A Decision Support System for Planning Manufacturers'Sales Promotion Calendars

A Decision Support System for Planning
Manufacturers’ Sales Promotion Calendars
Jorge M. Silva-Risso • Randolph E. Bucklin • Donald G. Morrison
J. D. Power and Associates, 30401 Agoura Road, Agoura Hills, California 91301 and Anderson School, University of
California at Los Angeles, Los Angeles, California 90095-1481, jorge.silva@anderson.ucla.edu
Anderson School, University of California at Los Angeles, Los Angeles, California 90095-1481,
randy.bucklin@anderson.ucla.edu
Anderson School, University of California at Los Angeles, Los Angeles, California 90095-1481,
donald.morrison@anderson.ucla.edu
Abstract
pass-through constant rate of 80%, provided to us by the
collaborating firm, the optimal promotion calendar produced
A common event in the consumerpackaged goods industry
is the negotiation between a manufacturer and a retailer of
by the modeling system followed a pattern of frequent and
the sales promotion calendar. Determining the promotion
shallow temporary price reductions with no feature or dis-
calendar involves a large number of decisions regarding lev-
play activity. We also analyze how that result would change
els of temporary price reductions, feature ads, and in-store
under different retailer pass-through scenarios.
displays, each executed at the level of individual retail ac-
Ourfindings indicated that the manufacturercould sub-
counts and brand SKUs over several months or a year.
stantially improve the profitability of its sales promotion ac-
Though manufacturers spend much of their marketing
tivity and that there would be a concurrent positive effect on
budget on trade promotions, they lack decision support sys-
retailer profit and volume levels. Management reported to
tems to address the complexity and dynamics of promotion
us that the insights from the use of the system were imple-
planning. Previous research has produced insights into how
mented in their promotion-planning process and produced
to evaluate the effectiveness of promotional events, but has
positive results. A validation analysis on follow-up data for
not addressed the planning problem in a dynamic environ-
one market showed that promotion activity could be signifi-
ment. This paper develops a disaggregate-level econometric
cantly reduced, as recommended, with no adverse effect on
model to capture the dynamics and heterogeneity of con-
the brand’s market share, as predicted.
sumer response. By modeling the purchase incidence (tim-
To generalize the model beyond the specific category
ing), choice and quantity decisions of consumers we decom-
where it was implemented, we conducted a sensitivity anal-
pose total sales into incremental and nonincremental
ysis on the profile of the calendar (i.e., frequency, depth, and
(baseline plus borrowed).
duration of deals) with respect to changes in market re-
The response model forms the basis of a market simulator
sponse, competitive activity, and retailer pass-through. First,
that permits us to search for the manufacturer’s optimal pro-
we found that the optimal depth, frequency, and timing of
motion calendar(subject to a set of constraints, some of them
discounts is stable for price elasticities ranging from near
imposed by the retailer) via the simulated annealing algo-
zero to around four (in absolute magnitude). We also found
rithm. Calendar profits are the net result of the contribution
no systematic impact of competitive promotions on the pro-
from incremental sales minus the opportunity cost from giv-
file of the optimal calendar. For example, variation in com-
ing away discounts to nonincremental sales and the fixed
petitive activity did not affect the optimal depth orfrequency
costs associated with implementing promotional events (e.g.,
retagging, features, displays). Incremental sales result from
of discounts. Lastly, we found changes in retailer pass-
promotion-induced switching, the acceleration and quantity
through to have a significant effect on the optimal depth and
promotion effects on those switchers, increased consumption
number of weeks of trade promotion that a manufacturer
and the carryover effect from purchase event feedback.
should offer. This emphasizes the importance to manufac-
We applied our approach to the promotion-planning
turers of having accurate estimates of pass-through for pur-
problem of a large consumer-packaged goods company in a
poses of promotion budgeting and planning.
nonperishable, staple product category suggested by com-
(Trade Promotion; Brand Management; Decision Support Sys-
pany executives (canned tomato sauce). Subject to a retailer
tems; Scanner Data)
Marketing Science
1999 INFORMS
0732-2399/99/1803/0274//$05.00
Vol. 18, No. 3, 1999, pp. 274–300
1526-548X electronic ISSN

