Shelf management and space elasticity

TL;DR: It is found that location had a large impact on sales, whereas changes in the number of facings allocated to a brand had much less impact as long as a minimum threshold (to avoid out-of-stocks) was maintained.

About: This article is published in Journal of Retailing.The article was published on 1994-12-01 and is currently open access. It has received 652 citations till now.

Summary

1. Introduction

• Since the beginning of the last century, many studies have been conducted regarding the plastic deformation processes in metallic materials in order to improve the global understanding of the deformation mechanisms, of the elastic–plastic transition, of the deformation localisation and, obviously, of the damage processes leading to ultimate failure.
• An extensive review of the early work in this field was published by Bever et al. [5] including the pioneering works of Taylor et al. [6–8].
• There is a lack of information on energetics regarding the local deformation processes in heterogeneous material like polycrystals.
• The objective of this work is to propose such a comprehensive procedure.
• In the second, a calibration procedure is developed to reach a fine estimation of the temperature of all material points along their deformation path at the specimen’s surface.

2.1. Review of techniques

• To their knowledge, only four experimental techniques of combined in situ calorimetric and kinematic measurements at the microstructural scale of metals have been developed during the last few years.
• Its main advantage is that QIRT and DIC constraints are separated.
• Because of the resolution of currently available IR cameras, this technique seems to be much more adapted to aggregates whose grain size is greater, at best, than 200 μm. (3) Single-face measurement: Both imaging systems (CCD and IR camera) observe the same zone at the same instant.
• This technique was used in [17] and requires a correction of the distortions introduced by the set-up in the experimental fields.
• For better accuracy, the heterogeneous emission properties of the coating have to be identified.

2.2. Focus on our ‘single-face’ experimental set-up

• The experimental set-up and data on which their study is based were introduced in [19].
• The sample is filmed by a focal plane array (FPA) Cedip Jade III MWIR camera whose detector matrix is 320 240.
• It is used with a high magnification lens called G1.
• The key feature of the fully coupled measurements lies in the coating applied on the sample, also known as (3) Coating.
• The DIC displacement data are, therefore, used to track the displacement of the material points in order to express the temperature fields in the undeformed configuration.

3. Eulerian thermal metrology

• Therefore, it is essential to establish a calibration strategy that minimises the error at each step.
• This part focuses on the calibration steps that must be conducted in the Eulerian configuration.

3.1.1. Pixel to pixel

• The IR camera expresses the received flux (emitted by an object) in DL.
• The procedure is performed according to the following equation: UðIT; Tk ; iÞ ¼ Xp u¼1 auðDL i kÞ u ð1Þ where coefficients au are determined by the least squares method and p corresponds to the degree of the classic polynomial calibration law.
• Once the thermal field is recovered using a pixel-to-pixel calibration (Digital Level to flux) and then the Botlzman law (Equation (2), flux to temperature), a comparison between the measured thermal field and the uniform one of the observed BB could be done in order to estimate the accuracy of the calibration method.
• It shows that the mean error for each pixel, when the flux radiated by the object remains in the [405–465].
• According to Figure 2(b) and considering the interval [25–27 °C] corresponding to the specimen’s temperature variation during the monotonic tensile test3 considered in this study, one could conclude that the present calibration remains valid for a coating emissivity that would range from 0.92 to 0.98.

3.1.2. Temporal noise

• As previously mentioned, the calibration functions are obtained from averages over 100 IR fields at each given BB temperature.
• The effective measurement uncertainty will necessarily increase.
• Taking into account this additional constraint, this implies that the minimal resolution provided by the IR imaging system is 90 90 μm (3 3 pixels) which has been used in [24].
• Note that the low-pass filter will be applied on the Lagrangian signal and not directly on the Eulerian one.

3.1.3. Flux decomposition

• In order to perform proper quantitative IR thermography at a local scale, two phenomena have to be taken into account.
• A reasonable physical assumption is to consider that the reflections affect the field at low spatial frequency (LSF) and are Eulerian, whereas the ‘apparent emissivity’ field affects the observed field at high spatial frequency (HSF) and is Lagrangian (see Figure 4(b)).
• Analysing the LSF of / by spectral decomposition, one could write: /jLSF ¼ objr T 4 obj þ /refl rT 4 cam ð6Þ with /jLSF is the measured flux without high spatial frequencies.
• Its value is 416.6Wmm 2. Equation (6) leads to: /refl ¼ /jLSF objr T 4 obj þ rT 4 cam ð7Þ Combining Equations (7) and (5), it is now possible to determine the apparent emissivity field of the specimen at a thermal steady-state.
• The temperature error field is built from the difference between the field obtained with a uniform emissivity and the one obtained with the apparent emissivity map (see Equation (8)).

3.2. Digital image correlation

• Kinematic fields are obtained from visible images of the sample taken by the CCD camera and subsequently processed by the digital image correlation software CorreliQ4 [29].
• Obviously, the specimen must exhibit a sufficient speckle texture in terms of gray levels.
• CorreliQ4 assumes a bilinear kinematics within 4-noded square elements.
• The uncertainty on the displacements calculation for a given experiment and a given DIC software mainly depends on two points: (1) the coating, i.e. its random aspect and the gray level domain it covers and (2) the ZOI size: the larger the ZOI size, the greater the accuracy but the smaller the spatial resolution.

