Dynamic Revenue Management for Online Display Advertising

Transcription

1 Dynamic Revenue Management for Online Display Advertising Guillaume Roels UCLA Anderson School of Management, UCLA, 110 Westwood Plaza, Los Angeles, CA 90095, USA, Kristin Fridgeirsdottir Management Science and Operations, London Business School, Regent s Park, London, NW1 4SA, United Kingdom, kristin@london.edu In this paper, we propose an dynamic optimization model to maximize a web publisher s online display advertising revenues. Specifically, our model dynamically selects which advertising requests to accept and dynamically delivers the promised advertising impressions to viewers so as to maximize revenue, accounting for uncertainty in advertising requests and website traffic. After characterizing the structural properties of our model, we propose a Certainty Equivalent Control heuristic and then show with a real case study that our optimization-based method typically outperforms common practices. Our analysis thus highlights the importance of integrating the sales function with the advertisement delivery function in web publishing companies for globally maximizing revenues. Key words : Revenue Management, Online Advertising, Dynamic Programming, Linear Programming 1

2 2 Dynamic Revenue Management for Online Display Advertising 1. Introduction Online advertising has grown at a fast pace over the past decade, reaching a revenue of $21.2 billion in 2007 IAB 2007, and the growth is not expected to slow down in the near future as users spend more time online, rich media technology increases user interaction, and online publishers start discovering ways to monetize their remnant inventory Hof The value proposition of digital marketing is to provide real-time feedback on customer behavior and closely monitor the performance of advertising campaigns. Online advertising has changed the nature of marketing, requiring more quantitative approaches with sophisticated tools and algorithms Booz Allen Hamilton 2007 as well as dynamic adjustment of spending, in contrast to the traditional up-front spending in broadcast advertising Araman and Popescu Hence, different approaches are needed. The online advertising space can be divided into two parts: Search word advertising and display advertising. Search word advertising is done by search engine websites that post advertisements along with search word results. Display advertising, on the other hand, is done by web publishers who post advertisement banners across the top or along the side of their website pages. In this paper, we consider a web publisher that seeks to maximize its advertising revenues by delivering display advertisements ads on its website. Taking into account traffic uncertainty, the publisher needs to decide which advertising contracts to accept or reject and how to fulfill them. In practice, contract negotiation and advertisement delivery are often done independently by the sales team and delivery engines e.g. Dart by DoubleClick respectively, with little coordination between the two functions. We propose a unified approach where the web publisher dynamically decides to accept or reject advertising requests and dynamically delivers the promised advertising contract to the viewers, so as to maximize its revenues over a finite horizon. We formulate the problem as a dynamic program and characterize its structural properties. We then propose a Certainty Equivalent Control heuristic, similar to Bertsimas and Popescu Using a real case study, we show that our heuristic typically outperforms other approaches that are commonly used in practice.

3 Dynamic Revenue Management for Online Display Advertising 3 The paper is organized as follows. In Section 2 we review the related literature. We model the problem as a dynamic program in Section 3 and characterize its structural properties in Section 4. We then propose the Certainty Equivalent Control heuristic in Section 5 and illustrate its performance on a real case study in Section 6. Finally, we conclude in Section Literature Review The marketing literature on online advertising is abundant see Prasad et al and references therein. In contrast, there exist few guidelines for effectively managing online advertising inventory, despite the importance of that problem Bain & Company Araman and Popescu 2007 and Kimms and Muller-Bungart 2007 study revenue management for broadcast advertising. In contrast to broadcast media, where a big part of the advertising capacity is allocated at the beginning of the season, online advertising requests arise at any point in time during the season. Moreover, the delivery of online media advertising can be targeted to specific users demographics and behaviors. Hence, different approaches are needed. Araman and Fridgeirsdottir 2008 develop a pricing framework for web publishers facing uncertain demand and uncertain advertising inventory. Using a novel steady-state queuing model, they determine the optimal prices to quote to heterogeneous advertisers. Building on their work, Fridgeirsdottir and Najafi-Asadolahi 2008a characterize the optimal pricing strategy when advertisers are impatient, which results in new types of queueing models. In contrast, our model optimizes the contract acceptance/rejection decisions over a finite time horizon with exogenous prices. Our model also optimizes the advertisement scheduling. Ad scheduling can typically be formulated as a linear optimization problem Chickering and Heckerman 2003 but becomes NP-Hard when the geometrical features of the website are modeled Kumar et al Similar to ad scheduling on websites, Turner et al model ad scheduling in video games and develop a dynamic scheduling algorithm. Although the cost-per-impression CPM pricing scheme is prominent in online display advertising, there exist other pricing schemes, such as cost-per-click CPC and cost-per-action CPA,

