Sponsored search advertising and dynamic pricing for perishable products under inventory-linked customer willingness to pay

Accepted Manuscript

Sponsored Search Advertising and Dynamic Pricing for Perishable Products under Inventory-linked Customer Willingness to Pay Vaishnavi Tunuguntla , Preetam Basu , Krishanu Rakshit , Debabrata Ghosh PII: DOI: Reference:

S0377-2217(18)31078-6 https://doi.org/10.1016/j.ejor.2018.12.026 EOR 15550

To appear in:

European Journal of Operational Research

Received date: Accepted date:

27 July 2017 17 December 2018

Please cite this article as: Vaishnavi Tunuguntla , Preetam Basu , Krishanu Rakshit , Debabrata Ghosh , Sponsored Search Advertising and Dynamic Pricing for Perishable Products under Inventory-linked Customer Willingness to Pay, European Journal of Operational Research (2018), doi: https://doi.org/10.1016/j.ejor.2018.12.026

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ACCEPTED MANUSCRIPT Highlights of the Research We consider customers’ reservation price as a function of available inventory We develop a stochastic dynamic programming model We derive optimal bids and dynamic prices under sponsored search advertising We find variance and mean reservation price impact optimal bid and price decisions

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Sponsored Search Advertising and Dynamic Pricing for Perishable Products under Inventory-linked Customer Willingness to Pay

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Vaishnavi Tunuguntla PhD Student, Operations Management Indian Institute of Management Calcutta Diamond Harbor Road, Kolkata700104, India [email protected]; Tel.: +91-33-2467-8300

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Preetam Basu * Associate Professor, Operations Management Group Indian Institute of Management Calcutta Diamond Harbor Road, Kolkata700104, India [email protected]; Tel.: +91-33-2467-8300

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Krishanu Rakshit Assistant Professor, Marketing Group Indian Institute of Management Calcutta Diamond Harbor Road, Kolkata700104, India [email protected]; Tel.: +91-33-2467-8300

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Debabrata Ghosh Assistant Professor, Operations Management Group MIT Global Scale Network - Malaysia Institute for Supply Chain Innovation No. 2A, Persiaran Tebar Layar, Seksyen U8, 40150, Selangor, Malaysia. [email protected]; Tel: +6 03 7841 4888

* Corresponding Author

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Sponsored Search Advertising and Dynamic Pricing for Perishable Products under Inventory-linked Customer Willingness to Pay

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Abstract: Several online retailers provide inventory availability information on their websites in addition to leveraging sponsored search advertising to drive customer traffic to their retail websites. The increased ability of users to interact over the internet encourages retailers to shift to sponsored search advertising. In this paper, we design a decision support model to provide strategic bid and pricing decisions to a retailer selling a perishable product over a short horizon using sponsored search advertising to attract customers to his website. The retailer complements sponsored search bidding with dynamic pricing in a multi-period stochastic dynamic programming framework. Our analyses show that it is optimal for the retailer to invest heavily in bidding at low inventory levels, whereas at high levels of inventory he should use price promotions to enhance profits. We also find that the optimal bid and price increase with the increase in mean and variability of the customer’s reservation price.

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Keywords: E-Commerce, Sponsored Search Advertising, Dynamic Pricing, Customer Willingness to Pay, Stochastic Dynamic Programming 1. Introduction

Over the past two decades advertising has evolved from the traditional offline channels (such as newspapers, magazines and television) to more advanced online channels (such

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as webpage banners, display advertising and social media). Online advertising has enabled a shift from mass advertising to more targeted advertising as a consequence of the

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increased ability of users to interact with sellers in the online world (Chen, 2008; Ghose & Yang, 2009; Moe, 2013). As consumers increasingly use the internet to search for products and brands and make purchases, it has become critical for sellers to appear as

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‘results’ on the search engines. Sponsored search has witnessed significant growth in the recent past. In the United States alone, sponsored search spending reached $49 billion in

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2014 compared to $42 billion in 2013 (PWC; IAB, 2015a). It is further estimated that this would rise by approximately 15% annually, over the next few years (PWC; IAB, 2015b).

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In addition to the advantages discussed above, sponsored search advertising also allows significant scope for customization. The search engine learns the user’s characteristics and preferences and displays the advertisements accordingly. In contrast, in traditional advertising, firms can only choose the type of media that consumers may get exposed to, without any further scope of customization. Another advantage of using sponsored search is its measurability and accountability (Abhishek & Hosanagar, 2013). Data regarding the number of clicks generated by a keyword associated with a website is available with the search engine which the sellers can analyze to further improve their decisions. Given the fact that sponsored search is a more targeted means of advertising, studies have shown that the return on every advertising dollar is higher in cases of

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ACCEPTED MANUSCRIPT sponsored search than for traditional advertising (Laffey, 2007). Motivated by the above, in this paper, we study a retailer’s bid and pricing strategy in sponsored search

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Figure 1: Sponsored Listings

Source: www.google.com

advertising and develop a decision support model under inventory-linked customer

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willingness to pay.

1.1 Mechanism and Dynamics of Sponsored Search

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We illustrate the mechanism of sponsored search through a simple example. When a user keys in a query in a search engine such as Google, the user is displayed results as shown in Figure 1. Usually the top 3 searches are sponsored listings; advertisers bid for these

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positions to improve the visibility of their pages during keyword searches. Often the leads generated are related to the rank or, position of the firm in the search results (Ghose &

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Yang, 2009). However, merely bidding high does not ensure advertisers these coveted positions; most search engines employ a set of rules to ensure quality of searches. Quality of the webpage also plays an important part; poor user experiences with search

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advertisements could lead to advertisement avoidance and impact the search engine’s longterm revenue (Li, Liu, & Liu, 2013). So, the search engines use a combination of Quality Scores and bid values to determine the firm’s position in the searches. The quality score is an aggregation of parameters such as relevance, click through rate (CTR) (the ratio of number of clicks to the number of impressions) and landing page experience (Google Adwords, 2016). However, firms can only improve their Quality scores over a significant time, and in the short-term horizon, the bidding decision plays a key role in sponsored search advertising. The bidding strategy of the retailer is an important consideration in this paper.

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ACCEPTED MANUSCRIPT A search engine, for example, Google, potentially offers three different pricing schemes: viz. CPM, CPC, and CPA. CPM or, Cost per 1000 impressions is the price the advertiser is willing to pay for being listed in the search results of a user. Generally, this mechanism is adopted when the objective is primarily to create awareness. Cost per Click (CPC) is where the advertiser pays on a per click basis. This mechanism is adopted when the prime objective is to drive traffic to the website. Cost per acquisition (CPA) is the mechanism where the payment is made only when a customer converts, i.e. makes a

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purchase. In our paper, we develop a model using the CPC scheme as it can be employed by both online and offline stores. CPA scheme is a lower risk option for the advertiser where the advertiser pays only when a click leads to a purchase. However, the downside of using the CPA scheme is its high cost for a single convert. A table showing the differences in the pricing schemes offered by Google is presented below (Table 1).

Features Full form

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Table 1: Different Pricing Schemes offered by Google Pricing Schemes CPC

CPM Cost per mille (1000 impressions)

CPA

Cost per click

Cost per acquisition (converts)

Bid is the cost incurred for 1000 impressions

Bid is the cost incurred for a single click

Bid is the cost incurred when a single convert/purchase happens

Purpose

To create awareness

To generate traffic

Low risk option; Pays only when a purchase is made

Expression

𝐹𝑙𝑎𝑡 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ ∗ 1000 𝑇𝑜𝑡𝑎𝑙 𝑖𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛𝑠

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Definition

(𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 ∗ 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡) 100

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𝐹𝑙𝑎𝑡 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑙𝑖𝑐𝑘𝑠

1.2 Inventory Implications and Paid Search

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While bids are critical decisions in sponsored search, for an advertiser (or retailer in our problem), it is equally important to keep the right amount of inventory, while driving more

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traffic to the website. Among the various issues that have emerged following the use of paid search in driving traffic to the website, linking inventory decisions to sponsored search advertising has become quite important. Coordinating inventory decisions with bids becomes

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critical when a retailer bids high and generates a substantial demand through sponsored search.

