## Abstract

With few exceptions, today’s retailers sell products across multiple categories. One strategic consideration of such retailers is product location, which determines how easy or difficult different categories are for customers to access. For example, grocery or department stores determine which products will be located closer to the entrance of the store versus at the back of it, while online retailers decide which products to feature on the homepage, and which will require scrolling or keyword search to get to. In this paper, we study how a retailer should optimally locate products within a store, when the locations chosen affect consumer search costs. We show that the retailer has an incentive to prioritize products with lower utility, contrasting with prior work. The intuition for our result is that the consumer may be willing to search less preferred products only at the lower cost, while the more preferred products will be searched even at higher search costs. This strategy benefits the retailer by increasing the number of products the consumer searches and thus, the ones she may buy. Our finding is robust to several extensions: (i) a retailer determining not only product locations, but also prices, (ii) independent (e.g. categories), as well as substitute products, and (iii) a focal retailer that faces competition. From a managerial perspective, we show that allocating products in the store without taking into account how this affects consumer search costs, might mean consumers overlook products they would otherwise purchase.

This is a preview of subscription content, access via your institution.

## Notes

- 1.
Milk, as well as other products, when on sale, may serve as loss-leader products, encouraging consumers to enter the store (Johnson 2017). Distinct from this mechanism, we provide a novel rationale for placing high expected utility items in the back of the store that is unrelated to their price and does not require them to be sold below cost.

- 2.
If products represent different categories, one can think of

*ε*_{j}as the highest utility observed from the products considered in that category. - 3.
Consistent with the literature, we let

*F*_{j}(*x*) =*P*(*ε*_{j}<*x*). - 4.
A heat map describing navigation patterns at Ikea and showing that consumers’ path through the store mirrors the store plan can be found at http://www.dailymail.co.uk/femail/article-1349831/Ikea-design-stores-mazes-stop-shoppers-leaving-end-buying-more.html.

- 5.
- 6.
See https://www.addictivetips.com/web/get-continue-watching-on-top-in-netflix/ for details on where the “continue watching” content is displayed on Netflix.

- 7.
Our proof is adapted from Cormen et al. (2009)

- 8.
Our proof is adapted from Cormen et al. (2009).

## References

Ainslie, A., & Rossi, P. (1998). Similarities in choice behavior across product categories.

*Marketing Science*,*17*(2), 91–106.Anglin, P. (1990). Disjoint search for the prices of two goods consumed jointly.

*International Economic Review*,*31*(2), 383–408.Anderson, S., & Renault, R. (1999). Pricing, product diversity, and search cost: a Bertrand-Chamberlin-Diamond model.

*The RAND Journal of Economics*,*30*(4), 719–735.Arbatskaya, M. (2007). Ordered search.

*The RAND Journal of Economics*,*38*(1), 119–126.Armstrong, M., Vickers, J., Zhou, J. (2009). Prominence and consumer search.

*The RAND Journal of Economics*,*40*(2), 209–233.Armstrong, M., & Zhou, J. (2011). Paying for prominence.

*The Economic Journal*,*121*(556), 368–395.Athey, S., & Ellison, G. (2011). Position auctions with consumer search.

*The Quarterly Journal of Economics*,*126*(3), 1213–1270.Branco, F., Sun, M., Villas-Boas, J.M. (2012). Optimal search for product information.

*Management Science*,*58*(11), 2037–2056.Branco, F., Sun, M., Villas-Boas, J.M. (2016). Too much information? Information provision and search costs.

*Marketing Science*,*35*(4), 605–618.Burdett, K., & Malueg, D. (1981). The theory of search for several goods.

*Journal of Economic Theory*,*24*, 362–376.Carlin, B., & Ederer, F. (2018). Search fatigue.

*Review of Industrial Organization*. forthcoming.Carlson, J., & McAfee, P. (1984). Joint search for several goods.

*Journal of Economic Theory*,*32*, 337–345.Chandon, P., Hutchinson, J.W., Bradlow, E.T., Young, S.H. (2009). Does in-store marketing work? Effects of the number and position of shelf facings on brand attention and evaluation at the point of purchase.