3.3. Lagrangian metrology and thermography

• To express the IR scene in its undeformed configuration, it is necessary to follow the radiative flux associated with each material point of the observed zone before moving it back in the reference configuration.
• This task is carried out, thanks to the displacement fields obtained by DIC.
• It constitutes the concept of ‘Lagrangian thermography’.
• For this, a time and space matching between the kinematic and thermal fields has to be done.

3.3.1. Time and space matching

• Kinematic and IR measurements are first synchronised in space by using some marks made on the specimen that are observable in both visible and IR wavelengths.
• They allow us to rotate, translate and stretch the fields in order to precisely match each of them at the initial instant.
• A time synchronisation is obtained by triggering the beginning of the acquisition made by both cameras, which will thereafter run at their own frequencies.
• Thus, one assumes a spatio temporal interpolation of the kinematic and IR field on: the EBSD mesh for space, the IR grid for time.
• It constitutes a trilinear interpolation (2D in space, 1D in time) of data, which is implemented in Matlab using the interp3 function.

3.3.2. Lagrangian thermography

• Figure 7 recalls the principle of the Lagrangian thermography as presented in [26].
• PIR;i denotes a point in the IR camera coordinate system expressed in the current configuration, i. e. at time ti and PCCD;i a point in the CCD camera coordinate system in the same configuration.
• Note that PCCD;0 and PIR;0 are in the same coordinate system, thanks to space and time synchronisations and to spatio-temporal linear interpolation (see previous section).
• Then, the displacement between instant 0 and ti, expressed in the initial configuration and denoted U i 0, can be directly applied to PIR;i. Following Equations (9) and (10), one obtains: PIR;0 ¼ PIR;i U i 0 ð11Þ Equation (11) has to be applied to each material point PIR;i at each time ti.
• Finally, the displacement, radiative flux and emissivity fields are expressed in the same reference system.

3.3.3. Temporal noise correction

• The temporal noise that appears in IR fields (see Figure 4) is mainly due to the variation of flux in the room during the test and to the intrinsic noise of each pixel.
• It is not an easy task as a detector is traversed by different material points during the deformation of the specimen.
• Reversely, within the Lagrangian thermography framework, as a material point passes through different detectors during the deformation of the specimen, the material point associated with noise will change with the time.
• A classic low-pass filter that could be applied in order to remove high time frequencies in Fourier space.
• One can observe that the main variations of radiative flux are conserved in this case.

3.3.4. Apparent emissivity correction

• In Section 3.1.3, a local spatial variation of flux response was identified on the unloaded specimen.
• The nature of this flux distribution was quantified and attributed to the emissivity distribution of the coating.
• Then, in Section 3.3.2, Lagrangian thermography was performed on IR scenes in order to express both fields in the same initial configuration.
• Microstructural thermal fields on an AISI 316L austenitic stainless steel specimen.

4.1. Material and test

• The main features of the test analysed in this section are described in details in [19].
• The material studied is an AISI 316L austenitic stainless steel.
• Fully coupled kinematic and thermal fields measurements were performed during the monotonic test at the microstructure scale.
• Figure 9 presents the EBSD field of the 1st angle /1 of the Euler angle triplet (/1;U;/2), which characterises the 3D orientation of the material points in the global frame of the analysed area after the test.
• The EBSD analysis shows that, in the 5mm 5mm central area, the microstructure is composed of 1776 grains with a 118 μm mean grain size (measurement based on diameter approximation).

4.2. Field projection on microstructure

• In order to analyse all the available fields (temperature, displacements, crystallographic orientations …) and to obtain deformation and thermal flux fields by derivation of the primal ones, the authors proposed to use an original method presented in detail in [32].
• A minimisation, in the sense of the least squares method, between the calibrated thermal field and a polynomial function is done within each grain, regardless of its neighbours, at each time increment.
• Displacement fields within each grain and at each time increment are projected on a biparabolic base and as strain is calculated from the displacement gradient, the authors implicitly assume here a bilinear strain field within grains.
• As conductive fluxes are calculated from the temperature Laplacian, uniform conductive exchanges within grains at each instant are implicitly assumed through this hypothesis, also known as (2) Biparabolic thermal field.
• One could point out that more than 84% of the studied area contains grains whose size is greater than the spatial resolution.

4.3. Some results

• Figure 10(a) and (b) presents the calibrated temperature field and the projected one at 250MPa nominal stress.
• This is confirmed on the strain map presented in Figure 10(d), which corresponds to a nominal stress of 250MPa and a spatial mean strain of 2.5%.
• A simple point to point correlation is, therefore, difficult.
• The available calibrated data consist of the displacement and temperature fields (as illustrated in Figure 10) over time.
• Even if the projection method naturally accentuates the presence of such discontinuities, raw thermal data show that many of these discontinuities do exist at grain or twin boundaries and that their values are over the experimental error on temperature measurements [35].