Interestingly, some online retailers provide inventory availability information on their

websites (Figure 2). By displaying the stock in hand, the customer’s purchase intent may be influenced by creating a sense of urgency in the customers. A customer might be willing to pay a higher price for a product which has limited inventory and is expected to run out with no future replenishments. Several product categories, e.g. perishable items, display such characteristics. For example, airline tickets for a popular destination, tickets for a prominent maestro’s concerts, limited-edition items such as fashion, short-life-cycle electronic products

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ACCEPTED MANUSCRIPT etc. Several works have investigated the impact of perceived scarcity and consumers’ preferences (Parker & Lehmann, 2011; Stock & Balachander, 2005; Zhu & Ratner, 2015)

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Figure 2: Inventory Information on E-retailer’s website

Source: www.amazon.com

Based on the extant literature and examples of product categories cited above, we assume in our paper, that a customer’s willingness to pay increases with low levels of available inventory and vice versa. Based on the above context, we raise the following research

(i)

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questions related to perishable products over a short planning horizon: How does a retailer use sponsored search advertising when a customer’s

(ii)

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willingness to pay changes based on the information of available inventory? If dynamic pricing is also employed, then how can prices be adjusted at different levels of inventories for optimal revenue/profits?

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To answer the above questions, we develop a multi-period model where, at each time-period, the retailer, based on the inventory available, decides on the bid for sponsored

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search and the price of the product. In our paper, we consider a fixed inventory of perishable products over a finite time horizon. Bidding is used to generate traffic for the website (Google Adwords, 2016). The conversion (or, purchase) depends upon the price and the inventory

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available. We first model a scenario where the bid is the only decision variable for the retailer and the price of the product is fixed. Later, we extend our model to incorporate the dynamic pricing decisions of the retailer along with sponsored search bidding. Our analysis interestingly reveals that at low inventory levels, it is optimal for the retailer to bid high, whereas at high inventory levels, he should lower his bid. This is counterintuitive and is a result of the fact that when the price is fixed, the bid increases with reduction in stock levels. As a result, at lower inventory levels, the likelihood of conversion is higher. We also analyze the case of dynamic pricing where we derive sets of bids and prices

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ACCEPTED MANUSCRIPT that maximize the retailer’s revenue with respect to the stock-on-hand. We find that bid and price can be used as complements based on the inventory level. The contribution of our work lies in modelling and analyzing the optimal bidding and pricing policies of a retailer employing sponsored search in a dynamic setting to sell perishable products having short life cycle. Our work seeks to improve the understanding of sponsored search and illustrate the strategic importance of inventory, price, and bid in driving retail sales.

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The rest of the paper is organized as follows. In the next section, we discuss the background literature of this paper. Section 3 discusses the analytical models. Theoretical results are presented in Section 4. Section 5 discusses numerical results and managerial implications. Section 6 summarizes our findings and provides future research directions. 2. Literature Review

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Our work spans across four (4) streams of literature: (i) sponsored search advertising (ii) coordinating Inventory with advertising, (iii) impact of perceived scarcity on consumer evaluations as well as willingness to pay and (iv) dynamic pricing of perishable products. In the following section, we present an overview of the literature belonging to these streams. The stream of sponsored search advertising has generated a lot of interest over the

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past few years. To obtain best results from sponsored search, an advertiser needs to maximize the number of impressions, clicks and ultimately converts. According to extant literature, for smaller levels of advertising, there are increasing marginal returns whereas the

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returns diminish as advertising goes up. This is captured by modelling the click rate (or arrival rate) as an S-shaped curve (Johansson, 1979; Little, 1979; Villas-Boas, 1993; Ye,

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Aydin, & Hu, 2015). The primary objective of any advertiser using online mode of advertising is to gain visibility among the customer base whereas for a publisher (or, a search engine),

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the task lies in allocating or scheduling various advertisements over a given time horizon. Taking into account the uncertainty of supply of internet viewers, Deza, Huang, & Metel (2015) develop a chance constrained optimization model for the fulfilment of guaranteed-

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display internet advertising campaigns. The model suggests the combination of advertisement and the target set of users to which the advertisement should be displayed. Usually,

banner

advertisements

could

be

considered

as fixed

display-frequency

advertisements in the online context. Deane & Agarwal (2012) empirically show that allowing for variable display frequency will result in improved profits. Around similar lines, while employing a CPM (cost per 1000 impressions) scheme, Ahmed & Kwon (2014) study optimal contract problems for online display advertisements with pay-per-view pricing scheme. Beltran-Royo, Escudero, & Zhang (2016) further extend these models of optimal allocation of advertising budget to the multiproduct, multi-period advertising scenario and

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ACCEPTED MANUSCRIPT suggest that models, which attempt to capture customer intent, need to include click rates in their estimation. In this direction, Ghose & Yang (2009) analyze the importance of each of the factors that affect the click rate. Using real time data, they develop logit models for calculating click rate probability as a function of the keyword length, brand, retailer, rank, etc. Later, Ghose, Ipeirotis, & Li (2014) incorporate the effect of customer rating as a factor in determining the click rate. Abhishek & Hosanagar (2013) consider the overall attractiveness of an advertisement (keyword), and impact of position on clicks, to derive the relationship

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between the bid and position, and position and clicks. Edelman & Ostrovsky (2007) present evidence of strategic bidder behavior in sponsored search auctions. They suggest an alternative bidding mechanism that could reduce the amount of strategizing by bidders, raise search engine revenues and increase efficiency of the market. Ayanso & Karimi (2015) show that the position of advertisements for web-only retailers is dependent on bid values and advertisement relevancy factors whereas multi-channel retailers are more reliant on the bid

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values. Varian (2007) discusses the Vickrey auction (second price auction) mechanism employed by search engines to rank websites.

However, our focus is not on competition or, the equilibrium behavior of advertisers in dynamic auctions. We distil the effect of competition into a known bid-arrival rate relationship. Asdemir, Kumar, & Jacob (2012) describe a game theoretic environment with

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the search engine and advertiser as players. A model is developed to yield the optimal bid in a CPC scheme by establishing an equilibrium between the advertiser and the search engine.

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Yang & Ghose (2010) analyze the interdependence between organic listings and paid search listings. The authors empirically demonstrate that there is a positive correlation between the two listings. This corroborates the importance of using sponsored search for a

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firm. Gopal, Li, & Sankaranarayanan (2011) investigate the effect of interactions between search and content listings. They reveal empirically that for intermediate budget values, it is

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optimal to use both search and content channels; whereas for very low (very high) budgets, it is optimal to use content (search) channel. The most recent work of Ye et al. (2015) discuss an on-and-off bidding style for a cake manufacturer who wishes to advertise online.

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They assume that a customer’s reservation price is a function of bid, i.e. a customer’s likeliness of conversion is dependent on the rank (bid as proxy) of the website in a search. An algorithm is developed to decide on an optimal daily bid and price for his product, given a fixed inventory. Zhang, Yang, Li, Qin, & Zeng (2014) argue that both the bid and advertiser’s daily budget need to be dynamic for an effective advertising strategy. One of the gaps that we identified in this stream of research is that the effect of “inventory left” on a customer’s purchase decision has not been modelled. We capture this explicitly in our model along with the bid and pricing decisions.

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ACCEPTED MANUSCRIPT Next, we focus on the literature on coordinating advertising with inventory. Prior to incorporating the effect of inventory on sponsored search, we study the literature on the effect of inventory management for traditional advertising modes. In joint inventorypromotion problems, inventory replenishment follows a base stock policy (refer, Cheng & Sethi, 1999 and Sogomonian & Tang, 1993). Cheng & Sethi (1999) consider promotion cost to be a fixed cost in each period. Sogomonian & Tang (1993) develop a baseline model to analyze production and promotion problems. This model suggests the timing and level of

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promotion and production. A similar problem in the context of partially controllable demand is modelled by Balcer (1980). The inventory and advertising decisions are made taking the firm’s goodwill into account. Shah, Soni, & Patel (2013) design an algorithm to find the optimal inventory and marketing policies considering an inventory system with deteriorating items in which demand rate is a function of advertisement of an item and selling price. Mesak, Bari, Luehlfing, & Han (2015) study the impact of advertising competition on

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inventory decisions. Zhang, Chen, & Lee (2008) deal with price and promotion as substitutes and complements of each other. By decreasing the price, the demand generally goes up. In such cases, the level of advertising can be decreased, which acts as a substitute; or, advertising can be increased to further enhance the demand thereby acting as a complement. In such scenarios, the optimal promotion policy is a threshold policy and once

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the level of promotion is determined, the inventory and pricing policy becomes a base stock list price policy. For various levels of inventory, our model provides the bid (CPC) amount

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that needs to be invested. Traditional models of advertising provide the total amount to be invested in promotional activities over a period. Our model provides a more granular decision in terms of bid, as per the context of sponsored search advertising. Simultaneously,

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our model suggests optimal price at those levels of inventory where the retailer has a dynamic pricing policy.

