8 L5-II
L5-I plus: shoulder belt Ht. adjustment, parking assist mirror adjustment, personalized remote key entry RKE
– OP9
L5-III L5-I plus: easy close doors, easy up windows
– OP10
L5-IV All Level 5 options
– OP11
be higher than conventional mechanization, but this cost penalty is calculated under the assumption that
volume-related experience is accumulated only within a content level, with different content levels evaluated
independently. In practice, the marginal cost for us- ing multiplexing depends on the cumulative amount
of LCM hardware used for all multiplexed OP. When cumulative volumes are explicitly factored into the
analysis, using multiplexing on lower content vehicles may be attractive, even when the technology cannot
be cost justified for individual low-content levels.
To illustrate, suppose five OP are offered, represent- ing each of the five levels identified in Table 3. Fig. 1
depicts unit costs realized when either the conven- tional C or multiplexing M technology is used to
mechanize all option content levels, under the assump- tion that all levels of option content use the same base
LCM hardware for multiplexing mechanization. Each multiplexing cost curve Mv depicts the average unit
cost incurred if an 80 experience curve is relevant and vehicle volumes are uniformly distributed across
the five content levels. For a given content level, the
Fig. 1. Relationship between content complexity and unit mecha- nization costs when base LCM hardware is sufficient for all com-
plexity levels.
L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238 229
Fig. 2. Relationship between content complexity and unit mech- anization costs when additional LCM hardware is required for
higher complexity levels.
set of multiplexing cost curves reflects the decreas- ing unit costs realized when the volume of vehicles
manufactured with the advanced technology increases Fig. 2.
Fig. 3. Economy vehicle mechanization costs under alternative policies.
Figs. 3 and 4 show the unit costs and total costs associated with four policies that incorporate both
mechanization technologies, based on 1997 demand forecasts for economy and luxury vehicles, respec-
tively. These figures illustrate the importance of in- tegrating mechanization technology decisions across
content levels. For example, in Fig. 3, the total cost of a policy that offers all economy vehicle content levels
with the conventional technology CL1, L2, L3 is less than the total cost of mechanizing option content
levels L1 and L2 conventionally and content level L3 with multiplexing CL1, L2ML3. Based on
this comparison, multiplexing would not be adopted. However, if both content levels L2 and L3 use mul-
tiplexing and level L1 uses conventional technology CL1ML2, L3, or if all three levels use multiplex-
ing ML1, L2, L3, then the combined volumes are sufficient to reduce total cost below that for policy
CL1, L2, L3. Similarly, note in Fig. 4 that if we ex- amine unit costs for luxury vehicle content level L3,
we conclude that multiplexing is more costly than the conventional technology, even when all levels of con-
tent are multiplexed, ML3, L4, L5. However, total costs are minimized under this mechanization policy
due to the reduced costs for L4 and L5 that result from the contribution of L3 vehicles to total LCM volume.
230 L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238
Fig. 4. Luxury vehicle mechanization costs under alternative policies.
4.2. Demand and cost data for model application Two vehicle platforms are included in the analysis,
corresponding to economy and luxury vehicles, re- spectively. Marketing information from DE indicates
that option content for the economy vehicle ranges from L0 no significant option content to L3, while
option content for the luxury model ranges from L3 to L5. A total of seventeen candidate OP are identified in
the analysis to represent varying degrees of complex- ity across the five levels of option content outlined in
Table 1. Table 3 specifies the OP associated with each
Fig. 5. Distribution of demand across candidate OP for economy vehicle.
Fig. 6. Distribution of demand across candidate OP for luxury vehicle.