4 4 Dynamic Revenue Management for Online Display Advertising if the advertiser s objective is to generate traffic or sales rather than brand awareness. The attractiveness of one pricing scheme over the other is studied by Fridgeirsdottir and Najafi-Asadolahi 2008b and Mangani The pricing model of search word advertising is primarily based on clicks CPC. Because the ad click-through rates are unknown a priori, scheduling search word ads must balance exploration with exploitation, see Rusmevichientong and Williamson Some web publishers not only generate revenues from advertising but also from subscriptions. Prasad et al suggest that websites can increase their revenues by offering a menu of contracts, where high subscription fees are associated with a small number of ads and vice versa. Using an optimal control model, Kumar and Sethi 2008 dynamically determine the optimal subscription fee and the amount of advertising on a website. However, Baye and Morgan 2000 argue that competition mitigates the attractiveness of subscription fees. In this paper, we develop an integrative approach that simultaneously optimizes contract negotiation and advertisement delivery. Our model draws on traditional network revenue management models Talluri and van Ryzin 2004 and in particular on the solution technique developed by Bertsimas and Popescu Model We consider an online content publisher who seeks to maximize its revenue from display ads over a time window [0, T ] e.g., a quarter, a fiscal year, by i accepting or rejecting advertising requests and ii dynamically delivering the advertisement impressions to the website viewers. The publisher s objective is thus to match supply advertising inventory with demand advertising requests so as to maximize its revenues. In the following, we first formalize these concepts of supply and demand and detail the sequence of events. We will decompose the time window [0, T ] into subintervals, which will lead to a dynamic programming formulation for solving the publisher s problem.

5 Dynamic Revenue Management for Online Display Advertising Supply Advertising impressions are uniquely characterized by combination of page and banner location, delivery time, and viewer type. For instance, an ad impression could be a top banner on the website homepage during the first week of the second quarter, viewed by an old male originating from California. Let P be the set of potential pages and banner locations on the website and U be the set of viewer types. For simplicity, we consider discrete time periods and define T as the set of delivery time windows. As a result, the set of possible types of ad impressions can be defined as the cross-product set, i.e., W = P U T. In any period t T, let W t denote the set of possible ad impressions in period t, i.e., W t = P U {t}. The number of ad impressions, also known as the ad inventory, is however uncertain at the time the advertising requests must be accepted or rejected because they are generated by the web traffic. We denote by [I k ] k W t the random ad inventory in thousand units available to the publisher in period t T of each type k W t. If only one ad is delivered per page view, k W t I k exactly corresponds to the website traffic in period t. In general, however, our model allows for multiple ads to be displayed on the same page. To simplify the analysis, we make the following standard assumption: Assumption 1. The number of advertising impressions [I k ] k W t in any period t T follows a Markov process. Although web traffic could in principle be correlated over time, there is empirical evidence that a Poisson process is a reasonable approximation for web traffic Cao et. al 2002, which makes Assumption 1 reasonable Demand Advertisers submit their advertising requests to the publisher either directly or through the intermediary of an advertising agency. Let C denote the potential set of contracts. Each contract i C requests a number of impressions n i in thousands to be delivered on a particular set of pages to

6 6 Dynamic Revenue Management for Online Display Advertising a particular set of viewers in a particular time window also known as flight, denoted by W i W. Each ad impression generates a unit revenue r i also known as Cost-per-Thousand, or CPM to the publisher. If the advertising contract specifies a cost-per-click CPC or cost-per-action CPA, instead of a cost per impression, r i is the expected revenue per impression, obtained by multiplying the CPC or the CPA by the probability that a user will click or take the specified action. This approach is an aggregated way to incorporate these performance based payments schemes. For more details see Fridgeirsdottir and Najafi-Asadolahi 2008b. Whenever a publisher does not fulfill a contract, it incurs a goodwill penalty π i per under-delivered impression. Traditionally, advertisers have requested make-goods in case of underdelivery, typically amounting to 10%-50% of the average CPM of the shortfall. To summarize, a contract i C specifies four parameters: the number of impressions n i, the set of pages/viewers/dates W i, the CPM r i, and the goodwill penalty π i. In addition, we assume that the null contract i.e., no request, denoted by the index 0, also belongs to C. When publishers do not have enough advertisement contracts to fill their advertising slots, they usually have recourse to advertising networks. Advertising networks also known as ad networks offer significantly lower rates than regular advertisers typically ten times lower and do not require any specific impression guarantee. As a result, ad networks are typically utilized for filling up the remnant inventory. We model ad networks as an additional contract, say contract a, already accepted in period 0, with an infinite number of requested impressions but no underdelivery penalty, i.e., n a, W a, r a, π a =, W, r a, 0 where r a r i for all i C \ {0}. In general, an advertising contract consists of a bundle of contracts n i, W i, r i, π i. A bundle must be accepted in full or rejected. Let B bet the potential set of bundles, including the null contract i.e., no request and the ad network contract. For any bundle j B, let C j C be the set of contracts bundled together. Arrivals of advertising requests are assumed to be uncertain at time 0. For any bundle j B, let p jt be the probability that bundle j will be requested in period t. We also assume that the time

