Using the Pack‐and‐a‐Half Rule to Eliminate Backroom Inventories in Retail Operations

• Published date: 01 September 2018
• DOI: http://doi.org/10.1111/jbl.12191
• Date: 01 September 2018
• Author: Brent D. Williams,Cuneyt Eroglu,Matthew A. Waller

Using the Pack-and-a-Half Rule to Eliminate Backroom Inventories

in Retail Operations

Cuneyt Eroglu

1

, Brent D. Williams

2

, and Matthew A. Waller

2

1

Northeastern University

2

University of Arkansas

In the retail industry, backroom inventories are typically associated with higher labor costs and greater operational complexity. Thus, retailers

look for ways to eliminate backroom inventories. A heuristic used for this purpose is the pack-and-a-half rule which suggests that the shelf

space allocated for a product should be at least 50% larger than the case pack quantity in which the product is delivered. Despite its popularity

among retailers, the pack-and-a-half rule has been ignored in the academic literature. We introduce the pack-and-a-half rule, assess its impact

on a retailer’s profits, identify cost, demand, and product characteristics driving this impact, and propose a modification. Based on an analysis

of data obtained from a retailer on 1,986 SKUs in 20 categories, we find that the pack-and-a-half rule decreases a retailer’s profits, on average,

by 10% when applied uniformly across all SKUs. Further, this decrease is significantly affected by product depth, product width, demand elas-

ticity, case pack quantity, and inventory carrying cost. Finally, we develop a set of modifications based on these variables where the pack-and-

a-half rule is applied selectively and in a stepwise fashion. These modifications limit the decrease in a retailer’s profits to a range between 6%

and 7%.

Keywords: retail operations; shelf space allocation; case pack quantity; pack-and-a-half rule; inventory management; replenishment

INTRODUCTION

Retail shelf space has been referred to as “the most expensive

real estate of the world”(Kaikati and Kaikati 2006, 141). In the

retail supply chain, shelf space is scarce and the competition for

the limited shelf space is intense (Kurtulus and Toktay 2011;

Mart

ınez-de-Alb

eniz and Roels 2011). Effectively managing

retail operations is challenging because retailers face many trade-

offs related to shelf space scarcity in their decisions regarding

product assortment, shelf space allocation, and inventory man-

agement (Mantrala et al. 2009). Recognizing the importance of

these decisions to a retailer’s operational and financial perfor-

mance, researchers have produced extensive retail operations lit-

erature over the last few decades (K€

ok et al. 2009). Similarly,

consulting firms and software vendors offer a growing variety of

category and inventory management solutions for retailers

(H€

ubner and Kuhn 2012). While both academics and practition-

ers realize the critical nature of retail operations, it is widely

acknowledged that there is a major discrepancy between theory

and practice. When describing the extent of this disconnect

between these two communities, K€

ok et al. (2009) observe that

“the language or terminology of each group is substantially dif-

ferent and neither group acknowledges the existence of the

other”(p. 146).

While no single paper can bridge this sizable gap, we would

like to take a step in this direction by considering a common

practice that remains largely overlooked in academic research,

namely the pack-and-a-half rule. The pack-and-a-half rule sug-

gests that the shelf space allocated to a stock-keeping unit (SKU)

must be at least one-and one-half times the case pack quantity in

which that SKU is delivered (Food Marketing Institute and Gro-

cery Manufacturers of America 2000; Gruen and Corsten 2007;

Baumann 2010; Eroglu et al. 2011). For example, if an SKU is

delivered in a case pack which contains 12 consumer units, the

shelf space allocated to that particular SKU must be large

enough to hold at least 18 units.

The goal of the pack-and-a-half rule is to avoid the need for

backroom storage. This rule is based on the case pack quantity in

which a particular SKU is delivered because the case pack quantity

often becomes the de facto order quantity or minimum order quan-

tity (Chow et al. 2012) as “a large portion of SKUs sell fewer than

one item per store per week”(Norek 1998, 387). The expectation

is that when a replenishment order arrives from the supplier, the

shelf will have enough space to accommodate all consumer units

in a case pack. If there is not enough empty space on the shelf,

some inventory must be moved to the backroom for storage, which

can lead to increased costs and greater operational complexity for

a retailer (DeHoratius and Raman 2008). First, holding inventories

in two locations (on the shelves and in the backroom) increases

labor costs as shelves have to be restocked from the backroom

between supplier deliveries (Wen et al. 2012). Second, when

shelves are not instantly restocked from the backroom as soon as

shelf inventory is depleted, it is possible to have an empty shelf

when there is inventory in the backroom. If a customer sees an

empty shelf, he or she may assume that the store is out of stock

and forgo the purchase, which increases the amount of lost sales

(Gruen and Corsten 2007). Third, with a backroom, store invento-

ries have to be tracked at two different locations, which compli-

cates the monitoring of inventories and can increase inventory

record inaccuracies (Gruen and Corsten 2007). Fourth, products

can be misplaced, forgotten, damaged, or stolen in the backroom

(Wen et al. 2012). Fifth, inventories displayed on shelves stimulate

demand while inventories stored in the backroom do not (Balakr-

ishnan et al. 2004). Thus, a retailer may want to use the entire

retail floor to display inventories and avoid backroom storage.

Corresponding author:

Cuneyt Eroglu, Supply Chain and Information Management Group,

D’Amore-McKim School of Business, Northeastern University, 360

Huntington Avenue, Boston, MA 02115, USA; E-mail:

c.eroglu@northeastern.edu

Journal of Business Logistics, 2018, 39(3): 164–181 doi: 10.1111/jbl.12191

© 2018 Council of Supply Chain Management Professionals

To the best of our knowledge, there are no surveys about the

popularity of the pack-and-a-half rule. However, we contacted

two vendors of shelf space management software, namely, JDA

and Nielsen, who collectively account for more than two-thirds

of the market (H€

ubner and Kuhn 2012). Both companies indi-

cated that the pack-and-a-half rule is available in their space

planning tools and many of their customers are actively using

this rule. Consequently, it can be argued that the pack-and-a-half

rule is widely applied by retailers.

