Optimal Markdown Timing for Perishable Goods: A Dynamic Programming Approach Using PoS Sell-Through Rates
Formulate the markdown-timing decision as a finite-horizon dynamic program, optimizing expected revenue against expiry risk using real-time sell-through velocity.
Key Takeaways
- Dynamic programming provides an optimal markdown schedule by working backward from the product expiration date, computing the value of delaying or initiating markdowns at each decision epoch.
- Real-time sell-through velocity from the PoS system serves as the primary state variable, enabling the markdown policy to adapt to actual demand conditions rather than relying on pre-set schedules.
- The optimal markdown policy exhibits a threshold structure: reduce price when sell-through velocity falls below a time-dependent threshold that increases as expiration approaches.
The Perishable Goods Markdown Problem
Perishable goods — fresh produce, bakery items, dairy products, prepared foods — present a unique markdown challenge because unsold inventory at expiration has zero or negative value (disposal cost). The retailer faces a dynamic tradeoff: maintaining full price maximizes per-unit margin but risks expiry-driven waste; marking down early reduces per-unit margin but increases sell-through probability. The optimal markdown strategy depends on the current sell-through rate, the remaining shelf life, the current inventory level, and the price sensitivity of demand. Traditional approaches use fixed markdown schedules: reduce by 25% two days before expiration, 50% on the final day. These heuristic schedules are suboptimal because they ignore the actual sell-through performance of each product batch. A product selling faster than expected needs no markdown, while one selling slowly may need an earlier and deeper reduction than the schedule prescribes. Dynamic programming (DP) provides the theoretical framework for computing the optimal state-dependent markdown policy that maximizes expected revenue (or equivalently, minimizes expected waste cost) over the remaining shelf life. askbiz.co formulates the markdown decision as a finite-horizon dynamic program, computing optimal price reductions conditioned on current inventory and sell-through performance as measured by the PoS system.
Dynamic Programming Formulation
The markdown optimization problem is formulated as a finite-horizon Markov Decision Process (MDP) with the following elements. The state at each decision epoch (typically each day or shift) is characterized by the remaining inventory quantity and the remaining shelf life in periods. The action at each epoch is the price level to charge, selected from a discrete set of feasible prices (full price and several markdown tiers). The transition dynamics specify how inventory evolves: given the current price and state, demand is drawn from a price-dependent stochastic demand model, and inventory is depleted accordingly. The one-period reward is the revenue generated (demand times price). The terminal condition assigns zero value (or negative disposal cost) to inventory remaining at expiration. The Bellman equation expresses the optimal value of being in a given state as the maximum over available prices of the expected immediate revenue plus the discounted future value of the resulting next-period state. Working backward from the terminal period, dynamic programming computes the optimal price for every possible state at every period, producing a complete markdown policy table. The policy exhibits a natural threshold structure: for each remaining-shelf-life period, there exists a critical inventory level above which the optimal action is to mark down and below which full price is optimal. This threshold increases as expiration approaches, reflecting the increasing urgency to clear inventory. askbiz.co solves the Bellman equation numerically for each perishable product category, generating state-dependent markdown policies that adapt optimally to current inventory and remaining shelf life.
Demand Modeling Under Price Variation
The quality of the dynamic programming solution depends critically on accurate modeling of the demand response to price changes. The price-demand relationship for perishable goods has several distinctive characteristics. First, demand is typically more elastic at markdown prices than at full price, because markdowns attract price-sensitive customers who would not purchase at full price. This elasticity asymmetry means that a simple constant-elasticity model may underestimate the demand lift from markdowns. Second, reference-price effects cause the markdown response to depend on the markdown depth relative to the original price: a reduction from $5 to $3 generates more demand lift than a reduction from $4 to $3, even though the final price is identical. Third, freshness perception affects willingness to pay: customers may discount the value of a perishable item as its visual freshness declines, independent of any price reduction, creating a time-varying willingness-to-pay that the demand model must capture. Estimating these effects from PoS data requires observing demand at multiple price points, which creates a tension with the optimization objective: the retailer must occasionally charge suboptimal prices to gather demand-response data. Bayesian demand models with informative priors from product-category-level data can mitigate this tension by bootstrapping demand estimates from limited per-product price variation. askbiz.co estimates price-response models for perishable categories using pooled PoS data across similar products, applying Bayesian shrinkage to stabilize estimates for products with limited markdown history.
Real-Time Sell-Through Monitoring
The practical implementation of dynamic markdown optimization requires real-time monitoring of sell-through velocity — the rate at which inventory is depleting — as the primary input to the markdown decision. Sell-through velocity is computed from PoS data as units sold per unit time (per hour or per day) and compared against the velocity needed to clear the remaining inventory before expiration. The required clearance velocity is simply the current inventory divided by the remaining shelf life in periods. When the actual velocity exceeds the required velocity, the product is on track to sell through at full price and no markdown is needed. When actual velocity falls below the required velocity, the gap indicates the magnitude of the demand shortfall and the urgency of intervention. The ratio of actual to required velocity serves as a dimensionless sell-through index that normalizes across products with different inventory levels and shelf lives: an index above 1.0 indicates healthy sell-through, while an index below 1.0 signals the need for markdown consideration. Intraday velocity tracking enables sub-daily markdown decisions for ultra-short-shelf-life products such as prepared foods, where the decision to mark down for afternoon sales can be informed by morning sell-through performance. askbiz.co computes real-time sell-through indices for all perishable inventory, generating markdown recommendations when the index falls below the optimal threshold derived from the dynamic programming policy.
Implementation Constraints and Waste Reduction
Deploying dynamic markdown optimization in practice requires accommodating constraints that the pure DP formulation may not capture. Price-change costs include the labor required to relabel items, update PoS records, and communicate new prices to customers. These costs favor fewer, larger markdowns over frequent small adjustments, which can be incorporated into the DP formulation as a fixed cost per price change. Customer fairness considerations may limit the frequency of markdowns or require consistent pricing within a single shopping day, imposing constraints on the action space. Regulatory requirements in some jurisdictions mandate that perishable items be sold before their use-by date and may restrict the marketing of items near expiration, further constraining the optimization. Despite these constraints, dynamic markdown optimization consistently reduces waste relative to fixed-schedule approaches because it directs markdowns precisely where they are needed based on actual sell-through data. Empirical studies report waste reductions of 20-40% compared to naive markdown schedules, with corresponding revenue improvements from selling products at moderate discounts rather than disposing of them entirely. The environmental impact of reduced food waste adds a non-financial dimension to the business case for optimized markdown timing. askbiz.co incorporates configurable price-change constraints and regulatory rules into its markdown optimization, reporting both the revenue impact and the waste-reduction benefit of algorithmically optimized markdown timing versus fixed schedules.