Serving two masters? Optimizing mobile ad contracts with heterogeneous advertisers

Abhijeet Ghoshal, Radha Mookerjee, Zhen Sun

Research output: Contribution to journalArticlepeer-review


Our research question is motivated by a real problem faced by an existing demand aggregator. The aggregator represents multiple advertisers, each of whom signs one of two types of contracts with the aggregator for bidding on an RTB (real-time bidding) platform. A quality contract occurs on a cost-per-impression (CPM, i.e., cost per thousand impressions) basis. The advertiser is promised a minimum number of impressions and pays a CPM that is a function of the targeting quality as measured by the realized click-through rate (CTR). In a performance contract the advertiser pays on a CPC (cost-per-click) basis constrained by a budget. We develop and solve a generalized profit maximization problem that jointly optimizes the aggregator's bidding and allocation decisions. The allocation policy optimally assigns each arriving bidding opportunity to a specific advertiser. The bidding policy then computes a bid amount for that allocation based on the estimated click probability of the opportunity. Our solution has nice theoretical properties. First, neither policy depends on the memory carried in the system, that is, the sequence of previous states and decisions, making the solution easy to implement. Second, the allocation policy is shown to have a threshold structure. This enables the assignment of arriving opportunities into one of two distinct sets, each corresponding to a specific advertising contract type. The assessment of the impact of the change in various parameters on the solution is used to derive several interesting and important implications for the management of advertising contracts.

Original languageEnglish (US)
Pages (from-to)618-636
Number of pages19
JournalProduction and Operations Management
Issue number2
StatePublished - Feb 2023


  • Lagrangian relaxation
  • digital advertising
  • mobile ads
  • real-time bidding

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation


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