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Measuring Consumer Willingness to Pay has been an intriguing area; one of the seminal works in this area have been by Wertenbroch & Skiera (2002). In our paper, we attempt to investigate whether the retailer’s strategy of displaying available stock information

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has an impact on consumers’ willingness to pay. Stock & Balachander (2005) investigated whether scarcity could be used as a signaling mechanism to highlight the product’s desirability and therefore, consumers’ greater willingness to opt for it. Similar contributions (Parker & Lehmann, 2011; Zhu & Ratner, 2015) highlight that consumers’ evaluation of the product type among comparable alternatives is altered due to scarcity. Soysal & Krishnamurthi (2012) show how consumers accelerate their purchases and purchase at higher prices when they anticipate scarcity in future periods. Su & Zhang (2009) analyze a case where the sellers provide information on inventory available to attract ‘strategic customers’ who have higher perceived need to procure the product. In their earlier work, Su

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ACCEPTED MANUSCRIPT & Zhang (2008) show that a lower stocking quantity intensifies the threat of stock-outs and thus also increases consumer’s willingness-to-pay. Liu & van Ryzin (2008) extend this stream of work by investigating the optimal amount of rationing risk that the producer can create in the consumer’s mind. They consider stocking quantity as the primary decision variable in evaluating the profits through strategic customers. In the related literature, ‘strategic customers’ (who have higher valuations of the products, and therefore, willing to pay higher prices; ref: (Su & Zhang, 2009)) would hasten their purchases due to the

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shortages/ scarcity, which increase the firm’s profits. Zhu & Ratner (2015) present a survey, where a general sense of scarcity versus abundance increases choice share of the most preferred option from a product class. They examine how the salience of scarcity influences choices of individual items from a product class.

Reservation price captures the highest possible price that the customer will be willing to pay for a product, and several researchers (e.g. Wang, Venkatesh, & Chatterjee, 2007)

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have considered ‘reservation price’ and ‘willingness to pay’ as synonymous. Further, Wang et al. (2007) offer a more nuanced understanding of the consumer decision making process, by postulating reference price as a ‘range’ following the incentive-compatibility mechanism; (1) Floor reservation price is the maximum price at or below, which a consumer will definitely buy one unit of the product (i.e., 100% purchase probability). (2) Indifference reservation

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price is the maximum price at which a consumer is indifferent between buying and not buying (i.e., 50% purchase probability) and (3) Ceiling reservation price is the minimum price

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at or above which a consumer will definitely not buy the product (i.e., 0% purchase probability).

Finally, the effect of dynamic pricing of perishable inventory on customer purchase

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decisions has been studied extensively in the revenue management literature. Over the years, dynamic pricing has been considered in various combinations- demand, inventory

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policies, etc. A basic model was formulated by Gallego & Ryzin (1994) to frame a dynamic pricing policy based on the inventory level of perishable products over a finite horizon. Zhao & Zheng (2000) suggest optimal prices by modelling the revenue impact of dynamic pricing

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policy over time. The pricing strategies vary with the retailer’s inventory policies as well. Zhao & Cao (2004) show a comparison of two e-tailers having different inventory policieszero inventory policy and positive inventory policy. Taking into account customer impatience, Abad (2008) decides on the optimal price and order size while allowing for a period where in the demand can be backlogged. Zhu (2012) analyze the dynamic pricing policy for a retailer with flexibility to return or expedite the order. Yet another pricing policy employed by Chew, Lee, & Liu (2009) uses the product lifecycle and the inventory level, similar to an airline revenue management problem. We extend this stream of research by incorporating both bidding and dynamic pricing when customer’s willingness to pay becomes a function of the

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ACCEPTED MANUSCRIPT inventory available. The extant literature has not incorporated the effect of “inventory left” on a customer’s purchase decision. At low inventory levels, there tends to be significant variation in the reservation prices among individual customers. We capture this in our model along with the bid and pricing decisions and believe that the model would have practical implications in various revenue management applications. In the following section, we explain the analytical models developed in this paper. 3. Model Description

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We consider a retailer having limited stock of a perishable product with a predetermined selling season and with no opportunity to replenish inventory during the selling season, e.g. airline tickets for a popular destination, tickets for a prominent Maestro’s concert, or limitededition fashion items. As a promotional tool, the retailer uses sponsored search advertising. The search engine follows the CPC pricing scheme where in the retailer must pay a fixed

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amount for each customer that clicks on his link. In line with the seminal work done by Bitran & Mondschein (1997), we take the discrete time periods short enough such that one time period corresponds to at most one customer clicking on the retailer’s link during that period. “Click rate” is defined as the probability with which a customer clicks a retailer’s link within one time-period.

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In this paper, we aim to develop a decision support model that permits the user to formulate the problem as precisely as possible with respect to real world circumstances. We develop two variations of a decision support model– one where the retailer uses his bid 𝑏𝑡

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only as a decision variable to boost sales (referred as bid-only model). Then we extend this model to a scenario where the retailer can adjust the bid 𝑏𝑡 as well as the price 𝑝𝑡 of the

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product at the start of each time period 𝑡 (referred as bid-and-price model). Bid 𝑏𝑡 is the amount paid by the retailer to the search engine when a customer clicks on the link, i.e.

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Cost-per-click (CPC) scheme. In the next stage, whether a click converts into a purchase depends on the price of the product and the reservation price of the individual customer. Whenever the posted price is below the reservation price of a customer, a purchase is

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made. Nowadays, some retailers display their stock-on-hand information to influence customer’s purchase behavior. We capture the dynamic pricing decision based on the customer’s reservation price that is modelled as a function of the retailer’s inventory on hand. As explained earlier, for products that have limited stocks and no future replenishment opportunities, information on low stock levels create an urgency amongst customers and they would be willing to pay a higher price. The customer reservation price is a random variable that follows a distribution that may be estimated by the retailer through past data. Next, in sections 3.1 and 3.2, we discuss our specific assumptions on the click rate and the reservation price distributions. In section 3.3 and 3.4, we formulate the retailer’s profit

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ACCEPTED MANUSCRIPT maximization problem as a stochastic dynamic programming problem with fixed and dynamic prices. 3.1 Click rate In our paper, we model the probability of a customer clicking on the retailer’s link (click-rate) as a Poisson arrival process that varies with the ranking on the search results page. Each search engine has its own mechanism to rank the websites. Generally, it is done by calculating a quality score (which depends on relevance, metadata, etc.) and bid. The

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information about quality score is furnished by the search engine (for example, Google) for individual websites in their Ad Words account statistics. Usually, a quality score is an accumulated score, which requires long-term effort by the retailer. Bid is the only parameter that the retailer can control over a short-term window. Through a higher bid (with quality scores being similar across websites), the retailer can achieve a higher rank, which could, in

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turn, result in a higher click rate. Hence click-rate is a function of the retailer’s bid, λ(b) (Ye et al., 2015, Selçuk & Özlük, 2013). The retailer, when making its bidding decision, can estimate the functional relationship between the click-rate and the bids based on experience. As highlighted in the extant literature, the click-rate function exhibits an S-Shape, that captures the diminishing marginal returns with the increasing bid amounts ((Little, 1979) ,

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(Johansson, 1979), (Villas-Boas, 1993)). The click rate is similar to the arrival rate in the earlier literature on dynamic pricing (e.g., Bitran & Mondschein, 1997), with the very important exception that in our model the retailer can influence the click rates by changing its

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bid on the search keywords.

