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Nowadays, procurement managers in the different industries rely on the Reverse Combinatorial Auctions (RCAs) as a trading mechanism that had shown to be very efficient in allocating resources in several applications. RCAs allow the bidders to optimally express their economies of scope, since they can formulate their bids as a bundle of items, rather than on single item. Each bundle should be then either accepted or rejected all together without splitting. Here, we review and discuss the underlying mathematical optimisation models that represent the basis of the decision support system and discuss the possible benefits of using such paradigms for the different actors involved in the auctioning process. In addition, the paper highlights the advantages of employing RCAs in two major application fields, namely the logistics and food industries, in which this advanced trading paradigm had remarkable success by …