A Note on Mathematical Modelling of Practical Multicampaign Assignment and Its Computational Complexity

TL;DR

This paper examines the computational complexity of multicampaign assignment in personalized marketing, demonstrating its NP-hardness with a realistic response model, and supports the use of heuristics for practical solutions.

Contribution

It introduces a more practical response suppression function and proves the NP-hardness of the multicampaign assignment problem with this model.

Findings

The problem is NP-hard under realistic response functions.

Heuristics are justified due to computational complexity.

A new response suppression model learned from data.

Abstract

Within personalized marketing, a recommendation issue known as multicampaign assignment is to overcome a critical problem, known as the multiple recommendation problem which occurs when running several personalized campaigns simultaneously. This paper mainly deals with the hardness of multicampaign assignment, which is treated as a very challenging problem in marketing. The objective in this problem is to find a customer-campaign matrix which maximizes the effectiveness of multiple campaigns under some constraints. We present a realistic response suppression function, which is designed to be more practical, and explain how this can be learned from historical data. Moreover, we provide a proof that this more realistic version of the problem is NP-hard, thus justifying to use of heuristics presented in previous work.