Reconstructing End-User Demand under Batch-Level Ambiguity: Flow-Constrained Record Linkage and Audit Allocation in Orthopedic Consignment Networks

In the high-stakes world of modern surgery, the moment a surgeon uses a medical device is only the beginning of a complex administrative journey. When a hospital uses an orthopedic implant, such as a screw to hold a broken bone in place, a clinical record is created to document the event. However, the financial record that confirms who paid for that screw and where it came from often arrives later, sometimes in a different format, and frequently grouped together with other devices. This gap between the physical act of surgery and the paper trail of commerce creates a blind spot. Hospitals and distributors must know exactly which device was used to manage inventory and billing, but when records arrive late or are bundled together, it becomes difficult to match a specific screw to a specific surgery. This uncertainty is not just a paperwork nuisance; it can lead to lost revenue, incorrect inventory orders, and a lack of clarity about how medical supplies are actually moving through the system.

A researcher named Hongjie Jiang set out to solve this puzzle within the specific context of orthopedic consignment networks. In these networks, medical devices are placed in hospitals before they are sold, meaning the hospital holds the inventory but only pays for what they use. The challenge is that the records of what was used often arrive in batches, making it hard to tell which specific batch of screws from a distributor corresponds to a specific surgery. Jiang focused on a single family of spinal screws used in a large network of distributors and hospitals. By looking at one month of surgical records and comparing them against nine months of settlement data, the study attempted to reconstruct the true demand for these devices, even when the paper trail was incomplete or delayed. The goal was to figure out not just which screws were used, but to understand why some records remained unmatched and how to spend limited time and resources to fix those mismatches.

The study began by treating the matching process as a flow problem rather than a simple list comparison. Imagine trying to match a set of unique keys to a set of locks where some keys might fit multiple locks, and some locks might have been opened by keys that arrived late. The researcher built a model that respected the physical limits of the system: a distributor cannot supply more screws than they have in their batch, and a single surgery cannot use more screws than were recorded. By applying these strict rules, the model could determine which matches were possible and which were impossible. When the model ran, it found that out of 540 surgical records that could be compared, only 229 had a clear, single match to a settlement record. Another 84 had a match, but it was one of several possibilities. The remaining 311 records had no clear match at all. This left a large group of "unresolved" demand that needed to be understood.

To make sense of these 311 unmatched records, the study looked at the timing and the nature of the missing links. It turned out that the reasons for the mismatch were not random. About one-third of the unmatched records were simply waiting for their paperwork to arrive; the surgery happened, but the financial settlement had not yet been processed by the deadline. Another quarter of the unmatched records were blocked because multiple surgeries were competing for the same batch of screws, or because the distributor's records were too vague to pinpoint a single source. The largest group, accounting for nearly half of the unmatched records, appeared to belong to a different path entirely. These were likely screws that had moved through wholesale channels or other inventory systems that did not show up in the specific consignment records being studied. The model assigned probabilities to each of these scenarios, effectively creating a map of where the uncertainty lay.

The most significant part of the research was not just identifying the mismatches, but figuring out how to fix them efficiently. Hospitals and distributors have limited staff and time to review these records. They cannot check every single unmatched entry. The researcher asked: if you can only review a small fraction of the records, which ones should you pick to get the most clarity? A common instinct is to check the largest orders first, assuming that big numbers matter most. However, the study found that this approach was inefficient. Many large orders were already clear and stable, so checking them yielded little new information. Instead, the study proposed a strategy based on "value of information." This method prioritizes records that are both large in quantity and highly uncertain. It looks for the specific cases where a review could resolve a major ambiguity, such as a surgery that could have been supplied by any of three different distributors.

When the researcher tested this new strategy against the old method of checking the biggest orders, the difference was stark. With a budget to review only 20% of the records, the new strategy resolved more than half of the total uncertainty in the system. In contrast, the traditional method of checking the largest orders only resolved about a third of the uncertainty. The new approach was able to recover the same amount of clarity with 40% fewer reviews than the old method would have required to achieve a similar result. This means that by focusing on the specific records where the confusion was highest, rather than just the records with the biggest numbers, organizations can save time and money while gaining a much clearer picture of their supply chain.

The study also tested whether these findings would hold up if the data looked slightly different. For instance, what if some records were duplicates of the same surgery? Or what if the most active distributor was removed from the analysis? In every scenario, the new strategy remained superior. Even when the data was simplified or the network changed, the method of targeting high-uncertainty, high-volume records consistently outperformed the standard approach. The research also showed that the uncertainty was not evenly spread; it was heavily concentrated in specific distributors and specific times of the month, particularly near the end of the billing cycle when records were most likely to be delayed.

Ultimately, this work provides a practical guide for managing the invisible gaps in medical supply chains. It demonstrates that uncertainty is not a single problem to be solved by checking more data, but a resource to be managed by checking the right data. By combining the timing of events with the physical limits of inventory, the study offers a way to turn a chaotic pile of mismatched records into a clear, actionable plan. For the managers who oversee these networks, the message is clear: do not just look at the biggest numbers. Look for the places where the story is unclear, and focus your attention there. This approach allows them to reconcile their accounts faster, manage their inventory more accurately, and ensure that the devices used to heal patients are properly accounted for, even when the paper trail is imperfect.