5. Conclusion

• A complete metrological procedure was introduced in order to obtain in situ fully coupled kinematic and thermal fields expressed in the reference configuration.
• Special attention was given to the decomposition of the measurement in errors: a Eulerian part related to the sensors dynamics, a Eulerian part related to reflections due to the environment and the experimental set-up, a Lagrangian part related to the intrinsic emission properties of the specimen’s surface.
• The metrological procedure was applied to the digital level and gray level frames recorded by IR and CCD cameras, respectively, in [19].
• The uncertainty of measurement is lower than 30mK and the frequency of the phenomena that can be captured reaches 25Hz.
• This analysis was performed assuming a projection of the thermal fields on the specimen’s microstructure.

Figures

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Figure 7), there seemed to be an almost linear relationship between space and sales potential, suggesting significant opportunities for improving performance. One possible explanation for this linear relationship is that Campbell's dominates the category, and from a distance, all red and white Campbell's cans look alike. Hence one has to read each label individually in order to find the soup one desires, making the probability of being chosen directly proportional to a brand’s space allocation.

Table 1

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Table 3

Frequently asked questions

Q1. What have the authors contributed in "Shelf management and space elasticity" ?

Through a series of field experiments, the authors measured the effectiveness of two shelf management techniques: “ space-to-movement, ” where they customized shelf sets based on store-specific movement patterns ; and “ product reorganization ” where they manipulated product placement to facilitate cross-category merchandising or ease of shopping. This technical report is available at ScholarlyCommons: https: //repository. The authors would like to thank Dominick 's Finer Foods, Information Resources Inc., and Market Metrics for their assistance and provision of data. Xavier Drèze is Director of MIS and a doctoral student, Stephen J. Hoch is Robert P. Gwinn Professor of Marketing and Behavioral Science, and Mary E. Purk is Manager of the MicroMarketing Project, all at the University of Chicago. 

Q2. Why did the authors remove all25 promotional sales from the dataset?

Because the authors were interested in understanding space elasticity for permanent display space, the authors removed all25promotional sales from the dataset. 

Q3. What is the main challenge facing retailers?

one of the many challenges facing retailers is how to properly allocate shelf space to the multitude of products they sell. 

Q4. Why is the evidence on the sales impact of space management limited?

Evidence on the sales impact of space management is limited because of the high costs of implementing controlled experiments in the field. 

Q5. What are the reasons for the emergence of slotting allowances?

Retailers claim (Freeman 1991, Supermarket News 1984) that slotting allowance are used to defray the administrative and logistic costs associated with the introduction of new items rather than to buy a certain amount of shelf space. 

Q6. How many purchases are planned in advance of visiting the store?

Long-standing surveys of supermarket shopping behavior have found that only about 1/3 of purchases are specifically planned in advance of visiting the store (Dagnoli 1987). 

Q7. What would be the way to reduce the overall space allocated to a category?

If the low space34elasticities that the authors encountered were to hold up, retailers could cut costs substantially by reducing the overall space allocated to a category. 

Q8. What is the way to maximize shelf space?

Retailers want to maximize category sales and profits, regardless of brand identity; they must allocate a fixed amount of shelf space in the best possible way. 

Q9. What did the authors do to increase the difficulty of making price comparisons?

In the bath tissue category the authors physically separated different size packages of the samebrand by about 12 feet in order to increase the difficulty of making price comparisons and possibly increase sales of higher margin big sizes. 

Q10. What is the reminder for a cigarette smoker?

The best reminder for a cigarette smoker is probably the package of their favorite brand; so when arranging the singlepack cigarette fixture at the express check-out line, the retailer can maximize reminders across consumers by placing the highest share brands in the most visible locations. 

Q11. How did Bultez and his colleagues extend the shelf management experiment?

Bultez et al. (1989) extend this work by utilizing an asymmetric attraction model and incorporate multiple sizes of the same brand. 

Q12. How many supermarkets do consumers visit a week?

This means that, on average, consumers shop at 3 to 4 different supermarkets on a regular basis to satisfy their consumption needs. 

Q13. What is the way to avoid out-of-stocks?

In such cases where space is very tight, correct in-store inventory levels will be much more crucial to avoid out-of-stocks and at the same time maintain reasonable restocking cycles. 

Q14. How was the laundry care planogram originally arranged?

laundry care originally had been vertically blocked, moving horizontally14from liquid detergent to powder detergent to fabric softener. 

Q15. What is the likely reason for the increase in sales generated by the test planograms?

It is more likely that the increase in20sales generated by the test planograms comes from consumers purchasing a higher share of their category requirements at Dominick’s rather than the competition. 

Q16. How many feet of softeners were placed between the liquid and powder detergents?

To enhance complementary purchase, the authors placed 8-12 feet of softeners in between the liquid and powder detergents where it was more likely to be noticed by buyers of both forms of detergent. 

Q17. Who monitored the integrity of the planograms?

Auditors from the Graduate School of Business at the University of Chicago monitoredthe integrity of the planograms (spatial layouts of the category) bi-weekly.