Mobile Harbor (MH) is a type of mobile floating port system with an on-board crane for off-shore container handling capability. Due to its unique operational features, it creates a new type of operational scheduling problem. Container loading and unloading sequence schedule for the MH on-board crane is one such problem. An optimal schedule should minimize the on-board crane's moves in a stem-to-stern direction while satisfying MH's stability constraint. This paper presents a mathematical programming model to formally define the problem, and two heuristic methods, Genetic Algorithm (GA) method and local search method, are developed. Experimental results show that both GA and the local search method generate solutions of similar quality when the stability constraint is loose and that the local search method is not effective in finding a feasible solution for problems with a tight stability constraint.