Towards designing and operating physical internet cross-docks: Problem specifications and research perspectives

•Cross-dock optimization problems in the Physical Internet context are presented.•Strategic, tactical and operational decision levels are considered in the review.•Design and operations of the π-cross-docks (π-hubs) are presented.•Functional design of the π-cross-dock and the classical one are discussed.•An example of a multi-modal π-cross-docking model is formulated and solved.