As if Yemen didn’t have enough problems (unemployment, water shortages, crime, civil war, Islamic terrorism) it now finds that most major shipping companies, which deliver most cargo (including most of the food) have ordered vessels to divert to other (non-Yemeni) ports. That should not be a problem as this often happens when there are major storms. But the situation in Yemen right now is worse than that. Most of the main roads into Yemen come from Saudi Arabia via northwest Yemen. But that is where the Shia rebels come from and those roads are subject to attack by Saudi warplanes and the Saudis have closed those border crossings. There is one main road not from Saudi Arabia and that comes from the east (Oman) and runs along the coast. Most of eastern Yemen is thinly populated but as you approach the more densely populated areas you reach parts of the coast controlled by al Qaeda.
The major ports are all unavailable because most are either controlled by Shia rebels or Islamic terrorists. The largest port (Aden) is controlled by the government but the Shia rebels are currently inside the city trying to take control of the place. So the Port of Aden is off limits for the major shipping companies.
At the moment the only alternative is to go to a non-Yemen port and turn the cargo over to a local shipping company that is willing (for a higher fee) to risk going to a “disputed port” and deliver the cargo. The owners of the cargo, assuming they are not the government of Yemen, can then endeavor to deliver it to its customers (retailers or wholesalers). That will drive the costs up and delay deliveries. A lot of the food is foreign aid and the aid groups will have to negotiate with various warring parties before the aid can be delivered to the hungry Yemenis who need it.
In anticipation of these delays the prices of food are already rising (doubling or more) in some places. People will go hungry and some will be hungry for a long time if they are in an area that is difficult for trucks to reach because of fighting or bandits.