7 Dynamic Revenue Management for Online Display Advertising 7 intervals are so small that the arrival probability of two simultaneous requests is negligible. That is, in each period t, at most one bundle will be requested. Therefore, for any t T, p j B jt = 1. To simplify the analysis, we make the following standard assumption see, e.g., Talluri and van Ryzin 2004: Assumption 2. The arrivals of advertising requests follow a Markov process Sequence of Events In each time period the publisher faces two decisions. First he needs to determine which advertising requests to accept, balancing the high CPMs against the underdelivery penalties. Then he needs to decide which ad impressions to deliver on its website in any period t T, balancing immediate revenues against potential future profits. In contrast to broadcast networks, online publishers can observe their traffic in real time and dynamically adjust their advertisement delivery strategy. To model this flexibility in a discrete-time framework, we make the following assumption. Assumption 3. In each period t, the publisher observes the traffic on its website before delivering the ads. Note that this last assumption is not restrictive if the time intervals are small. Moreover, with the current internet technology, publishers are able to first observe the characteristics of the viewers before deciding which ads to serve. Under these three assumptions, the following sequence of events/actions takes place in every period t: 1. Advertisers request a bundle i B. 2. The publisher decides to accept, or reject, the request. 3. The publisher observes the traffic on its web pages, i.e., how much advertising inventory of each type page/viewer is available in period t. 4. The publisher decides which impressions to deliver, from the pool of advertising contracts it has accepted.

8 8 Dynamic Revenue Management for Online Display Advertising 5. The publisher delivers impressions and collects revenues. For every contract that reaches the end of its flight, the publisher incurs goodwill penalties in case of under-delivery. This sequence of events naturally gives rise to a dynamic programming formulating for solving the publisher s problem, which we present next Dynamic Programming Formulation. Suppose that at time t, the web publisher has a set S C of contracts in progress. Let V t be its expected profit-to-go from t onwards, before any request arises in t, given that y i thousand impressions remain to be delivered, for each contract i S. We denote by V t {i, y i } i S {i, n i } i Cj the expected profit-to-go if bundle j B has been accepted, consisting of the contracts i C j with a request for n i impressions each. Similarly, we denote by V t the expected profit-to-go from t onwards if no contract is accepted in period t. Accordingly, for t < T, the decision of accepting or rejecting an incoming request can be modeled as follows: V t = j B } p jt max {V t, V t {i, y i } i S {i, y i } i Cj. 1 Without loss of generality, we assume that the goodwill penalty fees are incurred at the end of the horizon. That is, if y i impressions, i S, have not been delivered by the end of the horizon T, the publisher s profit equals V T = π i y i. For the contracts that end at or before T, the loss of goodwill parameter π i will be positive. In contrast, for contracts which flight extends beyond T, the parameter π i may represent the salvage value associated with these contracts, and may therefore be negative; it will however never be smaller than r i. According to Assumption 3, the publisher observes the web traffic before delivering the ad impressions. Let Ṽt, [I k ] k W t be the profit-to-go in period t after having observed the amount of available ad inventory [I k ] k W t. Accordingly, i S V t = E [Ṽt, [I k ] k W t ], 2

9 Dynamic Revenue Management for Online Display Advertising 9 in which the expectation is taken with respect to the amount of advertising inventory of each type or equivalently, to the web traffic in period t. After observing the amount of available ad inventory, the publisher decides which ad impressions to deliver from its pool of contracts. Let x ik, i S, k W i, be the number of impressions of ads from contract i delivered on a page/viewer/time k. Let also W t i = W i W t be the set of page and viewer types that are available in period t for delivering ad impressions for contract i S. The publisher s problem can therefore be formulated as the following recursion: Ṽ t, [I k ] k W t = max r i x ik + V t+1 {x ik } i S,k W t i, y i i s.t. i S i S:k W t i k W t i x ik I k k W t, k W t i x ik i S x ik y i i S, 3 k W t i x ik 0 i S, k W t i. The objective function balances the immediate revenues against the potential future profits. The number of impressions to be delivered in the future is equal to the number of impressions to be delivered at the beginning of period t, y i, minus the number of impressions that have been delivered in period t, k W i t x ik. The first constraint imposes that the number of impressions delivered on a particular page to a particular viewer type cannot exceed the available ad inventory. If the publisher has access to advertising networks, this first constraint will always be tight because the publisher can always sell its remnant inventory at lower rates through the ad network. The second constraint restricts the number of deliveries to be no greater than the requested number of impressions specified by the contract. The last constraint requires nonnegativity of the delivered impressions. In addition, we have V t+1 {yi } i S Vt {yi } i S, for all t, because setting xik = 0 for all i S, k Wi t is a feasible solution for the assignment problem 3 in period t. Moreover, for any j S, the marginal value of an impression V t {y i } i S\{j} {y j + 1} V t {yi } i S rj because the CPM does not change over time. With these two results, one can show that it is never optimal to delay the delivery of an ad impression in the hope of selling it at a larger rate in the future.

