Title: Marketing mix optimisation with practical constraints

Authors: Hsin-Chan Huang; Jiefeng Xu; Alvin Lim

Addresses: Retailer Products Research and Development, NielsenIQ, Chicago, IL 60008, USA ' Retailer Products Research and Development, NielsenIQ, Chicago, IL 60008, USA ' Retailer Products Research and Development, NielsenIQ, Chicago, IL 60008, USA

Abstract: In this paper, we address a variant of the marketing mix optimisation (MMO) problem which is commonly encountered in many industries, e.g., retail and consumer packaged goods (CPGs) industries. This problem requires the spend for each marketing activity, if adjusted, be changed by a non-negligible degree (minimum change) and also the total number of activities with spend change be limited (maximum number of changes). With these two additional practical requirements, the original resource allocation problem is formulated as a mixed integer nonlinear program (MINLP). Given the size of a realistic problem in the industrial setting, the state-of-the-art integer programming solvers may not be able to solve the problem to optimality in a straightforward way within a reasonable amount of time. Hence, we propose a systematic reformulation to ease the computational burden. Computational tests show significant improvements in the solution process.

Keywords: marketing mix optimisation; MMO; optimisation; semi-continuous variable; cardinality constraint; perspective reformulation; mixed integer quadratic program; MIQP; mixed integer second-order cone program; MISOCP.

DOI: 10.1504/IJOR.2024.141330

International Journal of Operational Research, 2024 Vol.51 No.1, pp.128 - 149

Received: 20 Oct 2021
Accepted: 02 Nov 2021
Published online: 09 Sep 2024 *

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