Which general staff member is responsible for ensuring that assigned incident personnel are fed and have communications, medical support, and transportation as needed to meet the operational objective?

Logistics Section Chief.

Explanation:

A military staff or the general staff may be defined as the group of officers that are civilian officer and personnel. They are responsible for the logistics, operational and logistic services.

The logistic section chief is the officer included in the general staff that are mainly responsible to provide the medical facilities to the operational objective. The logistics section chief officer main role is to provide the transportation and also provide communication.  

Thus, the answer is logistics section chief.