Although there certainly was a degree of autonomous trade throughout the life of both Republics (and after the 16th century, increasing economic diversification away from trade) it is important to remember that the two states were Mercantilist Aristocratic Governments in the truest sense; the Aristocracy was the Government, and vice versa. It seemed natural, to the Venetians and Genoese, that the largest profits were to be had in the state-regulated trading fleets. I'm familiar with the Venetian system, but less with the specific mechanics in Genoa.

Although attempts by the Venetian government to organize a "cartel" in major trade markets date to the thirteenth century, a true state organized trading expedition would only occur the very end of the century, in 1294. In the period immediately preceding the Republic of Venice's apogee in the fifteenth century, a system definitively emerged whereby the senate organized yearly trade convoys, called Mude. The Mude, which have an uncertain etymology, were convoys of anything between three and eight ships. Space on the ships was decided by a public bidding procedure, and its allocation was strictly regimented down to the very spot in the hull where goods were to be loaded. Two state officials, a Captain for navigation and an Admiral for administration, were appointed to oversee the trip, which would be set a strict date and time of departure.

The winners of each bid, often a consortium of merchants which could be involved in a complex series of sub-contracts allocating space on board, nominated a Patrono (typically the bidding partner with the largest share) who was obligated to participate in the voyage. The Patrono also oversaw the recruitment of sailors, guards, and officers like the navigator and ship's doctor.

At the Republic's height in the fifteenth century, up to eight Mude set out each year: one to Cyprus and Lebanon, one to Egypt, one to Constantinople, one to Tunis, one to the Berber coast (typically Marocco), one to Marseilles, and one to Bruges, London, and Southampton. For the meticulous planning, not all destinations were fixed year-to-year: often the voyage to Egypt also included an additional stop in Lebanon, while the voyage to Tunis might also include a stop to Egypt. Sometimes the voyage to Marseilles also included a stop in Barcelona, while the trip to the berber coast could also entail a stop in Spain. Along the way, Venetian ships stopped in the Republic's colonies, typically Istria and Dalmatia, in order to stock up on supplies and pick up additional goods to sell abroad (Istrian lumber seems to have been a favorite). In times of instability, a stop to link up with the Venetian war-fleet in its historic base in Corfu could also be organized, such that the fleet could have an escort.

Ugo Tucci at the Ca'Foscari University in Venice meticulously examined the ledgers of Francesco Contarini, a Venetian Magistrate in the 16th century (and ancestor to a homonymous Doge). You can read his analysis in Mercanti, navi, monete nel Cinquecento veneziano (Il Mulino, Bologna. 1981). There is also Luzzato's old Storia economica di Venezia dall'XI al XVI secolo. If you cannot read Italian sources, Frederick C. Lane's latest revisitation of Venetian ships and shipbuilders of the Renaissance could interest you.