3.2. The Reservation Price Distribution

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Once the customer arrives at the retailer’s page, the conversion from a visit to a transaction depends on the individual customer’s reservation price. Only when the posted price is less

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than the reservation price, a customer makes a purchase. Recently, websites have started displaying information of quantity of items left for a certain product. It has been observed that

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this creates a positive impact in generating demand (Donovan, 2013; Marcus, 2015). Hence, we model the reservation price of the customer base as a random variable that follows a probability distribution that is influenced by the inventory left for a product. Information on inventory left creates a sense of urgency amongst customers to complete a purchase. As the customer becomes aware that the product could soon go out of stock, the need to procure the product is higher. Any delay in decision making might lead to missing out on the product. Hence, intuitively, at lower levels of inventory, the probability of conversion is higher than compared to higher inventory levels. In other words, the mean reservation price of the customers increases as the inventory decreases. Similarly, we assume that lower stocks

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ACCEPTED MANUSCRIPT create an urgency amongst customers and this leads to standard deviation of the reservation price to increase with decreasing inventory. We formulate the reservation price distribution as follows: Let 𝜗(𝐼) denote a customer’s reservation price for a given inventory𝐼, 𝜗(𝐼) is given by 𝜗(𝐼) =

𝜇(𝐼) + 𝜎(𝐼)𝑅

(1)

where 𝜇(∞) = 0, 𝜎(∞) = 1 We model customer’s reservation price 𝜗(𝐼) as a function of the mean reservation

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price of customers’(𝜇(𝐼)), standard deviation of reservation price of customers’ (𝜎(𝐼)), and 𝑅 which is the distribution of reservation prices of customers when the inventory on hand is very large. In other words, 𝑅 is the distribution of reservation prices of customers at very high inventory levels i.e. when the level of inventory does not have any impact on the customers’ reservation price. We assume 𝜇(∞) = 0 and 𝜎(∞) = 1 implying that at very high inventory

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levels, customer’s reservation price is 𝑅. We assume 𝑅 takes values between 𝑦 and 𝑦̅ (where 𝑦 ≥ 0, and 𝑦̅ can approach infinity). The minimum reservation price that any customer would have for a given product (at high inventory levels), is thus, denoted by 𝑦 . Similarly, the maximum that any customer would pay for a given product (at high inventory levels), is captured by 𝑦 . Further, we assume the mean reservation price of the customers’

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increases as the inventory reduces according to our main underlying assumption of scarcity impacting a customer’s purchase decision. Also, the standard deviation in reservation prices

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of customers’ increases as the inventory reduces. We assume the coefficient of variation of the customers’ reservation price decreases with decreasing inventory, which implies mean reservation price increases at a faster rate than the standard deviation with decreasing

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inventory. This assumption is similar to Ye et al. (2015) who model a similar functional form of reservation price distribution as a function of bids. Let 𝐺(. ) and 𝑔(. ) denote the cumulative

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distribution function (cdf) and probability density function (pdf) of 𝑅. We assume that 𝐺(. ) has an increasing failure rate (IFR); i.e., 𝑔(. )/𝐺(. ) is increasing.

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Equivalently, if we denote the cdf of 𝜗(𝐼) as 𝐹(. |𝐼), we may write 𝐹(𝑝|𝐼)

=

𝐺(

𝑝 − 𝜇(𝐼) ) 𝜎(𝐼)

(2)

We choose this form as it incorporates both the additive and multiplicative effects of

the retailer’s inventory on the customer’s reservation price distribution. The retailer can influence the conversion rate through price and information on inventory left. In the context of our model, we define the conversion rate in a given period as the probability that a customer who clicked the retailer’s link in that period purchases. It follows from the definition that the conversion rate is essentially the probability of reservation price 𝜗(𝐼) exceeding the posted price; i.e.

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ACCEPTED MANUSCRIPT 𝐹(𝑝|𝐼)

=

1 − 𝐹(𝑝|𝐼)

(3)

We make the following assumptions to ensure smoothness of the profit function. (a) 𝐺(. ) has a continuous first-order derivative within its support. (b) µ(𝐼) and 𝜎(𝐼) have continuous first-order derivatives. These assumptions are satisfied by many general probability distribution functions such as Gamma distribution, Beta distribution, Weibull distribution, etc.

we extend the model where bid and price both act as levers. 3.3 The Maximization Problem- Only Bid as lever

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Next, we develop the maximization model with bid as the only decision variable and then

Given that the retailer faces a multiple(𝑇) period problem to maximize his profits based on the inventory on hand, we develop a finite-horizon stochastic dynamic programming model

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from the retailer’s profit maximization objective. The notations used in the stochastic dynamic programming model are given in Table 2.

Table 2: Notations used in the Stochastic Dynamic Programming model Time periods in the horizon

𝐼

Inventory on hand

𝑏

Bid/ Cost-per-click

𝑝

Price of product

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𝑡

𝜋

Profit of the retailer

λ(𝑏)

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𝑅

Click rate at bid b Customer reservation price distribution at 𝐼 = ∞

𝜗(𝐼)

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Reservation price distribution at inventory 𝐼

𝑔(. )

PDF of distribution of 𝑅

𝐺(. )

CDF of distribution of 𝑅

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𝐹(𝑝|𝐼) 𝑠

Conversion rate probability Salvage value of the product at the end of the time-horizon

The retailer starts with 𝐼 units of inventory over a 𝑇 period horizon, and uses bids (b ) at each time period to maximize his profit. The functional equation is given by: 𝜋(𝐼, 𝑡)

=

(1 − λ(𝑏))𝜋(𝐼, 𝑡 − 1) + λ(𝑏)𝐹(𝑝|𝐼)(𝜋(𝐼, 𝑡 − 1) − 𝑏) + max { } 𝑏>0 λ(𝑏)𝐹̅ (𝑝|𝐼)(𝑝 + 𝜋(𝐼 − 1, 𝑡 − 1) − 𝑏) for 𝐼 > 0, 𝑡 = 1,2, … 𝑇

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(4)

ACCEPTED MANUSCRIPT 𝜋(0, 𝑡)

=

0

for 𝑡 = 1,2, … 𝑇

𝜋(𝐼, 0)

=

𝐼∗𝑠

for 𝐼 > 0

Whenever a retailer places a bid, one of the three scenarios arise: (1) the customer does not click the link at all; (2) the customer clicks the link but does not make a purchase;

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and (3) customer clicks the link as well as makes the purchase. Please refer to Figure 3 for a

Figure 3: Pictorial Representation of the Stochastic Dynamic Programming Model

(1 − λ(𝑏))

𝜋(𝐼, 𝑡 − 1)

Probability customer does not click on the sponsored search link

Profit function at time t

b, p

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(λ(𝑏)𝐹(𝑝|𝐼))

𝜋(𝐼, 𝑡) Retailer decides bid and price

−𝑏 + 𝜋(𝐼, 𝑡 − 1)

Probability customer clicks on the sponsored search link but does not buy the product

(λ(𝑏)𝐹̅ (𝑝|𝐼)

𝑝 − 𝑏 + 𝜋(𝐼 − 1, 𝑡 − 1)

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Probability customer clicks on the sponsored search link and buys the product

pictorial representation of the modeling framework. The figure explains the model where

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both bid, and price are used as decision variables. For the bid-only model, the action set will be limited to only bids. In the basic formulation, we do not model inventory holding cost since

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the time period considered is considerably small given by the time for a ‘click’ (Ghose & Yang, 2009) of a prospective customer on the sponsored search keyword. Inventory holding

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cost from one period to the another will not have a significant impact. This is in line with the extant literature on inventory decisions for perishable products (Bitran & Mondschein, 1997). Later in Section 5.3, we analyze the impact of inventory holding costs as an extension.