level of content complexity, and indicates the type of vehicle economy or luxury offered with each option
package. Demand forecasts for the next model year were ob-
tained for the specific economy D = 200,000 units and luxury D = 40,000 units vehicle platforms,
with the anticipated distribution of vehicle demand across the designated levels of option content as indi-
cated in Figs. 5 and 6. According to these estimates, 15 of all consumers purchasing an economy vehicle
will select the base vehicle with no significant content represented by OP0 in Fig. 5. In addition to the base
L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238 231
Table 4 Price, cost, and demand data for economy vehicle
OPj p
j
US c
j 1
US c
j 2
US r
j
B
j
US Single-model demand D = 20000
Category demand D = 1M d
j t
d
j t
OP1 240
120 120
1.0 27
20000 100000
OP2 280
140 125
1.0 27
20000 100000
OP3 320
160 130
1.0 27
20000 100000
OP4 340
170 132
1.0 27
20000 100000
OPS 360
180 135
1.5 41
20000 100000
OP6 390
195 140
1.5 41
20000 100000
OP7 430
215 145
2.4 65
18000 90000
OP8 450
225 155
2.4 65
16000 80000
OP9 480
240 165
2.4 65
16000 80000
vehicle, n = 9 OP capturing the remaining 85 of forecasted demand are considered for the economy
vehicle. The luxury vehicle will be offered with con- tent from levels L3–L5, with n = 11 OP OP1–OP11
in Fig. 6 considered in the analysis.
We consider two demand scenarios for each vehicle category. In the first scenario, total annual demand is
set according to the single-model estimates obtained for the economy and luxury vehicles. The second de-
mand scenario extends the volumes to include multiple vehicle models in the same category, since automobile
manufacturers typically offer a variety of economy and luxury vehicles e.g. General Motors GM of-
fers several different economy vehicles, including the Pontiac Sunbird and Grand Am, Chevrolet Cavalier,
Buick Skylark, and Saturn SL1, and has announced plans to develop a small-car group to exploit synergies
Table 5 Price, cost, and demand data for luxury vehicle
OPj p
j
US c
j 1
US c
j 2
US r
j
B
j
US Single-model demand D = 40000
Category demand D = 200000 d
j 1
d
j 2
d
j 3
d
j 1
d
j 2
d
j 3
OP1 430
215 145
2.4 65
4400 4000
3600 22000
20000 18000
OP2 450
225 155
2.4 65
3600 3200
2800 18000
16000 14000
OP3 480
240 165
2.4 65
3600 3200
2800 18000
16000 14000
OP4 520
260 175
3.4 92
3600 3200
2800 18000
16000 14000
OP5 700
350 205
3.4 92
3600 3200
2800 18000
16000 14000
OP6 920
460 235
3.4 92
3600 3200
2800 18000
16000 14000
OP7 1100
550 260
3.4 92
3600 3200
2800 18000
16000 14000
OP8 1300
650 290
4.0 108
3600 4400
4800 18000
22000 24000
OP9 1460
730 310
4.0 108
3600 4400
4800 18000
22000 24000
OP10 1620
810 330
4.0 108
3600 4000
4800 18000
20000 24000
OP11 1800
900 350
4.0 108
3200 4000
5200 16000
20000 26000
across similar vehicle platforms, Wall Street Journal, 1994. To capture the volume benefits gained by co-
ordinating manufacturing across similar vehicles, cat- egory demand is set at five times the annual demand
estimates provided for the individual vehicle models in each category. Clearly, the configuration of manu-
facturing facilities and the level of coordination across vehicle divisions and brands are important factors in
determining whether or not experience benefits are shared across similar vehicles.
In Table 4, d
j t
denotes the annual demand for econ- omy vehicles with option package j in year t under
each demand scenario. Similar demand information is provided in Table 5 for the luxury vehicle category,
with demand figures reflecting a shift in luxury ve- hicle demand toward higher content levels for future
years as anticipated by DE marketing research this
232 L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238
Table 6 Alternative product substitution rates
a
90 substitution 80 substitution
OPj is offered All 100 customers purchase OPj
All 100 customers purchase OPj OPj is not offered
10 customers choose not to purchase vehicle 20 customers choose not to purchase vehicle
90 customers select similar alternative
b
80 customers select similar alternative
b a
Suppose 100 customers have option package j OPj as their first choice.
b
If customer’s second-choice option package is also not offered, then the customer does not purchase vehicle.
trend is not expected for the firm’s economy mod- els. Including demand trends in the model is signifi-
cant, since the optimal product mix and volume may change over the planning horizon accordingly. In this
case, the estimated shift in preferences toward higher content is conservative. By applying the model under
alternative assumptions about changing customer re- quirements, additional insights into the potential im-
pact of alternative technology adoption decisions can be generated. Revenue information is captured using
disguised prices p
j
for each candidate option pack- age, as shown in Tables 4 and 5 for the economy and
luxury vehicles, respectively. To be consistent with the framework of the cost study outlined in Section 3, we
use a 3-year planning horizon in our analysis and ag- gregate the demands in Tables 4 and 5 into a single
period demand volume.
