Coordinating Replenishment and Dynamic Pricing for Perishable Omnichannel Retail: A Fixed-Point Dynamic-Programming–Reinforcement-Learning Framework

In the world of modern retail, the challenge of selling fresh food has become a high-wire act performed across multiple stages. Shoppers no longer visit a single store; they buy through a complex web of options, picking up items at a local shop, ordering for home delivery, or buying online and collecting in person. This omnichannel approach offers convenience, but it creates a logistical nightmare for perishable goods like fruits and vegetables, which have a strict, ticking clock on their shelf life. The core difficulty lies in balancing two competing needs: keeping prices flexible enough to match what customers are willing to pay at any given moment, and ordering just the right amount of stock so that nothing rots before it is sold. If a retailer orders too much, the food spoils and becomes waste; if they order too little, they lose sales and frustrate customers. For decades, researchers have tried to build mathematical models to solve this puzzle, often treating the decision of how much to order and the decision of what price to charge as separate problems. However, the reality of a fresh produce aisle is that these two decisions are deeply intertwined, and the speed at which a store receives new deliveries plays a far more critical role than previously understood.

A team of researchers has developed a new way to tackle this problem by combining two different types of computer logic to manage the flow of perishable goods. Instead of trying to solve the entire complex system at once, they split the job into two parts that operate on different time scales. One part of their system uses a method called dynamic programming, which is essentially a rigorous, forward-looking planner. This planner looks ahead over a long period to decide exactly how many units of fresh produce to order, taking into account how long the food will last and the costs of waste. The second part uses a technique called reinforcement learning, which acts like a real-time trader. This agent watches the store's inventory age and the demand fluctuate, adjusting prices instantly to sell older stock before it expires. Crucially, the researchers did not just let these two parts work in isolation; they forced them to talk to each other. The long-term planner adjusts its ordering targets based on the prices the real-time trader actually sets, and the trader learns to price based on the inventory levels the planner creates. They tested this system in a detailed computer simulation of a fresh-produce retailer selling strawberries, which have a usable shelf life of four days, over the course of a full year.

The most striking discovery from this study is that the sophistication of the pricing algorithm matters far less than the schedule of the delivery truck. The researchers found that whether a store actually faces a problem of food waste depends entirely on the ratio between how often it gets new stock and how long that stock lasts. In their simulation, when the retailer received fresh deliveries every single day against a four-day shelf life, the waste rate was virtually zero, at just 0.04 percent. In this scenario, no amount of clever pricing or complex planning could improve the situation because the food was being sold so quickly that it never had a chance to age. The system was simply too efficient for the problem to exist. However, when the delivery schedule was stretched to a three-day cycle, the situation changed dramatically. The same store, using the same products, saw waste jump to nearly 6.6 percent. This revealed that the "perishability problem" is not always present; it is a condition created by the delivery calendar. If the time between deliveries is short enough, the food never gets old, and the advanced algorithms have nothing to optimize. The machinery of complex pricing only becomes valuable when the delivery cycle is long enough to allow the food to age.

Another major finding concerned the promise retailers make to online customers about how fresh their food will be. Many stores guarantee that online orders will have a certain number of days of shelf life remaining, assuming this will attract more customers. The study treated this guarantee not as a fixed marketing rule, but as a variable decision. The results showed that tightening this promise to guarantee fresher food actually hurt the business. When the researchers increased the guarantee from one day to two days, online sales did rise by about 10 percent, but the profit dropped by more than 3 percent, and the amount of wasted food tripled. The reason is that a stricter guarantee locks out older, but still perfectly edible, stock from being sold online. That stock is then pushed down to the physical store, where it is harder to sell, eventually getting marked down or thrown away. The study concluded that, in this specific environment, the best strategy is to offer the minimum possible freshness guarantee, as trying to promise more freshness simply creates more waste without enough extra profit to justify it.

The researchers also compared their coordinated approach against several other methods, including a system where the ordering and pricing decisions were made one after the other without feedback, and a system where a single computer agent tried to learn both ordering and pricing at the same time. The results were clear: a computer agent trying to learn everything from scratch performed the worst, earning significantly less profit and showing much more instability. This suggests that trying to learn the complex logistics of ordering fresh food is too difficult for a machine to figure out on its own; it needs the structured, logical framework of a planner to handle the ordering, while the machine learning is best left to the task of adjusting prices. The coordinated system that combined both approaches did not necessarily make the most money compared to a simpler sequential method, but it did something far more important: it stabilized the waste. By closing the feedback loop between ordering and pricing, the system cut waste by more than half compared to the sequential approach, preventing the occasional massive spikes in spoilage that occurred when the two decisions were not aligned.

Ultimately, the study offers a sobering but practical guide for retailers. It suggests that before investing in expensive, high-tech pricing algorithms, a store must first look at its delivery schedule. If the store receives fresh stock daily, the problem of waste is already solved by the calendar, and no amount of software will improve it further. If the delivery cycle is longer, then the problem exists, and the choice of how to manage it becomes critical. The research also highlights that the cost of the food itself, determined by the supplier, has a far greater impact on the store's bottom line than any pricing strategy. A small improvement in the price paid to the supplier can change the annual profit by tens of thousands of dollars, whereas even the best pricing algorithm might only shift profits by a few thousand. The study concludes that the most effective way to reduce waste is not to promise customers the freshest possible food, but to manage the internal cost of disposal and the timing of deliveries, ensuring that the supply chain is designed to match the natural lifespan of the product.