*Journal of Marketing*,*73*(6), 1–17.Chen, Y., & He, C. (2011). Paid placement: Advertising and search on the internet.

*The Economic Journal*,*121*(556), 309–328.Chen, Y., & Yao, S. (2016). Sequential search with refinement: Model and application with click-stream data.

*Management Science*,*34*(4), 606–623.Chib, S., Seetharaman, P., Strijnev, A. (2002). Analysis of multi-category purchase incidence decisions using IRI market basket data.

*Econometric Models in Marketing*,*16*, 57–92.Chick, S., & Frazier, P.I. (2012). Sequential sampling with economics of selection procedures.

*Management Science*,*58*(3), 1–16.Chintagunta, P., & Halder, S. (1998). Investigating purchase timing behavior in two related product categories.

*Journal of Marketing Research*,*35*(1), 43–53.Cormen, T., Leiserson, C., Rivest, R., Stein, C. (2009).

*Introduction to algorithms*, 3rd edn. Cambridge: MIT Press. Chapter 16.5 “Task scheduling problem”.De los Santos, B., & Koulayev, S. (2017). Optimizing click-through in online rankings with endogenous search refinement.

*Marketing Science*,*36*(4), 542–564.Erdem, T., & Winer, R. (1999). Econometric modeling of competition: A multi-category choice-based mapping approach.

*Journal of Econometrics*,*89*, 159–175.Ellison, G., & Ellison, S. (2009). Search, obfuscation, and price elasticities on the internet.

*Econometrica*,*77*(2), 427–452.Gamp, T. (2017). Guided search. Working article.

Gatti, R. (1999). Multi-commodity consumer search.

*Journal of Economic Theory*,*86*, 219–244.Ghose, A., Ipeirotis, P., Li, B. (2012a). Surviving social media overload: Predicting consumer footprints on product search engines. Working article.

Ghose, A., Ipeirotis, P., Li, B. (2012b). Designing ranking systems for hotels on travel search engines by mining user-generated and crowd-sourced content.

*Marketing Science*,*31*(3), 492–520.Ghose, A., Ipeirotis, P., Li, B. (2014). Examining the impact of ranking on consumer behavior and search engine revenue.

*Management Science*,*60*(7), 1632–1654.Granbois, D. (1968). Improving the study of customer in-store behavior.

*Journal of Marketing*,*32*(October), 28–33.Haan, M., Moraga-Gonzalez, J., Petrikaite, V. (2018). A model of directed consumer search.

*International Journal of Industrial Organization*, forthcoming.Hagiu, A., & Jullien, B. (2011). Why do intermediaries divert search?

*The RAND Journal of Economics*,*42*(1), 337–362.Hansen, K., Singh, V., Chintagunta, P. (2006). Understanding store-brand purchase behavior across categories.

*Marketing Science*,*25*(1), 75–90.Hui, S., Inman, J., Huang, Y., Suher, J. (2013). The effect of in-store travel distance on unplanned spending: Applications to mobile promotion strategies.

*Journal of Marketing*,*77*(March), 1–6.Johnson, J. (2017). Unplanned purchases and retail competition.

*American Economic Review*,*107*(3), 931–965.Ke, T., Shen, Z.M., Villas-Boas, J.M. (2016). Search for information on multiple products.

*Management Science*,*62*(12), 3576–3603.Ke, T., & Villas-Boas, J.M. (2017). Optimal learning before choice. Working article.

Koulayev, S. (2014). Search for differentiated products: Identification and estimation.

*The RAND Journal of Economics*,*45*(3), 553–575.Larson, J., Bradlow, E., Fader, P. (2005). An exploratory look at supermarket shopping paths.

*International Journal of Research in Marketing*,*22*(4), 395–414.Levav, J., Heitmann, M., Herrmann, A., Iyengar, S. (2010). Order in product customization decisions: Evidence from field experiments.

*Journal of Political Economy*,*118*(2), 274–299.Liu, T. (2011).

*Learning to rank for information retrieval*. Berlin: Springer.Manchanda, P., Ansari, A., Gupta, S. (1999). The “shopping basket”: A model for multicategory purchase incidence decisions.