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Given that the retailer adopts a CPC pricing scheme, when a customer does not click

at all, there is no cost to the retailer. When the customer clicks, and does not purchase, the retailer incurs cost per single click. If the customer clicks and makes a purchase, then the retailer earns the selling price of the product and the cost incurred is the cost per click. In equation (4), we consider the probability of clicking (λ(b)) and conversion (F̅(p|I)) as two independent events and build the expected profit equation combining three scenarios. The retailer chooses the optimal bid at the start of each time period such that the expected profit is maximized. The terminal conditions indicate that no replenishment is done (fixed inventory

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ACCEPTED MANUSCRIPT model) and that the product has a salvage value at the end of the last period. Next, we extend the above model where bid as well as price act as decision variables. 3.4 The Maximization Problem- Bid and Price as Levers In this model, while the problem scenario remains the same as above, the retailer, however, has two strategic decisions to make at the beginning of each period, namely, how much to bid and what price to charge (Figure 3). Incorporating the above decisions, the model is, (1 − λ(𝑏))𝜋(𝐼, 𝑡 − 1) + λ(𝑏)𝐹(𝑝|𝐼)(𝜋(𝐼, 𝑡 − 1) − 𝑏) + max { } 𝑏>0,𝑝>0 λ(𝑏)𝐹̅ (𝑝|𝐼)(𝑝 + 𝜋(𝐼 − 1, 𝑡 − 1) − 𝑏)

=

(5)

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𝜋(𝐼, 𝑡)

for 𝐼 > 0, 𝑡 = 1,2, … 𝑇 for 𝑡 = 1,2, … 𝑇

𝜋(0, 𝑡)

=

0

𝜋(𝐼, 0)

=

𝐼∗𝑠

for 𝐼 > 0

𝜋(𝐼, 𝑡)

=

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After some algebraic manipulation, 𝜋(𝐼, 𝑡) can be rearranged as follows: 𝜋(𝐼, 𝑡 − 1) + max {λ(𝑏)[𝐹̅ (𝑝|𝐼)(𝑝 − m(𝐼, 𝑡)) − 𝑏]} 𝑏>0,𝑝>0

(6)

Here, m(𝐼, 𝑡) is equivalent to the expected value of carrying one more unit of product into time period 𝑡 − 1 when there are already 𝐼 − 1 units in inventory.

=

𝜋(𝐼, 𝑡 − 1) − 𝜋(𝐼 − 1, 𝑡 − 1)

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𝑚(𝐼, 𝑡)

(7)

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In other words, m(𝐼, 𝑡) denotes the marginal value of the 𝐼-th unit of inventory in period 𝑡 or, alternatively, the retailer’s opportunity cost of selling the 𝐼-th unit in period 𝑡.

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4. Theoretical Results

The retailer adjusts his bids and the prices based on the level of inventory. Our analytical

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results prove that at high inventories, the retailer uses price discounts as the lever whereas at low inventories, he uses bid as the lever to maximize profits. These results have important

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managerial implications as they provide useful insights into the critical decision-making process in the domain of sponsored search advertising. Let, 𝜏(𝐼, 𝑝) =

𝑝−𝜇(𝐼) 𝜎(𝐼)

= 𝑦.

Using Eq.(6), the profit equation can be written as

𝜋(𝐼, 𝑦, 𝑚)

=

𝜆(𝑏)[𝐺(𝑦)(𝜇(𝐼) + 𝜎(𝐼)𝑦 − 𝑚) − 𝑏]

We now develop a supporting lemma to prove the nature of change in customer’s reservation price with respect to inventory and the posted price of the product.

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ACCEPTED MANUSCRIPT Lemma 1: 𝜏(𝐼, 𝑝) is increasing in 𝐼 𝑎𝑛𝑑 𝑝. Proof: See Appendix. Based on our assumptions, explained in section 3.3, both mean and standard deviation of reservation price decrease with inventory and coefficient of variation increases with inventory. This leads to the fact that the reservation price stochastically decreases with

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inventory. The result is formally stated in Lemma 2. Lemma 2:

𝜗(𝐼) is stochastically decreasing in 𝐼 (in the sense of first order stochastic dominance). Proof: See Appendix.

Consider Equations (5), (6), and (7). We derive the relationship between bid and inventory

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using marginal value of inventory as an intermediary. The next lemma shows the nature of change in the marginal value of inventory with respect to inventory. Lemma 3:

Marginal value of inventory decreases with increasing inventory. Proof: See Appendix.

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We develop another supporting lemma to understand the relationship between the optimal bid decision, inventory and marginal value of inventory. This will help us in deriving

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important results regarding the optimal bid and price decisions. Lemma 4:

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Let ℇ = {(𝐼, 𝑚): 𝑚 < 𝜇(𝐼) + 𝜎(𝐼)𝑦}. Given (𝐼, 𝑚) 𝜖 ℇ, the retailer chooses 𝑦 ∗ (𝐼, 𝑚) to maximise

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his profit such that 𝑦 ∗ (𝐼, 𝑚) is the unique value of ′𝑦′ that satisfies 𝜕𝑥 𝜋(𝐼, 𝑏, 𝑦, 𝑚) = 0. Then, (a) 𝑦 ∗ (𝐼, 𝑚) is increasing in 𝐼

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(b) 𝑦 ∗ (𝐼, 𝑚) is increasing in 𝑚 Proposition 1: The optimal bid as a function of the marginal value of inventory increases. In other words, the optimal bid decreases with inventory. Proof: See Appendix. The above proposition states that the retailer should bid higher at low inventory levels and alternately, bid lower at higher inventory levels. This counter intuitive result can be explained on the basis that a retailer would only invest in bidding and in the process, get a customer to visit his website if he knows the customer is likely to convert. However, since

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ACCEPTED MANUSCRIPT customer’s willingness to pay is a function of the inventory left, the probability of purchase is higher when the inventory is low. Hence, at low inventory levels, it is optimal for the retailer to bid higher and attract more customers to his website- because then the chance of conversion is higher. On the other hand, at high inventory levels, the customer’s willingness to pay is also lower and hence, it is not optimal to place high bids from the retailer’s perspective. This explains the phenomenon of high bids at low inventory levels and low bids at high inventory levels.

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The next proposition studies the pricing decision with respect to inventory. Proposition 2:

The optimal price decreases with inventory. In other words, at high levels of inventory, the retailer reduces prices to enhance sales.

In our model, the retailer has two levers to influence his profit function- bid and price.

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From Proposition 1, we find that at high inventory levels, the retailer does not invest in bidding anymore. Hence, to earn profits, the retailer plays on reducing the price of the product to attract customers and enhance sales. At low inventory levels, customer’s willingness to pay is high, hence the retailer places a higher bid and attracts more customers and simultaneously increases the price of the product to generate higher profits. In other

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words, the retailer uses bid and price as complements to maximize his profit. The above results have important implications for a retailer who uses sponsored search and employs

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dynamic pricing.

In the next section, we present numerical studies to derive critical managerial

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insights.

5. Numerical Analysis and Managerial Insights

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In this section, we present numerical studies to derive critical managerial insights. The parameters used in the numerical analysis are described in Table 3. At the start of each time- period, based on the level of inventory, the retailer decides on the price and bid

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amounts (only bid in case of the bid-only model). We study the decisions that lead to the most efficient outcomes, i.e. the ones that provide the retailer with highest rewards. Customers are drawn to the retailer’s website based on the sponsored search and then information about inventory Table 3: Parameters used in the Numerical Analysis 𝛼

Sharpness factor; Used to define the rate of change of click rate with respect to the bid

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ACCEPTED MANUSCRIPT

𝐾

𝜃 𝛿𝜇 𝛿𝜎

𝑘

Steepness factor; Used to adjust spread of bids Shape parameter of the Gamma distribution; Used to define skewness of the distribution of customer reservation prices Scale parameter of the gamma distribution; Used to scale the distribution of customer reservation prices vertically and horizontally Proportionality constant used to scale the mean reservation price Proportionality constant used to scale the standard deviation of customer

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𝛽

reservation price

Proportionality constant used to adjust the inventory range where the scarcity of the product impacts the customer willingness to pay

left provides an added impetus for conversion into sales. Each customer could have a

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different reservation price for the same product. These reservation prices are assumed to follow a gamma distribution. Multiple distributions can be derived from the gamma distribution based on the choice of shape (K) and scale (θ) parameters. Hence, we choose gamma distribution for our numerical analysis. The shape parameter is used to define the skewness of the distribution and the scale parameter is used to scale the distribution

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horizontally and vertically. To model the effect of inventory on a customer’s reservation price, various parameters such as inventory level, and reservation price have been used. Based on

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the different kinds of reservation price distributions, we obtain optimal bid and price decisions.