10 10 Dynamic Revenue Management for Online Display Advertising 4. Structural Properties In general, the objective function may not be concave, if bundles of contracts are required to be either accepted in full or rejected. Similarly, in the classic dynamic revenue management problem, the value function may not be concave with batch arrivals. In practice, however, contracts are negotiated and the publisher may have some flexibility in choosing the number of impressions to accept. Relaxing Equation 1 to allow for the publisher to choose less number of impressions than requested, i.e., V t {yi } i S = { p jt max 0 y i n i, i C j j B } V t {i, y i } i S {i, y i } i Cj, 4 makes the problem concave, as we show next. Proposition 1. If contracts can be partially accepted, as in 4, then for any i S, V t is jointly concave in y i, i S. Proof The proof is by induction. The function V T is linear, and therefore jointly concave in {y i } i S. For any t, suppose that the function V t+1 is jointly concave in { {y i } i S. Because concavity is preserved under affine transformations, V t+1 i, y i } k W i t x ik i S is jointly concave in x ik and y i, for all i S and k W t i. Therefore, the objective function and the constraint set in Problem 3 are respectively jointly concave and jointly convex in {x ik } i S,k W t i and {y i } i S. Because partial maximization of a jointly concave function over a convex set preserves concavity Boyd and Vandenberghe 2004, Ṽt, [I k ] k W t is jointly concave in {yi } i S, for any [I k ] k W t. Taking the expectation with respect to [I k ] k W t preserves concavity, so V t is also concave in {y i } i S. For any j S, maximizing V t with respect to yj over the convex set [0, n j ] in 4 preserves concavity based on the partial maximization argument above, so does taking a nonnegative weighted sum of concave functions. Therefore, V t is also concave in {y i } i S, completing the induction step. Because Problem 4 is a concave maximization problem over a convex set, the optimal number of impressions to accept may not necessarily be at the boundary of the interval. As a result, large contracts will typically tend to be renegotiated, especially if the web traffic forecasts are low.

11 Dynamic Revenue Management for Online Display Advertising 11 We next investigate the sensitivity of the publisher s value function to the problem parameters. For convenience, let us denote by V t {i, y i } i S ; θ the value function at time t when some parameter takes on a value θ. The next proposition shows that the value function is convexly increasing with the CPM and convexly decreasing with the penalty π i. In addition, if partial contracts are acceptable, the publisher benefits from larger number of impressions requested, but with decreasing marginal returns, which is in line with the findings in Araman and Fridgeirsdottir 2008 and Fridgeirsdottir and Najafi-Asadolahi 2008a. Proposition 2. For any j S, V t ; π j is convex decreasing in πj and V t {yi } i S ; r j is convex increasing in r j. If the contracts can be partially accepted, as in 4, then for any j S, V t ; n j is concave increasing in nj. Proof For each {y i } i S, the function V T ; π j is linear, and therefore convex, decreasing in π j. Because the successive pointwise maximizations in 3, as well as in 1 or 4, and the expectations in 2, preserve convexity, the value function V t ; π j is convex decreasing in π j, for any t. Let t be the last period of the duration of contract i, i.e., t = max{t : W i W t }. For each {y i } i S, the function Ṽt ; r j is convex increasing in rj, because it is the pointwise maximum of linear functions of r j in 3. Because the successive pointwise maximizations in 3 as well as in 1 or 4, and the expectations in 2, preserve convexity, the value function V t ; r j is convex increasing in r j, for any t t. Let t be the first period of the duration of contract j, i.e., t = min{t : W j W t }. Because n j is the right-hand side of the constraint in 4, V t ; n j is increasing in nj, and jointly concave in n j and {y i } i S. Because the successive partial maximizations, over convex sets, in 3 and 4, and the expectations in 2, preserve concavity, the value function V t ; n j is concave increasing in n j, for any t t. The function Ṽt, [I k ] k W t is also concave increasing with Ik. Thus, smaller profits will be obtained under second-order stochastically larger random variables. In particular, if the number