---

A DECISION SUPPORT SYSTEM FOR PLANNING
MANUFACTURERS’ SALES PROMOTION CALENDARS
Introduction
ber of control variables, nonlinear function, and mul-
Trade promotion continues to be the largest single
tiple local optima) involved in determining the pro-
spending category in the marketing mix budget of U.S.
motion calendarovera one yeartime horizon.
packaged goods companies (e.g., Kotler1997). Improv-
During the development of the decision support sys-
ing the productivity of trade promotion dollars there-
tem, we worked closely with senior management at the
fore remains a high priority in the consumer products
firm with whom we collaborated. The extensive inter-
industry. A significant opportunity to enhance the ef-
action allowed us to develop a system that was com-
patible with the trade promotion practices of the firm,
ficiency and effectiveness of marketing spending lies
thereby enhancing management understanding and
in the implementation of trade promotion policies.
acceptance of the system. Based on the insights pro-
This process involves a very large number of tactical
vided by the model, the collaborating firm made sig-
decisions regarding desired levels of temporary price
nificant changes to its trade promotion policy in the
reductions, feature ads, and in-store displays, each exe-
product category we analyzed and obtained positive
cuted at the level of individual retail accounts and
results. (In a subsequent section, we present follow-up
brand SKUs. When viewed over several months or a
data that validates ourmodel.) A stated long-term goal
year, these decisions collectively make up what is
of management was to have a portable version of the
known as the sales promotion calendar.
system installed in the laptops of the sales represen-
The promotion calendar reflects not only numerous
tatives to support the sales force in its negotiations
decisions but inherently complex ones. Each should
with retailers.
take into account a variety of factors, including mar-
keting mix effects, the dynamics of consumerresponse,
competition, and retailer behavior. In this environ-
Sales Promotion Planning
ment, a decision support system (e.g., Little 1979) of-
Ourmodel is based on a dynamic view of the pro-
fers the potential to improve decision making (cf. Hoch
motion decision-making process. Manufacturers’ cur-
rent practice often pays little consideration to the fu-
and Schkade 1996) and, of course, to save an enormous
ture impact of promotional offerings. For example, at
amount of time. By programming the system to pro-
the packaged goods company with which we collab-
duce “win-win” promotion calendars (i.e., where both
orated, planners based their promotion budget allo-
manufacturer and retailer come out ahead), a manu-
cations on response elasticities that were assumed to
facturer’s gains need not come at the expense of the
be fixed overtime and did not take into account the
retailer. By presenting “win-win” calendars, backed up
effects of previous marketing activity. Our approach
by forecasts of category profitability, sales represen-
allows manufacturers to consider the dynamic effects
tatives should be able to streamline trade promotion
of sales promotion on consumer response (e.g., house-
discussions with retailers and devote more time to
hold inventory, increased category usage or consump-
brand-building activities.
tion, and purchase event feedback) and to adopt a
Ourpapershows how scannermodeling technology
longer-run view of the promotion calendar.
and optimization methods can make it possible to be-
This paperfocuses on what promotions the manu-
gin to automate the process of planning the promotion
facturer would like to see in front of the consumer over
calendar. First, we develop and demonstrate the bene-
a prespecified time horizon. What the consumer sees,
fits of an implementable decision support system for
however, is the result of the way the retailer imple-
the tactical decisions that comprise the sales promotion
ments the manufacturer’s promotional offerings. Thus,
calendar. Second, we provide insight about the profile
a decision-support system for this problem must in-
of the promotion calendar and what is robust with re-
clude the role of the retailer. Our approach assumes
spect to variations in the marketing environment and
that the manufacturer has good knowledge of the na-
rates of retail pass-through. Finally, we show how to
ture of retailer response. Managers at our collaborating
apply simulated annealing (Kirkpatrick et al. 1983) to
firm had historical data on how each retailer had re-
solve the complex optimization problem (large num-
sponded to different promotional offerings, from
Marketing Science/Vol. 18, No. 3, 1999
275