*Marketing Science*,*18*(2), 95–114.Mehta, N. (2007). Investigating consumers’ purchase incidence and brand choice decisions across multiple product categories: A theoretical and empirical analysis.

*Marketing Science*,*26*(2), 196–217.McAfee, P. (1995). Multiproduct equilibrium price dispersion.

*Journal of Economic Theory*,*67*, 83–105.Ngwe, D., Ferreira, K., Teixeira, T. (2019). The impact of increasing search frictions on online shopping behavior: Evidence from a field experiment. Working paper.

Petrikaite, V. (2018). Consumer obfuscation by a multiproduct firm.

*The RAND Journal of Economics*,*49*(1), 206–223.Redden, J.P. (2008). Reducing satiation: The role of categorization level.

*Journal of Consumer Research*,*34*(5), 624–634.Rhodes, A. (2011). Can Prominence matter even in an almost frictionless market?

*The Economic Journal*,*121*(556), 297–308.Seetharaman, P., Ainslie, A., Chintagunta, P. (1999). Investigating household state dependence effects across categories.

*Journal of Marketing Research*,*36*(4), 488–500.Seetharaman, P., Chib, S., Ainslie, A., Boatwright, P., Chan, T., Gupta, S., Mehta, N., Rao, V., Strijnev, A. (2005). Models of multi-category choice behavior.

*Marketing Letters*,*16*(2), 239–254.Shelegia, S. (2011). Multiproduct pricing in oligopoly.

*International Journal of Industrial Organization*,*30*(2), 231–242.Singh, V., Hansen, K., Gupta, S. (2005). Modeling preferences for common attributes in multicategory brand choice.

*Journal of Marketing Research*,*42*(2), 195–209.Song, I., & Chintagunta, P. (2006). Measuring cross-category price effects with aggregate store data.

*Management Science*,*52*(10), 1594–1609.Song, I., & Chintagunta, P. (2007). A discrete-continuous model for multicategory purchase behavior of households.

*Journal of Marketing Research*,*44*(4), 595–612.Stigler, G. (1961). The economics of information.

*Journal of Political Economy*,*65*(3), 213–225.Ursu, R. (2018). The power of rankings: Quantifying the effect of rankings on online consumer search and purchase decisions.

*Marketing Science*,*37*(4), 530–552.Varian, H. (2007). Position auctions.

*International Journal of Industrial Organization*,*25*(6), 1163–1178.Weitzman, M. (1979). Optimal search for the best alternative.

*Econometrica*,*47*(3), 641–654.Wilson, C. (2010). Ordered search and equilibrium obfuscation.

*International Journal of Industrial Organization*,*28*(5), 496–506.Wolinsky, A. (1986). True monopolistic competition as a result of imperfect information.

*The Quarterly Journal of Economics*,*101*(3), 493–512.Yoganarasimhan, H. (2018). Search personalization using machine learning.

*Management Science*, forthcoming.Zhou, J. (2011). Ordered search in differentiated markets.

*International Journal of Industrial Organization*,*29*(2), 253–262.Zhou, J. (2014). Multiproduct search and the joint search effect.

*American Economic Journal*,*104*(9), 2918–2939.

## Acknowledgments

We are thankful for comments from Alixandra Barasch, Kristina Brecko, Xinyu Cao, Pradeep Chintagunta, Babur De los Santos, Chaim Fershtman, Tobias Gamp, Konstantin Korotkiy, Song Lin, Dmitry Lubensky, Eitan Muller, Cem Ozturk, Vaiva Petrikaite, Robbie Sanders, Andrey Simonov, Adam Smith, Monic Sun, Artem Timoshenko, Miguel Villas-Boas, Chris Wilson, Hema Yoganarasimhan, and attendees of the 2018 Consumer Search and Switching Cost Workshop, the 2018 Workshop on Multi-Armed Bandits and Learning Algorithms, and the 2018 Marketing Science conference. The usual disclaimer applies.

