Discount vs. Marketing Spend to maximise Revenue and Margin

Introduction

In a competitive market, businesses must strategically allocate their budgets between discounts and ad spend to maximize revenue and maintain profit margins. However, this is a complex optimization problem that requires careful consideration of factors such as price elasticity, ad spend elasticity, inventory constraints, and budget limitations.

This article presents a mathematical approach to distributing a given budget optimally between discounting and advertising using elasticity values and constraints.

Key Variables and Constraints

Let’s define the key variables:

• B = Total budget available
• D = Percentage discount applied to products
• A = Ad spend allocated
• E_d = Price elasticity of discount (impact of discount on demand)
• E_a = Elasticity of ad spend (impact of ad spend on demand)
• P = Selling price per unit
• C = Cost per unit
• Q = Forecasted quantity sold
• M = Profit margin
• S = Stock on hand

Objective Function

The goal is to maximise revenue and margin:

Constraints

Optimization Approach

We can solve this constrained optimization problem using Lagrange multipliers or numerical optimization methods like Linear Programming (LP) or Quadratic Programming (QP). A simple approach using LP is:

This can be implemented using optimization libraries like SciPy (Python)

Recommended Discount and Ad Spend Allocation

Based on the optimization model and given dataset:

• Optimal discount is chosen where the marginal gain in sales is balanced with margin loss.
• Optimal ad spend is allocated to maximize return on investment.
• The allocation respects inventory limits and price guardrails.

Using real-time elasticity values and budget constraints, businesses can dynamically adjust their strategy for profit-maximizing decision-making.

Conclusion

Optimizing discount vs. ad spend allocation is critical to revenue and profitability. By leveraging elasticity metrics and mathematical optimization, businesses can make data-driven pricing and advertising decisions while ensuring efficiency and sustainability in their operations. Implementing such models allows for better financial control and improved bottom-line performance.