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
which the retailer’s response function could be ap-
Raju et al. 1990) has shown that sales promotion can
proximated. Our model is designed to work by then
work as a price discrimination device, i.e., a marketing
searching for the promotional offering to the trade that
tool that takes advantage of consumerheterogeneity.
would result in the desired calendar in front of the
consumerat the point of purchase. (We also show how
Literature
variable rates of retail pass-through can be incorpo-
A number of recent articles are closely related to our
rated into the decision support system.)
work. Abraham and Lodish (1993) described a method
Oursystem is intended to be used as a planning and
to measure the effectiveness of promotional events us-
negotiating tool by a manufacturer’s sales representa-
ing store-level data. Because the approach uses store-
tives in the field. To avoid inefficiencies in the supply
level data, it does not decompose the promotional lift
chain, such as inventory build-ups by retailers, man-
(i.e., the volume of sales above baseline) into sales that
ufacturers need to design promotional offerings that
are truly incremental versus those that are borrowed.
reward the retailer for execution of the program rather
(Our approach uses panel data to estimate the pur-
than just forward buying. Our model is based on a
chase acceleration and/or stockpiling induced by a
“pay-for-performance” environment where the retailer
promotion.) Their approach also does not incorporate
has no incentive to forward buy. In this arrangement,
dynamics in consumerresponse orthe effects of pre-
the retailer is paid a promotional allowance based on
vious marketing activity on future promotional events.
the volume sold during the promotion period. This is
Midgley et al. (1997) use genetic algorithms to ana-
how the collaborating firm operated in the product
lyze marketing strategies under oligopolistic compe-
category we analyzed. This type of agreement is al-
tition. In their approach, demand is represented by an
ready a significant part of trade dealing, in part be-
aggregate or market-level model. Again, this does not
cause it places the focus on consumerdemand as the
permit a decomposition of the promotional “bump”
driving force for promotional decisions and thereby
into incremental and borrowed sales. Neslin et al.
attempts to minimize inventory held in the channel.
(1995) develop an aggregate model with three players:
One key premise of our approach is that the manu-
the manufacturer, the retailer, and a set of consumers.
facturer wants the right calendar in front of the con-
The manufacturer’s profit is maximized over sales to
sumer. We therefore optimize manufacturer profit
the retailer, not over sales to the consumer. A potential
oversales to the consumer, taking into account the
drawback of this approach is that sales could end up
pass-through response function of the retailer. Our fo-
in inventory build-ups in the channel, potentially over-
cus is to determine how to structure the offer to the
stating the true profitability of a promotion.
retailer so as to obtain the desired effects at the con-
In contrast to the work just described, Tellis and
sumerlevel.
Zufryden (1995) develop a retail promotion planning
A second key premise is that the market response
model that is based on a disaggregate consumer re-
model should be based on disaggregate data. This en-
sponse model. Their work differs from our approach
ables the “truly incremental” sales due to promotion
on several dimensions. First, they address the retailer’s
to be separated from not only baseline sales, but also
problem, taking the manufacturer’s behavior as given,
from borrowed sales (i.e., purchases that would have
i.e., the objective function is retailer category profits
been made in the future but were accelerated due to
given full knowledge of manufacturers’ trade promo-
promotion). Such a capability provides a critical dis-
tions. In contrast, the goal of our system is to determine
tinction from promotion evaluation models that are
manufacturers’ promotion programs, taking into ac-
based on aggregate-level data. By using a disaggregate
count the managerially calibrated response of the re-
model of demand, we can also naturally incorporate
tailer. Second, their demand model does not segment
consumer heterogeneity into the planning of the pro-
consumers in terms of their responsiveness to market-
motion calendar. We note that extensive previous re-
ing activity. This omits a key driver of price promo-
search (e.g., Stiglitz 1977, Varian 1980, Narasimhan
tions, i.e., the ability to identify consumersegments
1984, Jeuland and Narasimhan 1985, Narasimhan 1988,
with different demand functions (cf. Stiglitz 1977).
276
Marketing Science/Vol. 18, No. 3, 1999

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
Lastly, theiroptimization and sensitivity analyses are
Figure 2
Truly Incremental and Borrowed Sales
based on mean household values. While this greatly
simplifies the optimization problem, it implies that the
procedure does not take into account any preference
or response heterogeneity among panelists.
Overview of Decision Support System
Our system (see Figure 1) combines a disaggregate
market response model with an optimization proce-
dure that searches for the promotion calendar provid-
ing the greatest increment to the manufacturer’s profit.
To estimate a promotion’s incremental impact on
profit, the consumer response model computes ex-
pected sales and the proportion that is truly incremen-
tal from the promotion. Truly incremental sales are (1)
units sold to consumers who bought the brand as a
consequence of its promotional status and who would
Krishnamurthi and Raj 1988, Currim and Schneider
not have bought it otherwise (now or in the future), (2)
1991, Bucklin and Gupta 1992, and Bell et al. 1999), has
any promotionally-induced consumption increase,
shown that acceleration and stockpiling play signifi-
and (3) any positive carryover effect from purchase
cant roles in consumer response to promotional activ-
event feedback. The sales promotion “bump” (Figure
ity. Our response model captures consumers’ purchase
2) that is routinely observed in sales data also contains
incidence, choice and quantity decisions and handles
sales to consumers who accelerated their purchases or
consumerheterogeneity by using latent-class analysis.
bought more units than usual (stockpiled), but would
The system then uses parameter estimates from the re-
have bought the brand at the regular price (now or in
sponse model, togetherwith household specific vari-
the future) had the promotion not been run. These
ables (e.g., brand loyalty, consumption, and purchase
units (less any that may be attributed to a consumption
rates) and environment variables (e.g., competitive ac-
increase; see Ailawadi and Neslin 1998) are sales bor-
tivity, retailer pass-through, and mark-up) to simulate
rowed from the future, and are not truly incremental
the purchase decisions made by a large sample of
for the manufacturer.
panelists.
To decompose the promotional “bump,” we require
We link the market response model that simulates
a modeling approach that captures the source of con-
household decisions to an optimization module that
sumer response: switching, acceleration and/or stock-
uses the simulated annealing algorithm (Kirkpatrick et
piling. Previous research (e.g., Neslin et al. 1985,
al. 1983) to search for the set of decisions over the plan-
ning horizon that maximizes manufacturer profit.
Those decisions include when, forhow long, and, in
Figure 1
Overview of Decision Support System
the case of temporary price reductions, how deep to
run promotional events. The optimization procedure
is constrained to the set of schedules that would pro-
duce acceptable levels of expected category profit for
the retailer. Comparative statics analyses can be per-
formed by simulating different market characteristics
(e.g., by varying response parameter values, segment
sizes, competitive activity, retailer pass-through and
mark-up) and examining the changes, if any, in the
optimal promotion calendar. This feature of the model
Marketing Science/Vol. 18, No. 3, 1999
277