12 12 Dynamic Revenue Management for Online Display Advertising of page views is normally or log-normally distributed, the publisher s profit will be decreasing with the variance of the distribution Levy The state space of the dynamic program can however be very large, leading to the so-called curse of dimensionality and limiting the practicality of the approach. In the next two sections, we show that, even if the dynamic program is solved approximately, it stills yield many benefits over alternative, myopic approaches. 5. Certainty Equivalent Approximation Following Bertsimas and Popescu 2003, we propose a Certainty Equivalent Control CEC heuristic. Specifically, we assume that the ad inventory of each type determined by the web traffic is known in advance and equal to its expectation. We also assume perfect knowledge about the number and characteristics of future requests. In the dynamic optimization formulation, the occurrence of any request j B, consisting of the contracts in C j with characteristics n i, W i, r i, π i i Cj, has a binary nature: either request j is made in period t, with some probability p jt, or it is not. Instead, we assume that, for all i C j, a request for contract i will be introduced in period t, deterministically, with only n i p jt requests for impressions. Given the good performance of the CEC heuristic in network revenue management Bertsimas and Popescu 2003 and that controls based on the CEC are asymptotically optimal for the stochastic network revenue management problem Talluri and van Ryzin 2004, one expects these restrictions not to be too stringent in our setting. d Analogous to V t, we denote by V t the maximum profit-to-go in period t when there is no uncertainty the superscript d refers to deterministic. Let S be the set of contracts that have been accepted at time t and let B t be the set of future bundle requests. Because both the ad inventory and the future requests are assumed to be known at time t, the dynamic optimization problem is now deterministic and an open-loop control is optimal. In particular, let the binary variable δ j equal 1 if bundle j B t is planned to be accepted and equal 0 otherwise. Similarly, let x i,k,s denote the number of ad impressions from contract i S j Bt C j planned to be delivered

13 Dynamic Revenue Management for Online Display Advertising 13 in period s = t,..., T to the page/viewer type k W s i. Accordingly, the publisher s problem at time t can be formulated as the following mixed-integer optimization problem: T = max r i x i,k,s π i y i i S V d t s.t. i S j Bt C j s=t k W i s δ j p i n i j B t i C j π i i S j Bt C j:k W s i s=t k W i s T s=t k W i s x i,k,s T s=t k W i s x i,k,s x i,k,s E[I k ] k W s, s = t + 1,..., T, T x i,k,s y i i S, 5 T x i,k,s p i n i δ j i j Bt C j, j B t s=t k W i s x i,k,s 0 i S j Bt C j, k W s i, s = t,..., T, δ j [0, 1] j B t. The objective function in 5 consists of three terms: the total advertising revenue, summed over all contracts and future time periods, the underdelivery penalty associated with the contracts that have already been accepted at time t, and the underdelivery penalty associated with the future contracts, if they are to be accepted i.e., if δ j = 1 for any j B t. Similar to 3, the first constraint ensures that the number of ad impressions does not exceed the expected ad inventory, for all future periods. The second and third constraints guarantee that the delivered impressions do not exceed the number of impressions requested by the contracts, respectively for the contracts that have already been accepted in period t and for the future contracts. Finally, ad impressions are required to be nonnegative and future contracts can be either accepted in full or rejected. Analogous to 3, we define Ṽ d t d, [I k ] k W t in the same way as V t, where the right-hand side of the first set of constraints in 5 associated with period t, i.e., E[I k ], are replaced with the actual ad inventory I k for all k W t. Let us define A t the set of future bundles that are planned to be accepted, that is A t = {j B t : δ j = 1}. Moreover, let us denote by V d t ; A t the optimal revenue of the deterministic

14 14 Dynamic Revenue Management for Online Display Advertising problem if the set of future contracts that are accepted corresponds to A t. For a given set of contracts A t, the optimization problem 5 reduces to a simple transportation problem. The next proposition characterizes the sensitivity of the revenue with respect to the problem parameters for a given set of contracts A t. Similar to Proposition 2, we denote by V d t ; A t ; θ the optimal value of 5 when some parameter takes on the value θ. As in Proposition 2, we find that the optimal revenue of the deterministic problem is convex increasing with the CPM, convex decreasing with the goodwill penalty, and concave increasing in the number of impressions, when the set of future contracts is given. We also find that broader targets in terms of page types or banner locations, viewer types, and flights are beneficial to the publisher, because they give more flexibility, but exhibit decreasing differences. Proposition 3. Suppose the set of future contracts to be accepted is given by A t. Then, for any i S, V d t ; A t ; y i is concave increasing in yi ; for any i A t, V d t ; A t ; n i is concave increasing in n i. For any i S A t, V d t ; A t ; r i is convex increasing in ri, V d t ; A t ; π i is convex decreasing in πi, and V d t ; A t ; W i is submodular increasing on W. For any k W, V d t ; A t ; E[I k ] is concave increasing in E[I k ]. Proof All results follow form standard linear programming theory see Bertsimas and Tsitsiklis The submodularity of V d t ; A t ; W i follows from Theorem 4 in Wolsey Because Problem 5 reduces to a linear optimization problem when the set A t is fixed, the opportunity costs of the advertising space can be obtained as a byproduct of the optimization and be used in the negotiation process. For instance, some advertisers request the exclusive use of the homepage over a certain time window in exchange for a flat fee. Using the optimal shadow prices from 5 could help publishers set their fees, to account for the marginal opportunity cost of the advertising impressions. On the other hand, it may help an advertiser adjust its advertising time window to benefit from lower rates whenever the advertisement inventory exceeds the demand. When the set A t needs to be chosen, 5 is a capacitated facility location problem, which is known to be NP-Hard. Thus, if the number of potential contracts is large, the problem may not