We examine two mechanisms for distributing demand across alternative OP when one or more candi-
date OP are left out of the product mix, thereby allow- ing the sensitivity of customer demand to first-choice
option content availability to be varied. In the first scenario, 90 of the customers with first-choice de-
mand for option package j OPj on a given vehicle can be satisfied with a similar second-choice option
package e.g. OPj ± 1 or OPj ± 2 if their first choice OPj is not offered. Thus, 10 of the de-
mand for OPj is lost if OPj is not offered. Additional demand is lost if a second-choice option package is
also absent from the firm’s product mix. Under the second scenario, 80 of customers will purchase the
vehicle with an alternative option package if their first-choice option package is not offered, as illus-
trated in Table 6. Table 7 shows the second-choice distribution of demand under each scenario for the
economy vehicles, where α
jj
′
is the percentage of OPj
′
’s demand captured by OPj if OPj but not OPj
′
is offered. Second-choice distribution of demand for the
luxury vehicles follows an identical pattern i.e. OP1, OP2, OPn − 1, and OPn follow the same pattern for
either vehicle type, as do OP3 through OPn − 2.
There is evidence to support the assumption that customer demand is not extremely sensitive to spe-
cific content preferences. Recent efforts by GM to offer a simpler, more limited menu of OP won the ap-
proval of customers in California Wall Street Journal, 1996a, and GM is expected to extend use of the new
value pricing approach, citing customers’ preferences for more consistent pricing and a haggle-free buying
experience. Customers’ willingness to sacrifice some degree of choice flexibility in favor of a simplified
buying experience is also supported in the academic literature see, e.g. Purohit and Sondak, 1999.
Tables 4 and 5 provide cost data for each option package listed in Table 3. Specifically, c
j k
represents the cost of producing and assembling conventional
components for conventional k = 1 and multiplex- ing k = 2 mechanization of option package j, r
j
reflects the relative amount of LCM hardware needed to mechanize option package j with multiplexing, and
B
j
is the net investment cost penalty as described in Section 3. Setup and holding costs can also affect the
product mix and technology choice decisions. In this case, multiplexing results in significantly lower setup
times to change over between OP. As discussed in Sec- tion 2, these efficiencies result from the simplified in-
terface for option content mechanization, and become increasingly significant for higher content levels since
the conventional technology requires selection and in- tegration of an increasing array of wiring and electron-
ics for assembly of higher content vehicles. Fixed cost estimates that capture setup and holding cost implica-
tions are provided in Table 8 for each total demand scenario.
L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238 233
Table 7 Second-choice demand distribution
OPj
′
OPj OP1
OP2 OP3
OP4 OP5
OP6 OP7
OP8 OP9
Scenario 1 α
jj
′
OP1 0.00
0.80 0.10
0.00 0.00
0.00 0.00
0.00 0.00
OP2 0.45
0.00 0.40
0.05 0.00
0.00 0.00
0.00 0.00
OP3 0.05
0.40 0.00
0.40 0.05
0.00 0.00
0.00 0.00
OP4 0.00
0.05 0.40
0.00 0.40
0.05 0.00
0.00 0.00
OP4 0.00
0.00 0.05
0.40 0.00
0.40 0.05
0.00 0.00
OP6 0.00
0.00 0.00
0.05 0.40
0.00 0.40
0.05 0.00
OP7 0.00
0.00 0.00
0.00 0.05
0.40 0.00
0.40 0.05
OP8 0.00
0.00 0.00
0.00 0.00
0.05 0.40
0.00 0.45
OP9 0.00
0.00 0.00
0.00 0.00
0.00 0.10
0.80 0.00
Scenario 2 α
jj
′
OP1 0.00
0.70 0.10
0.00 0.00
0.00 0.00
0.00 0.00
OP2 0.40
0.00 0.35
0.05 0.00
0.00 0.00
0.00 0.00
OP3 0.05
0.35 0.00
0.35 0.05
0.00 0.00
0.00 0.00
OP4 0.00
0.05 0.35
0.00 0.35
0.05 0.00
0.00 0.00
OP4 0.00
0.00 0.05
0.35 0.00
0.35 0.05
0.00 0.00
OP6 0.00
0.00 0.00
0.05 0.35
0.00 0.35
0.05 0.00
OP7 0.00
0.00 0.00
0.00 0.05
0.35 0.00
0.35 0.05
OP8 0.00
0.00 0.00
0.00 0.00
0.05 0.35
0.00 0.40
OP9 0.00
0.00 0.00