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
also may be used by manufacturers to search for robust
observed “bump” is truly incremental for the manu-
strategies.
facturer. A traditional approach (e.g., Abraham and
Lodish 1987, 1993) is to estimate the volume of sales
that would have been achieved had the promotional
Market Response Model and
event not been run (baseline sales) and define as incre-
Incremental Sales Estimation
mental all the volume above the baseline. As we illus-
Using purchase histories, we compute for each house-
trate below, this approach has several limitations (cf.
hold the probability of visiting each store in the market
Abraham and Lodish 1993, p. 250, para. 2).
area. Conditional on a store visit, the consumer then
The Loyal Consumer.
Considerthe case of a hard-
decides whether to buy in the target category. Given a
core loyal (Colombo and Morrison 1989) consumer of
decision to purchase in the category, the consumer
brand A. Let us refer to that consumer as household 1.
then chooses a brand-size alternative. (If the promotion
Household 1 only buys brand A and will not consider
planning is to be performed at the UPC level, the
buying any competitive brands, even if they are on
model could be modified with the procedure devel-
promotion. Assume that brand A is on promotion in
oped by Faderand Hardie 1996.) Finally, given a cate-
period t. Household 1 may take advantage of that pro-
gory purchase and a brand-size choice, the consumer
motion by accelerating the timing of its purchase (in-
decides how many units of the brand-size alternative
cidence effect) and/orbuy mor
e units than usual
to purchase (cf. Ailawadi and Neslin 1998, Bucklin et
(quantity effect). Thus, brand A’s promotion would re-
al. 1998). The household-level demand model, condi-
sult in household 1 buying more units in period t than
tional on a store visit, is given by
it would had the promotion not been run. Following
h
h
h
E(Q )
Abraham and Lodish’s approach, those additional
it
E(Q |
it Qit
0)
units bought by the hard-core loyal consumer of brand
h
h
Pt (i|inc)
Pt (inc), where
(1)
A would be computed as incremental volume for the
h
h
E(Q |
manufacturer.
it Qit
0)
the expected numberof units that
household h will buy of brand-size alternative i at time
Considernow that household 1 has a constant con-
t given that household h has decided to buy brand-size
sumption rate, regardless of its inventory level. For ex-
alternative i at time t (i.e., given that
h
Q
ample, household 1 always consumes one unit of
it
0),
h
P
brand A per week, regardless of how many units it has
t (i|inc)
the probability that household h chooses
brand-size alternative i at time t, given that it has de-
in its pantry. In that case, the additional units bought
cided to purchase in the product category (i.e., given
by household 1 in period t will cannibalize future sales
purchase incidence), and
of brand A and will not be truly incremental for the
h
P
manufacturer in the long run. Therefore, those units
t (inc)
the probability that household h decides
to make a category purchase at time t, given a store
should
be
considered
“borrowed”
and
not
visit.
incremental.
The Appendix gives details of the response model
Assume that household 2 is also a hard-core loyal of
specification. We now describe how the response
brand A. It follows a purchase behavior similar to
model can be used to estimate incremental vs. nonin-
household 1, with the exception that holding addi-
cremental sales from promotions, thereby producing
tional inventory motivates household 2 to increase its
the inputs needed forthe calendaroptimization.
consumption rate. To simplify the example, assume
that all of the incremental household inventory be-
Using the Response Model to Measure a
comes incremental consumption for household 2. In
Manufacturer’s Incremental Sales
that case, the extra units bought when brand A was on
A promotion calendar is composed of a sequence of
promotion will be incremental for the manufacturer.
events that result in “bumps” in sales volume (see Fig-
Between household 1 and household 2, we can think
ure 2). The challenge is to estimate how much of the
of a continuum of hard-core loyal households for
278
Marketing Science/Vol. 18, No. 3, 1999