In our analysis, we have considered the click rate with respect to bid as an S-shaped

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curve. It is well established in the extant literature, that for small levels of advertising, there are increasing marginal returns whereas the returns diminish as advertising goes up. This is

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captured with the help of an S-shaped curve. We have used a similar S-shaped curve to represent the click rate as a function of bid. Equation (8) presents the click-rate curve. The 𝛼 and 𝛽 values decide the sharpness and steepness of the S-shape curve under

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consideration. The sharpness of the curve indicates the rate of change of the click rate with respect to the retailer’s bid. The steepness factor determines the spread of bids or the length of the tails of the S-curve. A smoother S-curve would result in a smooth change in the optimal bids rather than drastic jumps. A sensitivity analysis of the click rate curve by changing α and β is presented in the Appendix. 𝜆(𝑏)

=

λ∞ + λ0 𝑒 (𝛽−𝛼𝑏) 1 + 𝑒 (𝛽−𝛼𝑏)

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(8)

ACCEPTED MANUSCRIPT In the analysis presented henceforth we have taken α = 0.04 and β = 7 . Higher α values make the click rate curve sharper, that is, the click rate increases at a faster rate with the bid. Higher β values indicate more steepness of the curve, that is, the spread of bids is reduced. The retailer can estimate these values based on past data by relating the bids with the corresponding click rates. λ∞ is the maximum click rate the retailer can get, which therefore has a value of 1. λ0 is the minimum click rate, which corresponds to the click rate the retailer would be able to

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generate even if he does not bid anything in that particular time period. In our model, we take λ0 = 0.1.

Figure 4 presents the click-rate curve with respect to different bids. It can be seen in Figure 4 that the click rate changes drastically at certain points and remains constant over a wide range of bids.

As discussed, the customer willingness to pay is a function of the level of inventory.

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The reservation price in the model thus has the functional form: 𝜗(𝐼) = 𝜇(𝐼) + 𝜎(𝐼)𝑅

The relationship between inventory and reservation price is negative (Donovan, 2013; Marcus, 2015), i.e. a decrease in the inventory leads to an increase in the customer’s reservation price. However, we have assumed it follows a non-linear relationship captured

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with the help of exponential functions.

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Figure 4: Click rate curve

Equations (9) and (10) present the functional forms of µ(I)and σ(I) used in the numerical analysis respectively. We have used certain proportionality constants (δμ , δσ ) to scale these equations to maintain customer willingness to pay comparable with the price of the product. Higher value of the constants increases the magnitude of the mean reservation price and standard deviation of the customer willingness to pay. These values can be

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ACCEPTED MANUSCRIPT estimated through past data on mean and standard deviation of reservation prices. The parameter 𝑘 is used to adjust the inventory range where the scarcity of the product impacts the customer willingness to pay. This varies depending on the type of product under consideration. For instance, in case of seats on an airplane, the concept of scarcity becomes more relevant when the number of seats left at a certain price is less than 5 or 10, whereas for a high-end fashion item such as a limited edition watch an inventory level of 25-50 can

𝜇(𝐼) = 𝛿𝜇 𝑒 −𝑘𝐼 𝜎(𝐼) = 1 + 𝛿𝜎 𝑒 −𝑘𝐼

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significantly impact the customer willingness to pay.

(9) (10)

Here, we present a ‘10’ time period problem at different levels of inventory. We assume that the retailer’s bid varies between 0 and 350. Initially, for the fixed price model, we set the price at 400. We assume that the retailer does not wish to sell at a price lower

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than this, because of the cost associated with the product. For the model with both bid and price as levers, we allow the price to fluctuate between 400 and 1500. For now, we consider that the products have no salvage value. 𝐾, 𝜃 parameters are initially taken as 40 and 0.1 respectively. The mean of the reservation price distribution is given by 𝐾𝜃. High mean of the distribution indicates higher willingness to pay for the entire set of customers. Based on past

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data available with the retailer, 𝐾 and 𝜃 values may be selected to best represent the customer willingness to pay for the product. The impact of mean and variance of the

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customer willingness to pay on the optimal bid and pricing decisions are studied in detail in Section 5.2.

We ran the model for various other data sets also and obtained similar results.

dataset.

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However, for presentation brevity and illustration purposes, we use the results of the above

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Figure 5: Optimal Bidding at different levels of Inventory (Bid-only Model)

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Price = 400

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ACCEPTED MANUSCRIPT 5.1 Inventory Levels and Retailer’s Bid and Pricing Decisions In Figure 5, we present the plot of the bidding decisions (bid-only model) of the retailer at different inventory levels. We find that the retailer starts with the highest bid at low inventory levels and gradually decreases the bid to zero as the inventory left increases. The optimal bidding strategy, thus, moves from high to low as inventory levels increase. This change corresponds to the S-shaped curve of the click rate function. In Figure 6, we present the optimal bid and price decisions with changing inventory

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for the bid and price model. Here, the retailer has two levers to influence demand, the bid and the price. Generally, when a customer finds that the product might stock out soon, the customer’s willingness to pay for the product increases implying a higher probability of conversion (making a purchase). Hence, with low levels of inventory, the retailer focuses more on getting a customer to click on his link by increasing the sponsored search bids. Since, the probability of conversion is higher at low inventory levels, the retailer also in turn,

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charges a higher price to achieve higher profits. However, note that the click rates are a function of the bids modelled as an S-shaped curve. So, as the bids increase, beyond a point, there are diminishing marginal returns as maximum click rate would have been achieved for a particular bid and investing beyond that would not have a significant impact on enhancing the click rate. This explains why bids saturate after a point, though inventory

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levels decrease. In the simulation results presented, the bids were allowed to vary from 0 to 350. Based on the values of the different parameters, the bids saturate at an inventory level

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of 20 units. So, even with lower inventory levels, bids do not increase. Hence, our model provides inventory thresholds where it may not be optimal to increase bids arbitrarily.

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Figure 6: Optimal Bidding and Pricing at different levels of inventory (Bid and Price Model)

This explains the high bids and high prices at low inventory levels. On the other hand, at high levels of inventory, inventory does not significantly impact the purchase

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ACCEPTED MANUSCRIPT behavior of the customer. Hence, the retailer no longer invests in bidding in order to get a customer to visit the site owing to low conversion probability. Instead, the retailer focuses on increasing sales by lowering the price. Interestingly, by comparing the optimal bids in Figure 5 and Figure 6, we find that at same inventory levels, the retailer bids higher in the “bid-andprice” model compared to the “bid-only” model. The flexibility of bid and price as levers allows the retailer to extract a higher price from the customer while investing more in bidding vis-a-vis the case where the price is fixed, and bid is the only decision lever. This is

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understandable as even a unit sale at a higher price has enough margins to cover the higher bid amounts. Hence, the retailer bids aggressively to extract the maximum click rate.

To illustrate the bidding decision of the retailer with respect to the number of time periods in the selling season, we compare bids across both models (bid-only and bid-andprice models) with respect to remaining number of time periods in Figure 7.

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Figure 7: Bids in Comparison to Remaining Time periods

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We find that for a given level of inventory, the retailer increases his bids as the end of season nears in order to generate more traffic to his website and increase the chances of

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conversion to sale. It is interesting to note that in a given time-period, the retailer bids higher in the bid-and-price model than in the bid-only model. In the bid-and-price model, the retailer

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uses dynamic pricing along with optimal bidding to maximize his profits. The retailer uses a higher bid to attract more customers and uses pricing in conjunction to increase sales. Next, we compare the optimal decisions of the retailer under different scenarios

based on varying standard deviation of customers’ reservation prices. For this analysis, we kept the mean reservation price at a certain level of inventory constant and changed the corresponding standard deviation. For a given level of inventory, the reservation prices of customers could either be very close to each other (low standard deviation) or way different from each other (high standard deviation). This variability in customers’ reservation price has critical impact on the retailer’s bidding and pricing decisions.