0.00 0.00
0.00 0.10
0.70 0.00
4.3. Problem simplification For problems involving only a moderate number of
OP, the formulation can be solved using standard in- teger programming solvers. For larger problems, the
cost structures associated with the conventional and multiplexing technologies permit the development of
Table 8 Fixed cost data
OPj Economy vehicle
OPj Luxury vehicle
D = 200000 D = 1000000
D = 40000 D = 200000
f
j 1
US f
j 2
US f
j 1
US f
j 2
US f
j 1
US f
j 2
US f
j 1
US f
j 2
US OP1
397251 198625
1986254 993127
OP1 194918
123277 974592
616386 OP2
463459 231730
2317296 1158648
OP2 182449
115391 912245
576955 OP3
529668 264834
2648339 1324169
OP3 194612
123084 973062
615418 OP4
562772 281386
2813860 1406930
OP4 210830
133341 1054150
666703 OP4
595876 297938
2979381 1489691
OP4 283810
179497 1419048
897485 OP6
645533 322766
3227663 1613831
OP6 373007
235910 1865035
1179552 OP7
675217 337608
3373084 1688042
OP7 445987
082067 2229933
1410334 OP8
666210 333105
3331049 1665525
OP8 618050
390889 3090252
1954447 OP9
710624 355312
3553119 1776560
OP9 694118
438999 3470591
2194994 OP10
734343 464440
3671717 2322198
OP11 815937
516040 4079686
2580220
a simplified decision rule for assigning the profit max- imizing mechanization technology to selected OP. The
following result establishes the consequent relation- ship among the y
j k
decision variables, indicating that if option package j
′
∈ L is offered with the multiplex-
ing technology, then any OP j j
′
, j ∈ L offered on the vehicle will also use multiplexing.
234 L.O. Morgan, R.L. Daniels Journal of Operations Management 19 2001 219–238
Result: For content complexity level L, if y
j
′
2
= 1,
j
′
∈ L, then y
j 1
= 0 for all j j
′
, j ∈ L. A proof is provided in Morgan and Daniels 1999.
The result allows the following constraint to be added to the formulation:
J
L
X
h=j +1
J
h,1
≤ J
L
1 − y
j 2
, j ∈ L, L = L1, . . . , L5,
4 where J
L
denotes the index of the option pack- age with the highest content in level L. Constraint
set 4 significantly reduces the number of product linesmechanization technology pairs that must be
evaluated to determine the optimal solution. Specif- ically, without constraint set 4, the total number
of possible solutions is a combination of the to- tal number of possible product lines and the two
possible mechanization technologies that can be as- signed to each option package in the product line,
or
P
n i=0
\ begin{array}{l}n\\i\\\end{array} × 2
i
. For the luxury vehicle, the n = 11 candidate OP
translate into 177,147 possible solutions. Constraint set 4 reduces the number of solutions within each
content level to P
n
L
i=0
n
L
i i + 1. For the luxury
vehicle example with n = 11 OP in levels L3–L5, the number of possible solutions is decreased to
Q
L5 L=L3
P
n
L
i=0
n
L
i i + 1
, or 46,080. Thus, the result reduces the solution space to 26 of its original
size. Note that because the amount of LCM hardware
required to mechanize option content increases across levels L1 through L5 as reflected by increasing values
of r
j
in Tables 4 and 5, the model can be simpli- fied only within each content level. However, a more
general technology adoption context might be char- acterized by a unit cost advantage for the advanced
technology that is strictly increasing with product complexity across all products. In this case, constraint
set 4 would apply to the entire set of candidate prod- ucts, and thus would have an even greater impact on
the number of feasible solutions for the luxury vehi- cle example, the number of possible solutions would
be reduced to 13,312, or 7.5 of the original solution space. Note also that for the more general structure,
the model simplification result allows the problem to be decomposed into n smaller problems one for each
value of j, each requiring 2n fewer integer variables. Such a problem separation would be useful for larger
applications where problem tractability is an issue.
5. Insights into the technology adoption decision