## Author information

### Affiliations

### Corresponding author

## Additional information

### Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Appendix:

### Appendix:

Before proving Proposition 3 that Algorithm 1 maximizes the number of products searched by the consumer, we first demonstrate Lemma 1 below, which requires the following notation. Consider locations in increasing order of their search cost. Let \(C_{l}(\{L_{j}, j \in \overline {S}_{l}\})\) be the maximum number of products that can be searched starting with location *l*, given the set of products not yet allocated \(\overline {S}_{l}\) and their search cutoffs *L*_{j}.

###
**Lemma 1**

*For any* l*,*\(C_{l}(\{L_{j}, j \in \overline {S}_{l}\}) \geq C_{l}(L_{j}, j \in \overline {S}_{l}\setminus \{a\} \cup \{b\})\)*if**L*_{a} ≥ *L*_{b}*.*

In other words, swapping a yet-to-be-allocated product for a different product with weakly smaller search cutoff cannot increase the total number of products searched.

###
*Proof Proof of Lemma 1*

Any allocation of products that maximizes the number of products searched from the set \(\overline {S}_{l} \setminus \{a\} \cup \{b\}\) can also be used to generate an equal number of products searched from \(\overline {S}_{l} \), if it does not place product *b* in any location. If the search maximizing product allocation does place product *b* in a location, it can be swapped for product *a*, because *L*_{a} ≥ *L*_{b}. □

Using the result in Lemma 1, we can now prove Proposition 3.

###
*Proof Proof of Theorem 3*

Let *S* and *Q* be the sets of products resulting from Algorithm 1 and the optimal solution, respectively. If *S* = *Q*, then *S* is optimal and we have proven the claim. Suppose instead that *S*≠*Q*. If *Q* ⊂ *S*, then *Q* cannot be optimal, because *S* results in more searches. The case *S* ⊂ *Q* is also not possible. Any \(j \in Q \cap \overline {S}\) must have *L*_{j} ≥ *L*_{k}, ∀*k* ∈ *S*, because Algorithm 1 always selects products with the lowest *L*_{j}. So any such *j* could always be appended to *S* at the end. Because Algorithm 1 stopped, it means there are no such products. Finally, if |*S*| = |*Q*|, even though *S*≠*Q* (given that Algorithm 1 does not produce a unique allocation), then the claim is also proven.

Then there must be at least one element in *S* that is not in *Q* and vice versa. Consider locations in increasing order of their search cost. Let *l* be the first location in which \(\overrightarrow {j}^{S}\) differs from \(\overrightarrow {j}^{Q}\), i.e. \({j_{l}^{S}} \neq {j_{l}^{Q}}\). It must be that \(L_{{j_{l}^{S}}} \leq L_{{j_{l}^{Q}}}\), because Algorithm 1 chose to allocate \({j_{l}^{S}}\). Then for location *l*, the set of products not allocated as per Algorithm 1, \(\overline {S}_{l}\) is equal to the set of products not allocated as per the optimal algorithm, \(\overline {Q}_{l}\) except that the product \({j_{l}^{S}}\) was swapped for \({j_{l}^{Q}}\), that is \(\overline {S}_{l}=\overline {Q}_{l} \setminus \{{j_{l}^{S}}\} \cup \{{j_{l}^{Q}}\}\). Because \(L_{{j_{l}^{S}}} \leq L_{{j_{l}^{Q}}}\), we can apply Lemma 1 to show that \(C_{l}(\{L_{j}, j \in \overline {S}_{l}\}) \geq C_{l}(\{L_{j}, j \in \overline {Q}_{l}\})\). Therefore, by allocating \({j_{l}^{S}}\) and discarding \({j_{l}^{Q}}\) in the optimal solution, we obtain a solution \(\overrightarrow {j}^{Q^{\prime }}\) that results in \(N_{Q^{\prime }}\geq N_{Q}\) products being searched, and which differs from \(\overrightarrow {j}^{S}\) by one less product. By repeatedly applying this transform, \(\overrightarrow {j}^{Q}\) can be transformed to \(\overrightarrow {j}^{S}\) with no decrease in total number of products searched. This shows that S is optimal. □

###
*Proof Proof of Theorem 4*

^{Footnote 7} Suppose Algorithm 2 produces a set of allocated products *S*, while the optimal algorithm produces a set *Q*. If *S* = *Q*, then *S* is optimal and we have proven the claim. It is also clear that neither *Q* ⊂ *S* (contradicts *Q* being optimal), nor *S* ⊂ *Q* (could append any \(j \in Q \cap \overline {S}\) to *S* at the end) are possible. Then there must be at least one element in *S* that is not in *Q* and vice versa.