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ACCEPTED MANUSCRIPT 5.2 Mean-Variance Analysis in Pricing and Bidding Decisions Table 4 and Table 5 show the trends in bidding and pricing decisions of the retailer in different scenarios marked by high and low demand variability. In Table 4, we present the optimal bids from the bid-only model and in Table 5, we present the optimal bid and price from the bid-and-price model. We compare the optimal decisions at five inventory levels viz. very low (VL), low (L), medium (M), high (H) and very high (VH). The inventory levels have been denoted by

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𝐼𝑉𝐿 (8 − 15 𝑢𝑛𝑖𝑡𝑠), 𝐼𝐿 (15 − 30𝑢𝑛𝑖𝑡𝑠), 𝐼𝑀 (30 − 50𝑢𝑛𝑖𝑡𝑠), 𝐼𝐻 (50 − 70𝑢𝑛𝑖𝑡𝑠), 𝐼𝑉𝐻 (> 70𝑢𝑛𝑖𝑡𝑠). The optimal bids range from 100 to 300 and accordingly we have classified the bids as high, low and medium relative to the upper and lower caps on the bid amount.

Table 4: Optimal Bidding at different levels of demand variability (Bid-Only Model)

𝐼𝑉𝐿 = {8,15} 𝐼𝐿 ={15,30} 𝐼𝑀 ={31,50} 𝐼𝐻 ={51,70} 𝐼𝑉𝐻 >70

250, High 250, High 200, Medium 100, Low 100, Low

Variability in Customer Reservation Price: High 250, High 250, High 250, High 200, Medium 100, Low

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Variability in Customer Reservation Price: Low

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First, we discuss the results from the bid-only model. We find that the retailer bids high at lower levels of inventory, irrespective of the demand variability. At low inventory

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levels, customers have high willingness to pay, hence irrespective of the demand variability, the retailer bids high to attract more customers. However, the optimal bids vary with variability in reservation prices as the inventory-on-hand increases. It can be observed from

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𝐼𝑀 , that there is a difference in the retailer’s bid decision in cases of high and low reservation price variability. The retailer bids higher in case of high variability. When the reservation

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price variability is low, i.e. when the customers’ reservation prices are closely clustered, there need not be enough customers with a high reservation price. Hence, the retailer lowers

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his bid as the expected return on the bid in terms of profits that is generated reduces. On the other hand, when the variability in the customer’s reservation price is high, there is a higher chance of getting a customer with high reservation price. This gives the retailer an incentive to attract more customers, i.e. bid higher. The retailer bids higher as the variability in the customer’s reservation price increases when inventory on hand is at moderate to high levels. However, at very high inventory levels, again the variability in the customer’s reservation price has no impact on the optimal bid decisions and we find that the retailer bids low in both the cases.

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ACCEPTED MANUSCRIPT Similar to the results obtained above, in case of the bid and price model (Table 5), also we find that at relatively lower and very high inventory levels, the retailer bids and prices equivalently both in case of high as well as low variability in the customer’s reservation price. As explained earlier, at low levels of inventory the retailer bids high and charges a higher price and at very low inventory levels, the retailer bids low and also lowers the price to maximize sales. Optimal decisions change with variability in customer’s reservation price at moderate to high inventory levels.

𝐼𝐿 = {15,30} 𝐼𝑀 = {31,50} 𝐼𝐻 = {51,70} 𝐼𝑉𝐻 > 70

Variability in Customer Reservation Price: High Bid Price 280, High 1500, High Bid Price 280, High 1500, High Bid Price 280, High 1500, High Bid Price 200, Medium 500, Medium Bid Price 100, Low 300, Low

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𝐼𝑉𝐿 = {8,15}

Variability in Customer Reservation Price: Low Bid Price 280, High 1500, High Bid Price 280, High 1500, High Bid Price 200, Medium 500, Medium Bid Price 100, Low 300, Low Bid Price 100, Low 300, Low

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Table 5: Optimal Bidding & Pricing at different levels of demand variability (Bid and Price Model)

At these inventory levels, we find that the retailer bids higher and charges a higher

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price when the variability in customer reservation price is higher. With higher variability in the customer’s reservation price, the chance of getting customers with higher reservation price

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increases. Therefore, under these circumstances, the retailer bids higher to attract more customers and also charges a higher price in order to increase profits. At very high inventory

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levels, there’s no marked difference in the retailer’s optimal decisions and he bids low and also charges a lower price.

Next, we analyze the optimal decisions under different scenarios by varying the

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mean reservation prices at different inventory levels and keeping the corresponding variability constant. This helps us segregate the effect of mean and variance on decision

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outcomes.

When there are more customers having a high reservation price, the mean

reservation price tends to be higher. Similarly, when there are more customers having a low reservation price, the mean reservation price tends to be lower. We formulated these scenarios by changing the parameters of the gamma distribution. As stated earlier, the gamma distribution represents the customer’s reservation prices. Hence, by changing the parameters, we used two distributions where the variance was kept constant but the mean reservation prices varied. As done in the previous analysis, we compare the optimal

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ACCEPTED MANUSCRIPT decisions at five inventory levels viz. very low (VL), low (L), medium (M), high (H) and very high (VH). The ranges for these inventory levels were kept same as before. Tables 6 and 7 show the trends in bidding and pricing decisions of the retailer in different scenarios- High Reservation price and Low Reservation price. In Table 6, we present the optimal bids from the bid-only model and in Table 7, we present the optimal bid and price from the bid-and-price model. Table 6: Optimal Bidding at different levels of Customer Reservation Price (Bid Only Model) 250, High 250, High 200, Medium 100, Low 100, Low

𝑀𝑒𝑎𝑛 𝑟𝑒𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒: 𝐻

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𝑀𝑒𝑎𝑛 𝑟𝑒𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒: 𝐿 𝐼𝑉𝐿 = {8,15} 𝐼𝐿 = {15,30} 𝐼𝑀 = {31,50} 𝐼𝐻 = {51,70} 𝐼𝑉𝐻 > 70

250, High 250, High 250, High 200, Medium 100, Low

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We find that at low inventory levels, the retailer bids high to attract more customers in both the scenarios marked by low and high mean reservation prices. However, the optimal bids vary with mean reservation prices as the inventory-on-hand increases. For a given inventory level, the retailer bids higher and also price higher when the mean reservation price is high. At moderate to high inventory levels, when the mean reservation prices are

and also charge a higher price.

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relatively higher, there is added incentive for the retailer to bid higher and attract customers

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Table 7: Optimal Bidding & Pricing at different levels of Customer Reservation Price (Bid and Price Model) 𝑀𝑒𝑎𝑛 𝑟𝑒𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒: 𝐿

𝐼𝐿 = {15,30}

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𝐼𝑀 = {31,50}

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𝐼𝑉𝐿 = {8,15}

Bid 280, High Bid 280, High Bid 200, Medium Bid 100, Low Bid 100, Low

𝐼𝐻 = {51,70}

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𝐼𝑉𝐻 > 70

Price 1500, High Price 1500, High Price 700, Medium Price 300, Low Price 300, Low

𝑀𝑒𝑎𝑛 𝑟𝑒𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒: 𝐻 Bid 280, High Bid 280, High Bid 280, High Bid 200, Medium Bid 100, Low

Price 1500, High Price 1500, High Price 1400, High Price 600, Medium Price 300, Low

In other words, at high mean reservation price, the retailer bids higher for a given

inventory level as he knows the customers’ willingness to pay is high and hence the retailer has an incentive to attract the customer to his site. He also charges a higher price compared to the lower mean reservation price scenario as he is aware that the customer would be willing to pay a higher price for the same product. At very high inventory levels, the retailer bids low, and also charges a lower price irrespective of the changing mean reservation prices.

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ACCEPTED MANUSCRIPT 5.3 Impact of Inventory Holding Cost on Bid and Pricing Decisions In this section we analyze the impact of inventory holding costs on the optimal bid and pricing decisions. The per unit holding cost over each time-period is denoted by ℎ. We consider two scenarios: (a) when the per unit holding cost is high (ℎ=5) (b) when holding cost is low (ℎ=0.5). The holding cost per unit per time-period, ℎ, will not be very high since each time-period, defined as the time for a ‘click’ (Ghose & Yang, 2009) by a prospective customer on the sponsored search keyword, will be considerably small.