15 Dynamic Revenue Management for Online Display Advertising 15 be solvable in reasonable time. However, as demonstrated in Proposition 3.4 in Nemhauser et al. 1978, V t d ; A t is submodular on St and simple greedy or search algorithms that select the most promising contracts are associated with reasonable performance guarantees see, e.g., Nemhauser et al If there is no uncertainty about the request arrivals as in the case study we examine in the next section, V d t V t for all t and all S C. To see this, observe that, for any given acceptance/rejection policy, V t can be bounded from above by replacing the distribution of the number of advertising impressions [I k ] k W t, for all t T, by its mean, using Jensen s inequality. Maximizing then the upper bound over all policies exactly leads to V d t. The implementation of the CEC follows the following sequence. In every period t, 1. An advertising request j B t arises. 2. Request j is accepted if V d t {i, y i } i S {i, y i } i Cj V d t. If the request is accepted, update S S C j and B t B t \ {j}. 3. The publisher observes the available ad inventory in period t, i.e., [I k ], k W t. 4. Compute Ṽ t d, [I k ] k W t. Let {xi,k,s } i S,k W,s=t,...,T be the optimal solution of the associated capacitated facility location problem. 5. For all i S, k W t, deliver x i,k,t ad impressions from contract i to the page/viewer type k. Even though the number of contracts and the ad inventories are assumed to be known with certainty in 5, the policy is adaptable to changes in contract offers or demand because it is reoptimized on a folding horizon basis. If the number of future contracts is relatively small i.e., less than a few hundreds, Problem 5 can easily be solved to optimality in a reasonable amount of time, making the approach appealing for practical applications. 6. Case Study In this section, we evaluate the performance of our optimization-based approach on a real problem instance, detailed in Roels and Skowrup 2008, and compare it to common practices.

16 16 Dynamic Revenue Management for Online Display Advertising 6.1. Case Description An online content publisher, Break.com, seeks to determine which display advertising contracts to accept and which ad impressions to deliver over the course of the second quarter of Founded in 2005 as a cross between YouTube and Spike TV, Break.com quickly built a loyal audience around its ability to find and purchase funny, user-generated video content and games that appeal to young males. In 2005, the company made less than $1.4 million in display ad revenue; but by 2007, with nine million monthly unique visitors, the company wanted to achieve a ten-fold growth in advertising revenues. Supply. Break.com serves display ads on its homepage, on the video page, on the game page, as well as on any page of the website which is referred to Run-of-Site. Advertisements are targeted to only one type of viewers, namely the males, which constitute the website main audience. Finally, the second quarter is divided in weeks, from week 14 to week 27. As a result, the set of types of advertising slots W, defined as the cross-product P U T, consists of 56 elements. The amount of advertising inventory is unknown at the beginning of the quarter because it depends on the web traffic. A manager of the company estimated the daily mean number of page views for each targeted page homepage, videos, games, others, as well as a low and high estimates respectively equal to 50% and 150% of the baseline estimate see Exhibit 4 in Skowrup and Roels Due to the high traffic on the website, we modeled the number of visitors with a normal distribution, as a limiting approximation to the Poisson distribution of web traffic. We assumed that the low-high estimate range corresponded to the 95%-confidence interval about the mean, leading to an estimated daily standard deviation of one fourth the mean. Without correlation, the coefficient of variation of the weekly demand thus equals 1/4 7. Finally, we assumed that the number of ad impressions was equal to the number of page views, i.e., only one banner was displayed per page. Demand. The publisher has already accepted 24 bundle contracts and expects to receive 11 additional requests. Hence, the number of requests is known deterministically, in contrast to the