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
whom the extra inventory will result in some increase
up the sales bump forbrand A are clearly incremental.
in consumption but will also result in some cannibal-
Of the remaining 2 units, some, all, or none will be
ization of future sales. The computation of incremental
incremental, depending on how many become extra
sales should capture these effects.
household consumption and how many cannibalize
future sales. Our approach initially classifies these two
The Brand Switching Consumer. Let us now con-
units as borrowed sales. All, none, orpart of the borrowed
sider the case of a brand switching consumer. In the
units will ultimately be incremental for the manufac-
absence of any promotional activity, household 3 (a
turer, depending upon the extent to which the addi-
hypothetical brand switcher) has a 50-50 chance of
tional household inventory prompts an increase in
buying brand A or a competitor’s brand. When brand
consumption.
A is on promotion the choice probabilities shift to 1 for
We summarize below the preceding sales decom-
the promoted brand A and 0 forthe unpromoted com-
position according to how it would be computed from
petitor’s brand (and vice-versa when the competitor’s
the incidence, choice, and quantity response models at
brand is on promotion). Assume that when no brand
the level of an individual household. To simplify this
is on promotion, household 3 would make a category
example, we take the household’s initial inventory to
purchase of 4 units when its inventory reaches 0. When
be 0. Thus, the purchase incidence probability will be
a brand is on promotion, household 3 would buy
1 regardless of the promotional status of brand A.
enough units of the promoted brand to reach a house-
hold inventory level of 8 units (storage constraint).
Brand A Total Sales (Brand A on Promotion)
Consider the scenario where household 3’s category
Incidence Probability
1
inventory reaches 0 at time t and no brand is on pro-
Choice Probability
1
motion. In this instance, the household would make a
Quantity Model
8
category purchase of 4 units. With 0.50 choice proba-
Expected Total Quantity
8
bilities for both brands, the expected quantities are 2
Brand A Baseline Sales (Assuming No Promotions on
units forbrand A and 2 units forthe competing brand.
Brand A)
These units would be baseline sales (i.e., they occurin
Incidence Probability
1
the absence of promotional activity).
Choice Probability
0.5
Now consider the scenario where brand A is on pro-
Quantity Model
4
motion and household 3’s inventory reaches 0. Here,
Expected Baseline Quantity
2
household 3 would buy 8 units of brand A and 0 units
of the competing brand. The Abraham and Lodish
Brand A Baseline
Borrowed Sales (Assuming No
Choice Effect)
(1987, 1993) approach would compute incremental
Incidence Probability
1
units forbrand A by subtracting the baseline sales (2
Choice Probability
0.5
units) from the total sales on promotion (8 units), giv-
Quantity Model
8
ing incremental sales of 6 units. Truly incremental
Expected Baseline
Borrowed Quantity
4
sales, however, are likely to be less than 6 units. To see
this, begin by noting that those 6 units can be decom-
The Abraham and Lodish (1987, 1993) approach
posed into 2 units due to switching (0 units forthe
would estimate an incremental volume of 6 units (total
competitor’s brand vs. 2 units in the baseline case) and
sales minus baseline sales). This volume, however, is
4 units due to stockpiling (a category purchase of 8
truly incremental if and only if the 2 units of “bor-
units versus 4 units in the baseline case). Of the 4 units
rowed sales” all end up in incremental consumption
stockpiled, 2 are incremental for brand A, because they
forhousehold 3 (i.e., there is no cannibalization of fu-
can be attributed to the promotion’s effect on brand
ture sales). At the time of a promotion, we do not know
choice. (With a 0.50 baseline choice probability the in-
how many (if any) of those 2 borrowed units (4 base-
ventory is expected to be 50% brand A and 50% the
line and borrowed minus 2 baseline) will become in-
competitor’s brand.) Thus, 4 out of the 6 units making
cremental consumption for the household. (Note that
Marketing Science/Vol. 18, No. 3, 1999
279

