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Rapid and on-time baggage transport plays a crucial role in airport operation. Modular autonomous vehicles (MAV) are an emerging transportation technology that allows vehicles to adjust their capacity flexibly by assembling or dissembling identical detachable units. This innovative technology offers us a new perspective to solve the baggage transport problem for airports since it is promising in reducing the relevant operating costs and baggage delay time. To investigate this possibility, this paper proposes an operational design and a corresponding MAV scheduling model to optimize the baggage transport. The objective of the optimization model is to minimize the MAV operating cost while transporting baggage from the terminal to the aircrafts without any delay. To solve the proposed problem efficiently, a fast construction-merging heuristic algorithm is proposed based on the theoretical analysis of the feasible solutions. A series of case studies at the Tampa International Airport are conducted to evaluate the performance of the proposed operational design and the heuristic algorithm. The results indicate that the proposed operational design can effectively reduce the baggage transporting cost, and the heuristic algorithm can solve near-optimal solutions to the investigated problem much faster than the Gurobi solver without much loss of the optimality of the solutions. Results from this study can provide important managerial and operational insights into baggage transport for airport operators.