17 Dynamic Revenue Management for Online Display Advertising 17 dynamic programming formulation presented in Section 3. A bundle typically consists of two to four contracts, depending on the number of page types covered. Each contract specifies a targeted page type, a delivery time window which we rounded to full weeks, a CPM, and a requested number of impressions see Exhibits 5-6 in Skowrup and Roels We considered a constant goodwill penalty rate of 10% of the contract CPM, per underdelivered impression. We also assumed that the company had recourse to ad networks, offering a constant CPM of $0.30 per impression. CEC Heuristic. Because of the large number of bundles, together with the large number of types of advertising inventory, an exact optimization approach as proposed in Section 3 would have been computationally prohibitive. Instead, we considered the CEC approach presented in Section 5, re-solved at the beginning of each period. The CEC heuristic involves the solution of two mixedinteger optimization problems 5 per period, to sequentially decide i which bundles to accept and ii how to deliver the requested impressions to the website viewers. Benchmarks. As argued in the previous sections, V d 0 {yi, i} i S, where S corresponds to the set of 24 bundle contracts that have already been accepted at time 0, is an upper bound on the optimal profit-to-go, and consequently, on the profit generated with the CEC approach, if there is no uncertainty about the request arrivals. We refer to this upper bound as DET, for deterministic. Currently, the company is using a threshold policy to determine which requests to accept or reject, based on their average CPM. That is, a contract is accepted if and only if its CPM is larger than a certain threshold price, which was preliminarily determined based on a yearly sales goal. In our implementation, we considered several threshold values, ranging from $3 to $4.5, where a $3 CPM is among the lowest CPMs that were requested and $4.5 is among the highest CPMs that were requested. Using the threshold policy, the acceptance/rejection decisions of the bundles can be made at the beginning of the quarter, because it does not depend on capacity usage information. Based on the threshold policy, we consider the following two heuristics. First, we consider the threshold policy, for deciding which requests to accept, in conjunction with 5 for deciding which impressions to deliver. Because 5 reduces to a linear optimization problem once contracts have been selected, we refer to this heuristic as TH-LP, for threshold-linear program.

18 18 Dynamic Revenue Management for Online Display Advertising The second heuristic is based on the common industry practice of uniformly delivering impressions over time. Specifically, in each period, we consider all contracts that remain to be completed and define the current load as the total number of impressions remaining to be delivered, divided by the total number of periods until the end of the flight. We then solve a one-period version of 5 so as to match the current loads to the available ad inventory. We refer to this second heuristic as TH-UNI, for threshold-uniform allocation Results. Base Case. We simulated the performance of our CEC against TH-LP and TH-UNI over 100 runs. The optimization of 5 was implemented in CPLEX 10.0 and took less than a second. Table 1 compares the expected profit advertising revenue + ad network advertising revenue - goodwill penalties of all policies for different values of demand coefficient of variation. Table 1 Policy Expected Revenues as a Function of the Coefficient of Variation. Coefficient of Variation Threshold 1/4 7 1/2 7 1/ 7 2/ 7 DET 1,906,900 1,906,900 1,906,900 1,906,900 CEC 1,898,200 1,886,000 1,847,400 1,791,900 $3.0 1,885,000 1,870,800 1,832,400 1,778,200 TH-LP $3.5 1,853,500 1,840,400 1,805,000 1,791,900 $4.0 1,811,600 1,800,300 1,768,100 1,711,500 $4.5 1,784,700 1,778,600 1,752,600 1,697,000 TH-UNI $3.0 1,568,700 1,562,900 1,543,500 1,502,600 $3.5 1,557,600 1,554,200 1,535,100 1,493,000 $4.0 1,524,500 1,518,300 1,497,900 1,455,400 $4.5 1,507,100 1,503,100 1,486,200 1,445,900 Table 1 shows that the CEC is near-optimal in the base case Coefficient of Variation equal to 1/4 7. The optimality gap, relative to DET, slightly deteriorates as the coefficient of variation increases, but so does also the revenue under the optimal DP policy because it is smaller under second-order larger distributions. We therefore expect the CEC policy to be near-optimal under all web traffic scenarios. In addition, the CEC heuristic always dominates the threshold policies. Moreover, comparing the performance of TH-LP with TH-UNI reveals that adopting an optimization-based approach for

