Marketing Mix Optimization with Practical Constraints

In today's business environment, a company may employ a mix of many marketing activities (e.g., free samples, discount coupons, weekly specials and advertisements) to attract new customers, enhance customer loyalty, and induce sales. Given a marketing plan with a mix of marketing activities, each activity may be allowed a spend level that results in corresponding outcome. The company often needs to adjust the resource allocated to marketing activities due to various reasons (e.g., marketing budget change, change in scope of targeted audience, geographies and products, product demand and/or supply changes, and activity cost and/or performance changes), aiming to optimize the revenue, profit, or other goals of the company. In practice, the company may desire such adjustments to be planned and executed by considering resource availability for executing changes, contractual obligations, etc. Due to minimum incremental investments required for certain marketing activities (e.g., minimum cost of a targeted rating point in TV advertisements or minimum cost of implementing a promotional discount), there is a need to impose a minimum change in spend (investment) constraint for a marketing activity. Since resources will be required to implement changes in marketing activities and resources available are limited, a constraint on the maximum to number of activities with spend changes is also imposed. Therefore, to guarantee that the outcome of a marketing mix optimization (MMO) is feasible for practical implementation, there is a need to solve the MMO problem with these added constraints. Given an existing marketing plan (typically from a previous period), our MMO problem aims to adjust spend allocations on marketing activities with an objective of maximizing revenue subject to four sets of constraints: bounds on activity spend, total budget limits, the minimum change in spend for an activity, and the maximum number of activities associated with spend change.