## Problem Description and Modeling  
### Problem Description  
The scheduling problem of carrier aircraft support operations is about allocating the supporting resource (renewable resources and non-renewable resources) to complete the operations for preparing the aircraft well as soon as possible. It can be consider a MRCMPSP. Three kinds of constrained resource (renewable resources constraint, non-renewable resources constraint, operational space constraint) exist in the scheduling project. The renewable resources include support equipment resources (oiling station, oxygen and nitrogen station, hydraulic station, power station), the support resources of operational crews (machinery major, ordnance major, avionics major, and special equipment major), and the support space resources (cockpit and landing gear station). The resource station cannot support all of the aircraft in the deck because of the distribution position; a single station only can cover some of the settled carrier aircraft in the flight deck, but the different major operational crews can support all of the aircraft in the flight deck. The non-renewable resources, which are also called consuming resources, include oil, gas, weapons, etc. The support space resources such as the aircraft cockpit make up the support activity existing space constraints, so that the cockpit inspection of each major cannot proceed simultaneously.  
There are some rules restricting the operational activities with serial and parallel constraint relationships. (i) No oxygenation operation can be done at the time of refueling operation due to security considerations; (ii) The operational crews for a single major operation can finish different activities with different priorities; for example, the carrier aircraft inspection of ordnance appearance is preferable to the inspection of ordnance cockpit; (iii) The sequence of some activities can be processed simultaneously; for example, the operations of different majors can be exchanged with parallel constraint relationships; (iv) A stationary resource station can only support some settled carrier aircraft, (v) The alignment operation of inertial navigation is generally carried out after all of the activities. In the scheduling problem, the supporting activities of each carrier aircraft include about 14 activities.  
Besides, a virtual start activity and a virtual finish activity are set to combine the operational activities of each carrier aircraft to a multi-aircraft network flow. Figure 1 shows the support activities flow chart of a single-aircraft. The solid arrow indicates the serial and parallel constraint relationships of the operational activities. The dotted line indicates that the cockpit space constraint, which cannot proceed simultaneously in the four aircraft cockpit activities. The single-aircraft support process can be considered as a single project in the RCPSP.  
In the flight deck environment, some uncertainties and dynamic disruptions exist in the carrier aircraft scheduling, such as resource disruptions (resource station breakdown, the operators reduce), time disruptions (the operational time for the support equipment maintenance, which may become longer), and support tasks that are added, changed, or removed. Therefore, a proposal of a scheduling strategy for a dynamic port environment is required. The objective is to find a dynamic scheduling strategy that minimizes the makespan, improves the resource utilization, and reduces the influence of disruption. The mixed integer linear programming models are discussed next in this section.