19 Dynamic Revenue Management for Online Display Advertising 19 delivering impressions, rather than distributing them evenly over the flight duration, can generate 15-20% more profits. Optimization-based approaches can therefore lead to significant additional gains in managing advertising contracts. Because advertisers typically value uniform impressions to maximize the outreach of their campaigns, many publishers have adopted this ad delivery mode as common industry practice, even though it is not formally contracted on. However, the revenue differential between the TH-UNI and the CEC approaches reveals that uniform delivery comes at a cost to the publisher and should be incorporated in contract negotiations. In particular, it is paramount for publishers to assess whether uniform delivery is really valued by their clients and to choose to offer this free service only for advertisers with which they want to build long-term relationships. It is interesting to note that the performance of the threshold heuristics is not very sensitive to the actual threshold CPM. Two factors contribute to this effect. First, only 11 requests, out of the 35 available, are subject to optimization, making the base profit, common to all approaches, relatively high. Second, all threshold heuristics ignore capacity utilization and traffic variability in their decision of contracts to accept and therefore exhibit the same biases, independent of the magnitude of the threshold. Table 2 compares the performance of the policies for different values of the goodwill rate π i /r i, ranging from 0% to 150% of the CPM the base case was 10%. Hence, the dominance of the CEC approach over the threshold policies is even starker when the goodwill penalty is large. In fact, the TH-UNI heuristic s tendency to underdeliver impressions can even lead to a loss. Consequently, publishers who wishes to build long-term relationships with their advertisers or advertising agencies should consider adopting an optimization-based approach for managing their advertising contracts. Expanded Product Set. To evaluate the impact of switching to an optimization-based approach for managing all contracts, we now assume that the 24 initial bundles are also renegotiable. Therefore, the publisher needs to decide which requests to accept among the pool of 35 bundles available. Table 3 shows that, despite the increase in the number of requests, the performance of the CEC

20 20 Dynamic Revenue Management for Online Display Advertising Table 2 Expected Revenues as a Function of the Goodwill Penalty Rate. Policy Threshold Goodwill Penalty Rate 0% 50% 100% 150% DET 1,914,500 1,877,800 1,860,000 1,847,900 CEC 1,904,800 1,865,400 1,840,800 1,830,000 $3.0 1,891,000 1,850,600 1,790,800 1,763,400 TH-LP $3.5 1,857,800 1,829,300 1,790,600 1,766,100 $4.0 1,814,100 1,807,800 1,796,400 1,791,100 $4.5 1,786,800 1,783,900 1,779,700 1,775,600 $3.0 1,698,000 1,051, , ,200 TH-UNI $3.5 1,683,700 1,053, , ,500 $4.0 1,646,400 1,036, , ,000 $4.5 1,627,700 1,024, , ,900 heuristic is near optimal. Note also that the performance of the threshold policies is significantly more sensitive to the choice of the threshold value than in our base case because all 35 contracts are subject to selection. Table 3 Expected Revenues with the Expanded Product Set. Policy Threshold Expected Profit DET 2,051,000 CEC 2,037,400 $3.0 1,811,700 TH-LP $3.5 1,665,500 $4.0 1,506,900 $4.5 1,095,100 $3.0 1,472,800 TH-UNI $3.5 1,362,500 $4.0 1,214,900 $ ,900 More importantly, Table 3 reveals that adopting an optimization-based approach for both the selection of requests and the ad impressions can lead to about $200,000-$1,200,000 additional profits per quarter, i.e., $0.8-$4.8 million per year, a significant increase for a company with a $10-15 million sales goal. Random Occurrences of Requests. We have assumed so far that all requests were known in advance. We now relax this assumption by associating a 50% probability of occurrence with each request, realized at the beginning of the flight of the request.

21 Dynamic Revenue Management for Online Display Advertising 21 Table 4 reports the results. Note that when request arrivals are uncertain, the optimal value of 5 is no longer an upper bound on the maximum profit-to-go. Despite the additional uncertainty Table 4 Expected Revenues with Random Request Occurrences. Policy Threshold Expected Profit CEC 1,815,000 $3.0 1,806,100 TH-LP $3.5 1,787,100 $4.0 1,767,500 $4.5 1,756,000 $3.0 1,510,500 TH-UNI $3.5 1,505,000 $4.0 1,485,900 $4.5 1,477,000 on the request occurrences, the CEC approach still dominates the threshold heuristics. Even though the performance gap is smaller than in the base case, the improvement over the TH-UNI heuristic remains significant. 7. Conclusion The nature of online media has given rise to more quantitative approaches for advertising management. However, the current processes for contract negotiation and advertisement delivery are often ad-hoc and disconnected. In this paper, we develop a unified approach for contract negotiation and ad delivery for online display advertising revenue management, linking the selection of contracts with capacity utilization. Accounting first for the uncertainty in requests and web traffic, we model the problem as a dynamic program and characterize its structural properties. Because an exact solution of the dynamic program is infeasible for realistic problem instances, we then propose a Certainty Equivalent Control heuristic, test it using a real case study, and show that it performs significantly better than common approaches based on threshold-price contract selection and uniform ad delivery. References Araman, V. F., K. Fridgeirsdottir Online advertising: Revenue management approach. Working paper. London Business School.

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