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We first present the analysis for the bid-only model and then for the bid and price model. 5.3.1 Bid – Only Model

We compute the holding cost at the end of each time period and account for it accordingly in the three scenarios – (a) No click, (b) Click but no conversion, and (c) Click and convert. We

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first analyze the impact of holding cost in the bid-only model. The optimization equation with bid as the only decision variable is presented in (11). When a conversion happens, the inventory depletes by one unit and the holding cost incurred will correspond to (𝐼 − 1) units of inventory, otherwise the holding cost is computed for 𝐼 units of inventory. =

(1 − λ(𝑏))(𝜋(𝐼, 𝑡 − 1) − ℎ ∗ 𝐼) + λ(𝑏)𝐹(𝑝|𝐼)(𝜋(𝐼, 𝑡 − 1) − 𝑏 − ℎ ∗ 𝐼) + max { } 𝑏>0 λ(𝑏)𝐹̅ (𝑝|𝐼)(𝑝 + 𝜋(𝐼 − 1, 𝑡 − 1) − 𝑏 − ℎ ∗ (𝐼 − 1))

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𝜋(𝐼, 𝑡)

0

𝜋(𝐼, 0)

=

𝐼∗𝑠

for 𝑡 = 1,2, … 𝑇

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=

for 𝐼 > 0

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𝜋(0, 𝑡)

for 𝐼 > 0, 𝑡 = 1,2, … 𝑇

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Figure 8: Impact of Inventory Holding Costs on Optimal Bidding

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ACCEPTED MANUSCRIPT In Figure 8(a) and (b), we present the findings of the simulation with low and high holding costs. The retailer continues to place higher bids at lower inventories than at high inventories. However, as the holding cost increases, at high levels of inventory where conversion probability will be low (since customer reservation price is a function of stock-onhand), it becomes too costly for the retailer to incur both holding and bidding costs. Hence as the ratio of 𝑏/ℎ increases, the retailer stops bidding. Therefore, our model suggests inventory cut-offs where sponsored search bidding becomes relevant and this cut-off value

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decreases with higher inventory holding costs. Next, we study the impact of holding costs on the optimal bid and pricing decisions. 5.3.2 Bid and Price Model

The profit maximization model with both bid and price as levers with holding cost is given in equation (12). Like we did in equation (11), holding cost is computed at the end of each time

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period and accordingly in the three scenarios – (a) No click, (b) Click but no conversion, and (c) Click and convert. As before, only when a conversion happens, the inventory depletes by one unit and the holding cost incurred will correspond to (𝐼 − 1) units of inventory, otherwise the holding cost is computed for 𝐼 units of inventory. =

(1 − λ(𝑏))(𝜋(𝐼, 𝑡 − 1) − ℎ ∗ 𝐼) + λ(𝑏)𝐹(𝑝|𝐼)(𝜋(𝐼, 𝑡 − 1) − 𝑏 − ℎ ∗ 𝐼) + max { } 𝑏,𝑝>0 λ(𝑏)𝐹̅ (𝑝|𝐼)(𝑝 + 𝜋(𝐼 − 1, 𝑡 − 1) − 𝑏 − ℎ ∗ (𝐼 − 1))

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𝜋(𝐼, 𝑡)

0

𝜋(𝐼, 0)

=

𝐼∗𝑠

for 𝑡 = 1,2, … 𝑇

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=

for 𝐼 > 0

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𝜋(0, 𝑡)

for 𝐼 > 0, 𝑡 = 1,2, … 𝑇

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Figure 9: Impact of Inventory Holding Costs on Optimal Bidding

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ACCEPTED MANUSCRIPT In Figure 9 (a) and (b), we present the findings of the simulation with low and high holding costs. The retailer continues to place higher bids at lower inventories than at high inventories.

As before, with high inventory holding costs, it becomes too costly for the

retailer to incur both holding and bidding costs and at high inventory levels the retailer stops bidding. At higher inventory levels, the retailer uses price discounts to sell-off the product and the discounting is more pronounced with higher inventory holding costs. 6. Conclusion

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Internet penetration has enabled a shift from mass advertising to more targeted advertising in the recent past. This has led to significant growth in sponsored search marketing which several firms, including retail players, are taking advantage of. While retailers attract consumers to their websites, they also display inventory information to their customers. Such information affects the consumer’s purchase decision. Considering this, retailers can

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strategically decide on bidding and pricing strategies to maximize their profits. In this paper, we study the bidding and pricing strategies of a retailer selling a perishable product over a short selling horizon under inventory-linked customer willingness to pay. We develop a decision support model with two variations - one where the retailer decides on the bid amounts; another where the retailer coordinates bidding along with dynamic pricing

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decisions. The retailer determines the optimal bid such that sufficient traffic is generated to the website. In the bid-and-price model, the retailer complements the bid decisions with dynamic pricing.

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Our analysis shows that it is optimal for the decision maker to invest heavily in bidding at low inventory levels, whereas at high levels of inventory, the retailer should use

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price promotions to enhance profits. Intuitively, the decision maker should engage in increasing website traffic by bidding aggressively at high inventory levels. However, we find

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that at lower inventory levels, the likeliness of conversion is higher. Hence, the retailer has an incentive to increase his bids and attract more website traffic when the inventory on hand is low. In case of high inventory levels, the likeliness of conversion is low implying for every

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dollar invested in getting a customer to the site, the marginal return is lower. Accordingly, at high inventory levels the retailer lowers the price to induce higher sales. Therefore, bid and price can be used as complements based on the inventory level. These results have critical managerial implications as they give a retailer employing sponsored search and dynamic pricing important guidelines to maximize profits. Variability in customer reservation price at different inventory levels is an important consideration in the bidding and dynamic pricing decisions. We perform extensive numerical analysis by varying the customer reservation price and estimating the corresponding optimal bidding and pricing behavior. We find that the retailer bids higher when the variability in the

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ACCEPTED MANUSCRIPT customer’s reservation price is high compared to the low variability case. When the variability in the reservation prices of the customers is low, the retailer does not bid as high, as the probability of conversion at a higher price is low. However, as the variability in reservation prices increase, the probability of having at least one customer with a high reservation price increases. This gives the retailer an incentive to bid higher with increasing variability of the customer’s reservation price as the margin that the retailer gains upon making at least one such sale is high enough to cover the higher bids.

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We performed another set of numerical studies by varying the mean reservation prices. Here, we find that the optimal bids and the prices increase with an increase in the mean reservation price. When the mean reservation price is high, customers have a higher willingness to pay for the product. This incentivizes the retailer to drive traffic to the site by bidding high. Simultaneously, the retailer also charges a higher price to take advantage of the higher customer willingness to pay. Based on our analysis, we recommend a retailer to

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increase his bids and complement that with higher prices as the variability and the mean of the customer’s reservation price increases at a certain level of inventory. We also studied the optimal bidding pattern as the retailer approaches the end of season. We find that for a given level of inventory, the retailer increases his bids as the end of season nears. This is because there is increased pressure on the retailer to liquidate the

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inventory before the end of the selling season. The more the traffic generated, the easier it is to liquidate the inventory. Notably, in a given time period, the retailer bids higher in the bid-

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and-price model than in the bid-only model. In the bid-and-price model, there is the additional lever of pricing which acts as a complement to the bidding decision. The retailer uses a higher bid to attract more customers and uses pricing in conjunction to increase

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sales.

The decision support system tool developed in this paper can be extended in multiple

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directions. One important extension could be to consider non-perishable products with replenishment of inventory. This would incorporate ordering cost, set-up cost, etc. into our

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existing model. In this paper, we have not modelled competition explicitly. Sponsored search bidding and dynamic pricing in a competitive scenario can be another interesting research extension. In this paper, we have assumed rational, profit maximizing behavior of the retailer. We can analyze the strategic behavior of the retailer and the customers when the retailer wants to create intentional scarcity. Production capacity decisions under the impact of inventory-linked willingness-to-pay can also be an interesting future research topic1. Empirically testing some of the results obtained in this paper could be another worthwhile research endeavor.

1

We thank the reviewer for this suggestion

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