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
baseline plus borrowed sales include baseline sales plus
consequence of previous choice decisions. This is cap-
those sales that will turn out to be either stockpiled or
tured via the last brand purchased (LBP) variable in
extra consumption.) Therefore, our approach takes the
the choice model (see the Appendix, Equation (A2)).
difference between total sales (8 units) and baseline
Thus, a promotion for brand A which results in a pur-
plus borrowed sales (4 units) to be incremental at that
chase of brand A will increase the choice probability
time. We then determine how much, if any, of the 2
forbrand A at the subsequent choice occasion. We
borrowed units to classify as incremental by estimating
compute this carryover effect by simulating baseline
whetherthere is additional consumption by the house-
plus borrowed sales with the LBP variable set to the
hold in future periods (see the Appendix, Equation
value it would have had, had no promotions for brand
(A10)). Those units are then credited as incremental to
A been offered (see the Appendix, Equations (A13) and
the period in which the added consumption is realized.
(A14)).
The response model in Equation (1) provides an es-
Putting all of the above together, from the manufac-
timate of total sales, E( h
Q ). To obtain an estimate of
turer’s perspective, a promotional event can produce
it
incremental sales, we simulate baseline plus borrowed
truly incremental sales under three conditions: (1) con-
sumers switch to the target brand (choice effect), (2) a
sales, E(
h
BBQ ). Incremental sales are then given by the
it
temporary increase in consumption takes place (con-
difference between these two quantities. We note that
sumption effect), or (3) future sales increase due to pur-
simulated baseline sales,
h
E(BQ ), should be a function
it
chase event feedback. Nonincremental volume (base-
of the inventory and consumption levels that would
line
plus
borrowed)
is
simulated
by
setting
have been realized in the absence of promotional ac-
promotional variables to zero in the choice model, in-
tivity for the target brand (brand-size alternative i).
cremental consumption to zero, and removing pur-
Similarly, simulated baseline plus borrowed sales
chase feedback effects from the choice probabilities.
should be a function of the inventory and consumption
Mathematically, this is expressed as
levels that would have been realized if promotions on
the target brand resulted only in borrowed sales (via
h
h
h
h
h
E(BBQ )
it
E(Q |
it Qit
0)|INVt INVBBt
purchase acceleration and/or stockpiling). Thus, in
h
h
h
h
Pt (i|inc)|NO-PROMO
Pt (inc)|INVt INVBB
(2)
computing simulated baseline plus borrowed sales, we
t
NO-PURCH.FEEDBACK
remove the choice effect of brand-size i’s promotions.
We then compute how many of those borrowed units
where BBQ is baseline plus borrowed volume,
h
result in incremental consumption in future periods.
INVBBt is the household’s inventory given that the
Forthis computation we use the difference between
choice effect of promotions for brand-size i is removed,
the consumption rate for the simulated baseline plus
NO-PROMO sets promotional variables (e.g., tempo-
borrowed sales,
h
CRBB
rary price reduction, feature, display) to zero, and NO-
t , and the consumption rate per-
taining to baseline sales,
h
CRB
PURCH.FEEDBACK removes purchase event feedback
t . Thus, the borrowed vol-
ume that results in incremental consumption can be
effects from the choice model. For example, the three
estimated period by period by the difference between
factors in Equation (2) respectively correspond to the
the following two consumption rates,
h
magnitudes 8, 0.5, and 1 in the computation of the 4
t
t .
h
CRBB
CRB
Those units are then added to the incremental sales for
baseline plus borrowed units in our previous example.
period t. Thus, our model captures the incremental
Note that this numbermay be significantly higherthan
component, if any, of the “borrowed” sales from a pro-
the expected baseline sales given by:
motion by summing the consumption carryover effect
h
h
h
E(BQ )
it
E(Q |
it Qit
0)|NO-PROMO,
across
future
periods.
This
is
given
by
h
h
INV
INVB
t
t
h
s
t
1
s
s.
h
CRBB
CRB
h
h
Our model also includes the carryover effects of pur-
Pt (i|inc)|NO-PROMO
Pt (inc)|NO-PROMO, ,
(3)
h
h
NO-PURCH.FEEDBACK
INV
INVB
t
t
chase feedback. These effects result in an increase or
decrease in choice probabilities in future periods as a
where BQ refers to baseline volume and
h
INVBt is an
280
Marketing Science/Vol. 18, No. 3, 1999

