Two uncoupleable distributions, assigning missions to robots and allocating robots to home stations, accompany the use of mobile service robots in hospitals. In the given problem, two workload-related objectives and five groups of constraints are proposed. A bio-mimicked Binary Bees Algorithm (BBA) is introduced to solve this multiobjective multiconstraint combinatorial optimisation problem, in which constraint handling technique (Multiobjective Transformation, MOT), multiobjective evaluation method (nondominance selection), global search strategy (stochastic search in the variable space), local search strategy (Hamming neighbourhood exploitation), and post-processing means (feasibility selection) are the main issues. The BBA is then demonstrated with a case study, presenting the execution process of the algorithm, and also explaining the change of elite number in evolutionary process. Its optimisation result provides a group of feasible nondominated two-level distribution schemes.