Real-time temperature prediction in a cold supply chain based on Newton's law of cooling

Abstract Many goods, including pharmaceuticals, require close temperature monitoring. This is important not only for complying with regulations but also for guaranteeing safety of use. A particular challenge in controlling a product's temperature arises during transportation. In cold supply chains (SCs), temperature is maintained by refrigerated containers. However, many situations, e.g. cooling system failure, lead to ambient temperature changes, and this needs to be detected as early as possible to prevent product damage. Existing approaches to temperature prediction are confined to long-term forecasts with relatively stable ambient temperatures and/or rely on multiple sensors in the known fixed positions. Since interventions in a SC are required immediately, there is a need for methods that provide real-time predictions regarding regular ambient temperature instability, i.e. when the ambient temperature changes unexpectedly in the short term. We propose a novel method that extends the applicability of Newton's law of cooling (NLC) to changeable ambient temperatures based on a set of temperature stability conditions and a sensor measurement error. In the method, an optimal number of measurements that characterize stable ambient temperatures and improve prediction reliability are selected. We compare the adapted NLC with artificial neural networks and autoregressive moving average models with respect to deviation prediction, prediction error, and execution time. Our evaluation based on real-world data shows that the adapted NLC outperforms existing baseline methods. In contrast to existing solutions, our method does not require any knowledge about the positioning of products within the container, further increasing its practical value.