Dairy farmer Jason Leedle felt his stomach churn when he got the call on Tuesday evening.

"We need you to start dumping your milk," said his contact from Dairy Farmers of America (DFA), the largest U.S. dairy cooperative.

Despite strong demand for basic foods like dairy products amid the coronavirus pandemic, the milk supply chain has seen a host of disruptions that are preventing dairy farmers from getting their products to market.

Mass closures of restaurants and schools have forced a sudden shift from those wholesale food-service markets to retail grocery stores, creating logistical and packaging nightmares for plants processing milk, butter and cheese. Trucking companies that haul dairy products are scrambling to get enough drivers as some who fear the virus have stopped working. And sales to major dairy export markets have dried up as the food-service sector largely shuts down globally.

The dairy industry's woes signal broader problems in the global food supply chain, according to farmers, agricultural economists and food distributors. The dairy business got hit harder and earlier than other agricultural commodities because the products are highly perishable - milk can't be frozen, like meat, or stuck in a silo, like grain.