Multiperiod Advertising Budget Allocation Research

With the development of Internet,online advertising industries have been flourishing.In the online advertising market,real-time bidding is an important way for advertisers to gain impressions.In this case,advertisers entrust the demand-side platform to participate in bidding when a targeted impression arrives in order to obtain higher-quality one.However,three problems may arise: premature budget exhaustion,traffic reversal,and difficulty in post-analysis.Therefore,this paper divides the advertising period into multiple time slots and studies how to allocate the limited budget to each time slot so as to obtain the optimal amount of impressions.Since it is difficult for advertisers to obtain the exact distribution of amount of impressions and corresponding cost during the advertising period when making decisions.Therefore,we model and consider the problem of how to optimize the solution using distributionally robust optimization when only partial distribution information is known.The main work of this paper is as follows:1)Multiperiod advertising budget allocation with the uncertainty of the amount of impressions.The problem of optimizing multiperiod budget when advertisers entrust realtime bidding to demand-side platforms is investigated.Considering that although all the information required for decision making is not available,distribution information such as moment information is easily available based on historical data,distributionally robust optimization is used to establish a joint opportunity constrained mathematical model.We know only the joint distribution function support set of impression supply for each time slot and moment information.The model ensures that the cost in real-time bidding for each time slot does not exceed the allocated budget as much as possible,to maximize the probability of achieving the advertiser’s impression goals.Since the objective function is constant,an iterative algorithm is designed to obtain a more optimal budget allocation.Finally,the validity and robustness of the model and algorithm are demonstrated through numerical simulations,and management insights are given.2)Multiperiod advertising budget allocation problem with uncertainty of cost.Based on the existing studies,it is considered that too much remaining budget also leads to revenue loss for advertisers.Therefore,we further limit the upper bound of residual budget for each time slot.It is also considered that advertisers do not have access to the traffic of the ad audience when participating in real-time bidding,and thus cannot accurately predict their actual spending costs.Based on this,considering the cost of spending as a random vector with its distribution in an uncertain set within the ellipsoidal set,the problem is modeled using the distributionally robust optimization,where the objective of the problem is to maximize the sum of the advertiser’s impression goals,given the constraints of the remaining budget and the total budget cap.The problem is a relatively difficult distributionally robust joint chance constrained programming problem,so this paper uses Schur complement as well as cone dual to solve the model.We obtain a semi-positive definite programming.A related iterative algorithm is designed to solve the problem that the optimization solver cannot solve the mixed-integer semi-positive definite programming directly.The validity and robustness of the model and algorithm are demonstrated,and management insights are given.