We first show that there exist feasible product allocations \(\overrightarrow {j}^{S}\) and \(\overrightarrow {j}^{Q}\), such that all products that are included in both *S* and *Q* are placed in the same location. Let *j* be placed in location *l* in \(\overrightarrow {j}^{S}\) and in location *l*^{′} in \(\overrightarrow {j}^{Q}\). If *l* < *l*^{′}, then replace *j* in *l*^{′} in \(\overrightarrow {j}^{S}\). Now, *j* is placed in the same location in the two allocations. If *l* > *l*^{′}, the same transformation can be applied to \(\overrightarrow {j}^{Q}\). Therefore, we can transform any two feasible product allocations into allocations for which all common products are placed in the same location.

Denote by *ϕ*_{j} the expected payoff of a product *j*. Let *a* be the highest expected payoff product that is included in S and not in Q, that is *a* ∈ *S*, *a* ∉ *Q*. Then, it must be that *ϕ*_{a} ≥ *ϕ*_{b}, ∀*b* ∈ *Q*, *b* ∉ *S*. Otherwise, if *ϕ*_{b} > *ϕ*_{a}, Algorithm 2 would consider product *b* before product *a*, and include it in *S*.

Consider now the location at which product *a* is placed in \(\overrightarrow {j}^{S}\). Let *c* be the product placed in the same location in \(\overrightarrow {j}^{Q}\). Because all common elements are placed in the same location under both algorithms, we know that *a* ∈ *S*, *a* ∉ *Q* and *c* ∈ *Q*, *c* ∉ *S*. Swapping *c* with *a* in *Q* cannot decrease the total payoff from *Q* because *ϕ*_{a} ≥ *ϕ*_{c}, and it cannot increase the total payoff from *Q* because *Q* is optimal. Thus, swapping *c* with *a*, gives a feasible product allocation that differs from the set *S* in one less product than did *Q*. Through repetition, the set *Q* can be transformed to *S* with no decrease in payoff. Therefore, the set *S* was optimal. □

###
*Proof Proof of Theorem 5*

^{Footnote 8} If \(\overrightarrow {j}^{S}\) has allocated products with lower expected net utility to lower search cost locations, then the claim has been proven. Suppose instead that this does not hold. Then ∃*j*, *k* ∈ *S*, such that *γ*_{j} < *γ*_{k}, but *k* was located in a lower cost location than *j*. Without loss of generality, suppose *k* is located at *l* and *j* at *l* + *h*, where *h* > 0. Because *γ*_{j} < *γ*_{k}, then it follows that *L*_{j} ≤ *L*_{k}. Product *j* is located at *l* + *h*, which means that *L*_{j} ≥ *l* + *h*. Because *L*_{j} ≤ *L*_{k}, then it must also hold that *L*_{k} ≥ *l* + *h*. Thus, we can swap *j* and *k* in *S*. The resulting allocation is still feasible, because the consumer would be willing to search both products in their new locations. Also, this cannot increase the retailer’s expected payoff, because *S* is optimal. Thus, if \(\overrightarrow {j}^{S}\) has not allocated products with lower expected net utility to lower search cost locations, it can be arranged in such a way, while preserving optimality. □

## Rights and permissions

## About this article

### Cite this article

Ursu, R.M., Dzyabura, D. Retailers’ product location problem with consumer search.
*Quant Mark Econ* **18, **125–154 (2020). https://doi.org/10.1007/s11129-019-09214-6

Received:

Accepted:

Published:

Issue Date:

### Keywords

- Consumer search
- Multi-category retailer
- Product location problem

### JEL Classification

- L81
- D83
- D11