Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing

Abstract

Pricing food products to balance profitability with consumer welfare is a central challenge for retailers. Dynamic pricing is widely used to maximize revenue, yet most pricing models optimize business objectives while overlooking consumer fairness. This paper studies the risk of consumer exploitation under dynamic food pricing in Canada and proposes a methodology that embeds fairness constraints directly into retail sales forecasting. We model total retail trade sales with a log--log Autoregressive Distributed Lag (ARDL) specification, in which the coefficient on a product price is a sales elasticity, and pose the pricing problem as maximizing forecast sales subject to price bounds anchored to the Consumer Price Index (CPI). We solve this problem with both Linear Programming (LP) and Simulated Annealing (SA), under single-product and multi-product configurations. A key finding is that the fitted nominal elasticities are positive. As a result, an unconstrained sales-maximizer would push every price to its upper bound, and the CPI ceiling is the safeguard that prevents this. Simulated Annealing instead settles on conservative, interior prices that lower consumer cost while still meeting the sales target. We benchmark forecast accuracy against naive, seasonal-naive, ARIMA, and SARIMA baselines, and a CPI-deflated re-specification shows that the positive nominal elasticities are largely an inflation-driven artifact. The result is a transparent, fairness-aware pricing framework.