A data science team at a SaaS company is tasked with optimizing the pricing for two product tiers: 'Standard' and 'Premium'. The objective is to maximize total monthly revenue. The team has modeled the demand for each tier as a function of its own price and the price of the other tier, resulting in a non-linear relationship between price and quantity demanded. Additionally, management has stipulated that the Premium price must be at least 50% higher than the Standard price, and the total number of subscribers must not fall below a minimum threshold to ensure market viability.
Given this scenario, which optimization approach is MOST appropriate for determining the optimal prices?
The correct answer is to use a non-linear solver. The problem involves maximizing a revenue function (Price × Quantity) that is non-linear because the demand itself is a non-linear function of the prices of both tiers. Furthermore, the problem is subject to several constraints: one is a linear inequality (the Premium price relative to the Standard price), and the other involves the non-linear demand functions (the minimum total subscribers). This combination of a non-linear objective function and constraints makes it a non-linear programming (NLP) problem, which requires a non-linear solver.
The Simplex method is incorrect because it is designed specifically for linear programming problems, where both the objective function and all constraints must be linear.
The Traveling Salesman Problem is a well-known constrained optimization problem, but it applies to finding the shortest possible route that visits a set of locations, which is a network topology or routing problem, not a pricing problem.
A multi-armed bandit approach is used for unconstrained optimization, specifically to balance exploration and exploitation in a dynamic environment (e.g., testing different prices over time to see which performs best). It does not solve a problem with a pre-defined non-linear model and explicit constraints as described in the scenario.
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