The administrative Airport Slot Allocation (ASA) process comprises multiple interdependent processes. At the outset of the ASA, airlines submit requests for accessing airport landing/take-off slots and coordinators allocate the submitted requests to slots based on a complex set of priorities. Most airport slot allocation studies focus on the initial slot allocation phase of ASA without considering the value/difficulty of implementing each slot request and the acceptability of proposed allocations. This paper proposes a stable airport slot allocation model formulated as a Mixed Integer Program (MIP) that considers a surrogate cost function for each submitted request and provides guarantees on the stability/acceptability of the generated airport slot schedule. The model integrates time-dependent cost functions both for the airlines and the coordinators which consider multiple characteristics and comply with the requirements of the ASA regulatory framework. Our model enhances existing administrative ASA models since it enables pertinent parties to explore the trade-off between the stability and the gains in terms of displacement and spilled passenger demand