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
estimate of what the household’s inventory level
sales via the acceleration and quantity effects of pro-
would be if no promotions on brand-size i had been
motional events. For product categories which do not
run. (The three factors in Equation (3) would respec-
play the role of traffic builders, store competition in-
tively be the magnitudes 4, 0.5, and 1 in the compu-
volves capturing a higher share of the consumer’s cate-
tation of the 2 baseline units in ourprevious example.)
gory purchases, once the shopper enters the store. Con-
The expected incremental numberof units (forthe
sequently,
sales
that
are
borrowed
for
the
manufacturer) of brand-size alternative i sold to house-
manufacturer can be incremental for the retailer as a
hold h at time t is then obtained by (1) subtracting base-
result of this indirect type of store competition (see
line plus borrowed sales from total expected units, and
Bucklin and Lattin 1992, Abraham and Lodish 1993, p.
(2) adding back any previously “borrowed” sales that
250).
resulted in incremental consumption in period t
Latent Class Analysis
(
h
h
h
DCRt
CRBBt
CRBt ). Incremental units are
Heterogeneity in consumer response parameters is ad-
given by
dressed with latent segment analysis (e.g., Bucklin et
h
h
h
h
E(DQ )
al. 1998). In the latent segment model, Equation (1) is
it
E(Q )
it
E(BBQ )
D
it
CRt .
(4)
modified to
The expected numberof units at the household level
h
h
h
is estimated conditional on a shopping trip taking
E(Q )
it
p E
s (Qsi |
t Qsit
0)
s
place. To obtain the expected numberof units fora
given store or chain, we multiply those expected num-
h
h
P (
st i|inc)
P (
st inc),
(7)
berof units by the probability that the panelist makes
where ps equals the size of segment s (0
ps
1). Here
a shopping trip to that store or chain. This probability
h (
st i|inc) is the brand-size choice probability,
h
P
Pst(inc) is
is obtained from the household’s history of store visits.
the category purchase incidence probability, and
We assume that the marketing activity of the individ-
h
h
h
E(Qsit
qs |
it Qsit
0) is the expected numberof units
ual product category does not affect consumers’ store
bought given that household h bought item i and given
choice decisions (i.e., the category is not a traffic
that household h is a memberof segment s. To deter-
builder, cf. Tellis and Zufryden 1995). The final inputs
mine the numberof latent segments to retain, we com-
to the optimization model are
pare models according to the Bayesian Information
h
h
s
E(DQ )
Criterion (BIC) and select the number of segments that
it
h
E(
maximizes the BIC.1
DQ )
it
, and
(5)
H
h
h
s
E(BBQ )
Optimization Module
it
h
E(BBQ )
The purpose of the optimization is to search for the
it
, where
(6)
H
promotion calendar (i.e., the sequence of weekly price
H
the numberof panelists in the sample, and
discounts, features, and displays) that maximizes net
incremental contribution for the manufacturer’s target
sh
the probability that panelist h makes a shopping
trip to the store.
brand-size i, given retailer response and competitive
activity. Below, we present the mathematics for the ob-
Once the components of the consumerr
esponse
jective function, constraints, and variable definitions.
model (choice, incidence, and quantity) are calibrated,
We then describe them and discuss their properties.
parameter values together with the household specific
1
variables (e.g., brand and size loyalties, inventory, etc.)
Rust et al. (1995) have shown that the BIC (Schwarz 1978) is the
are used to compute the expected number of incre-
best overall model selection criterion. The BIC is given by LL (k/2)
ln (n) where LL is the log likelihood fit of the model, k is the number
mental (Equation (5)) and nonincremental (Equation
of parameters, and n is the sample size. Thus, models which add
(6)) units sold.
parameters without substantially improving the log likelihood will
Unlike manufacturers, retailers can increase their
be rejected.
Marketing Science/Vol. 18, No. 3, 1999
281

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
Manufacturer’s Objective Function
N
average number of category consumers
that shop in the store or chain (a scaling
max
K ,FEAT ,DISP
factor).
it
it
it
E(DQ
 T

it)
expected numberof incremental units of

dt
N
E(DQ
brand-size alternative i bought by a con-
it)
(BPRICEit

 t 1

sumerthat made a store visit in week t,

(1
Kit
DSTEP)
MCOSTit)

i.e., units bought by a consumerwho

T


dt
N
E(BBQ
would not have bought the brand-size
it)


t
1

had not it been on promotion (see Equa-

(BPRICEit
Kit
DSTEP)

tions (5)).

T


dt
(DISC
E(BBQit)
expected numberof baseline plus bor-
it
TCOSTit
FEATit


t
1

rowed sales, i.e., units of brand-size al-

FCOSTit
DISPit
DCOSTit)

ternative i bought by a consumerthat

T
13

made a store visit in week t and would

dt
N


t
T
1

have chosen brand-size i, regardless of its

E(DQ |
it RPRICEit RPRICE ,PC
t
it
0,FEATit 0,DISPit 0,)

promotional status (see Equation (6)).

(BPRICE
 (8)
BPRICE
i
MCOST ),
i
it
wholesale base (regular depromoted)
where t
1, 2, . . . , T is the planning horizon and t
price of brand-size i in week t.
T
1, T
2, . . . , T
13 are the subsequent 13 weeks
Kit
discount multiplierforbr
and-size i in
over which carryover effects are computed.
week t. If Kit
0, brand-size i is sold at
the base price in week t. When the man-
Constraints
ufacturer offers a discount, it is com-
puted as a multiple of a discount step
Kit are integer ∀t,
level, e.g., 5%.
where K
DSTEP
depth of discount step (orbase discount)
it
0, 1, 2, . . . , 10 ∀t,
(9)
according to manufacturer’s policy (e.g.,
DISCit are binary 0/1 variables ∀t,
(10)
5%).
MCOST
FEAT
it
manufacturer’s marginal cost of brand-
it are binary 0/1 variables ∀t,
(11)
size i in week t.
DISP
PRICE
it are binary 0/1 variables ∀t
(12)
it
shelf price of brand-size i in week t. Re-
lated to the previous variables by the
PROMOit
E,
(13)
equation
t
PRICEit
BPRICEit
(1
PTHRUit
T
PROMO
Kit
DSTEP)
(1
MKUP).
(17)
it
,
(14)
t
2
RPRICEit
regular (depromoted) retail price of
BPRICEjt [MKUP
Kjt
DSTEP
brand-size i, at time t [
BPRICEit
(1
j
t
MKUP)].
(1
PTHRUjt
(1
MKUP))]
P ,
R
(15)
PCit
retail price cut of brand-size i, at time t
PTHRU
[
BPRICEit
PTHRUit
Kit
it
f(K ).
it
(16)
DSTEP], so that shelf price can also be
Definitions and Relationships Among Variables
expressed as PRICEit
RPRICEIt
PCit.
t
week number.
PTHRUit
retailer’s pass-through, i.e., the propor-
i
manufacturer’s target brand-size.
tion of manufacturer’s discount the re-
j
a brand-size alternative in the category.
tailerpasses to the consumer.
d
discount rate.
MKUP
retailer’s markup in percent.
282
Marketing Science/Vol. 18, No. 3, 1999