When a retailer uses the pack-and-a-half rule, it deviates from

the original shelf space allocation which is typically an “optimal”

or a “near-optimal”solution according to some criterion. More

specifically, SKUs that were initially assigned a shelf space less

than one-and-one-half times their case pack quantity receive

additional shelf space while SKUs that were initially assigned a

shelf space greater than one-and-one-half times their case pack

quantity have to give up some of their shelf space to accommo-

date the other products. It is conceivable that the profitability of

the retailer may suffer as a result of this deviation. However,

many retailers prefer this deterioration over the necessity of

establishing and managing a backroom. Of course, a retailer can

negotiate with the manufacturer to customize the case pack quan-

tity for its operations and avoid both the backroom and the pack-

and-a-half rule. While this type of collaboration is certainly pos-

sible between larger retailers and manufacturers, the cost of cus-

tomizing the case pack quantity for each of their customers

would be prohibitive for most manufacturers. In many cases, a

manufacturer will unilaterally decide the case pack quantity, and

a retailer will have to resort to the use of the pack-and-a-half

rule. For some products, this may mean that a retailer’s shelf

space decision is effectively derived from a decision made by

the manufacturer.

This paper seeks to investigate the following research ques-

tions:

1 What is the effect of the pack-and-a-half rule on a retailer’s

profits?

2 What is the effect of the pack-and-a-half rule on shelf space

allocation?

3 How can a retailer reduce any negative effects of the pack-

and-a-half rule?

To address the first research question, we assess the effect of

the pack-and-a-half rule on a retailer’s profits using actual retail

data. Based on the seminal work by Urban (1998), we develop a

shelf space allocation model where the pack-and-a-half rule can

be applied. We measure the decrease in a retailer’s profits after

applying the pack-and-a-half rule. An analysis of data obtained

from a retailer (a supermarket chain) on 1,986 SKUs in 20 cate-

gories reveals that the pack-and-a-half rule, when applied uni-

formly across all SKUs, decreases the retailer’s profits by 10%,

on average, and by more than 38%, in some categories. This

finding establishes the substantial impact the pack-and-a-half rule

can have on the retailer’sfinancial performance. To gain a more

nuanced understanding of this impact, we estimate the moderat-

ing effects of several variables including shelf dimensions, SKU

dimensions, unit profit margin, unit cost, demand rate and elas-

ticity, case pack quantity, ordering cost, and inventory carrying

cost.

To address the second research question, we explore the

shelf space allocation process in three steps. First, we explore

how some SKUs are allocated more or less than pack-and-a-

half of shelf space, and which variables drive this distinction.

Second, we observe the additional shelf space allocated for the

SKUs that originally had less than a pack-and-a-half of shelf

space along with the variables that drive this increase in shelf

space. Third, we measure the amount of shelf space lost by

SKUs that originally had more than pack-and-a-half of shelf

space, and assess the effects of various factors on this loss in

shelf space. The results of this analysis shed light on what

type of SKUs gain or lose shelf space as a result of the

pack-and-a-half rule and tie these changes in shelf space to

the decrease in profits.

To address the third research question, we develop a num-

ber of modifications that a retailer can use to contain the

potential negative effects of the pack-and-a-half rule. At pre-

sent, retailers use the pack-and-a-half rule uniformly across all

SKUs in a category. However, it is plausible that any potential

negative effects of the pack-and-a-half rule can be reduced

when it is selectively and judiciously applied to SKUs with

diverse demand, supply, and cost characteristics. Having identi-

fied the variables that moderate the effect of the pack-and-a-

half rule, we test a number of modifications that a retailer can

make to limit the effects of the pack-and-a-half rule. Our

results show that a simple modification of the pack-and-a-half

rule based on the case pack quantity can lower the average

decrease in profits from 10% to under 7% and slightly more

complicated modifications can further lower the average

decrease in profits to under 6%.

This paper contributes to the existing literature in three ways:

First, we introduce the pack-and-a-half rule to the academic liter-

ature. As this popular yet overlooked practice receives more

attention in the academic literature, shelf space allocation models

should be more realistic and provide more relevant guidance to

practitioners. While no single paper by itself can close the gap

between academic and practitioner literatures described by K€

ok

et al. (2009), it is our hope that our paper serves to narrow this

gap to some degree.

Second, we identify the drivers behind the impact of the pack-

and-a-half rule. Our results indicate that the effect of the pack-

and-a-half rule varies across categories. We find that product

depth, product width, demand elasticity, case pack quantity, and

inventory carrying cost significantly influence the effect of the

pack-and-a-half rule on a retailer’s profits. In other words, we

identify conditions under which the pack-and-a-half rule will

have a smaller or greater effect on a retailer’s profits. This find-

ing provides retailers with a deeper understanding of the poten-

tial effects of the pack-and-a-half rule across the different

categories that they manage.

Third, based on our statistical results, we propose modifica-

tions of the pack-and-a-half rule where it is selectively applied to

SKUs with dissimilar characteristics. Using numerical simulation,

we assess the effectiveness of these various modifications in con-

taining the effect of the pack-and-a-half rule. Our results indicate

that a modification is most effective and easiest to implement

when it is based on segmenting case pack quantities into two

groups. Hence, these results can serve as a starting point for

The Pack-and-a-Half Rule in Retail Operations 165