In the modern economy, we see complex business processes with a physical character executed collaboratively by a set of autonomous business organizations. Examples are international container logistics, integrated supply and manufacturing networks, and collaborative healthcare chains - all of which handle physical objects. Over time, these processes have become more complex, more business-critical, more time-critical, and at the same time heavily mass-customized. This implies that the processes need to be managed more explicitly in an increasingly real-time fashion, with ample attention to individual process cases. To support this kind of processes, no single existing technology class suffices. Therefore, we propose to integrate technologies from the areas of business process management (BPM - to manage the processes), internet of things (IoT - to sense and actuate the physical objects) and distributed analytics (DA - to take the right decisions at the right place in real-time) into a trinity. We illustrate our position with an example from the domain of container logistics.