---

SILVA-RISSO, BUCKLIN, AND MORRISON
Planning Manufacturers’ Sales Promotion Calendars
DISCit
Discussion of Optimization Model Formulation
0 if K
We begin by noting that ourspecification of the objec-
it
0, i.e., if no discount is offered,
0 if K
tive function in Equation (8) is based on incremental
i,t-1
1, i.e., if a discount started in
(18)
a previous week,
profits, not total profits. This means that the objective
1 otherwise.
function does not include profits from baseline sales
or profits from borrowed sales. Instead, it includes the
TCOSTit
tagging cost, i.e., the fixed cost charged
opportunity costs associated with discounting prices on
by the supermarket chain to discount the
price of brand-size i in week t. This cost
those sales. Consumption and purchase feedback ef-
is charged only once during a promotion
fects impact future periods. Following Neslin et al.
period.
(1995, p. 755) we extend the time horizon for the op-
timization procedure to include a 13-week period sub-
FEATit
sequent to the planning horizon (t
T
1, T
2,
1 if a feature advertisement is offered
. . ., T
13). In this way, we allow the carryover effects
forbrand-size i in week t,
(19)
of promotions at the end of the planning period to be
0 otherwise.
realized, but we do not permit promotions beyond the
FCOST
planning period (t
1, 2, . . ., T). We note that in all
it
fixed cost charged by the chain to run a
feature advertisement for brand-size i in
the applications of the model, carryover effects were
week
negligible beyond the 9th week following a promotion
event.
DISPit
Turning to the specifics of Equation (8), note that the
1 if an in-store display is
offered for brand-size i in week t,
(20)
manufacturer has three decision variables for each
0 otherwise.
week: Kit, FEATit, and DISPit. Kit specifies the level of
discount offered each week. Manufacturers typically
DCOSTit
fixed cost charged by the chain to set up
offer temporary price reductions that are a multiple of
a display forbrand-size i in week t.
a discount step, e.g., 5%.2 Forexample, a TPR could
PROMO
range from 0% to 50% in steps of 5%.3 This behavioris
it
1 if FEATit
1 or DISPit
1 or Kit
1,
captured by defining TPR
(21)
it
Kit
DSTEP, and by
0 otherwise.
constraining Kit with Equation (9). FEATit, and DISPit
BPRICE
are 0/1 variables (see Equations (11) and (12)) that in-
i
average wholesale base (regular deprom-
oted) price of brand-size i during the
dicate whether a feature or display is run in week t.
planning period (t
1, 2, . . . , T).
The objective function has fourcomponents, each of
RPRICE
which is one term in Equation (8): (1) the expected con-
i
average regular (depromoted) retail
price of brand-size i during the planning
tribution from incremental units, (2) the expected op-
period (t
1, 2, . . . , T).
portunity cost of selling at a discount to consumers
MCOST
who would have bought the brand at the regular price,
i
average manufacturer’s marginal cost of
brand-size i during the planning period
(3) the fixed costs associated with promotion decisions,
(t
1, 2, . . . , T).
and (4) the carryover effects from consumption and
E
minimum
numberof
pr
omotional
purchase feedback over a 13-week period subsequent
“events” required by the retailer during
2
the planning period, E
0.
Evidence forthis decision behaviorcomes from ourdiscussions
T
numberof weeks orperiods in the plan-
with the collaborating consumer goods company and from contacts
with marketing research firms.
ning horizon.
3Note that here we are referring to discount levels offered by the
PR
minimum category profit level required
manufacturer to the retailer. The discount that the consumer will be
by the retailer to support the promotion
exposed to will depend on the retailer pass-through decision (see
program.
Equation (16)).
Marketing Science/Vol. 18, No. 3, 1999
283

---