The problem `human and work' in a model working group is investigated by means of cellular automata technique. Attitude of members of a group towards work is measured by an indicator of loyalty to the group (the number of agents who carry out their tasks), and lack of loyalty (the number of agents, who give their tasks to other agents). Initially, all agents realize scheduled tasks one-by-one. Agents with the number of scheduled tasks larger than a given threshold change their strategy to unloyal one and start avoiding completing tasks by passing them to their colleagues. Optionally, in some conditions, we allow agents to return to loyal state; hence the rule is hysteretic. Results are presented on an influence of i) the density of tasks, ii) the threshold number of tasks assigned to the agents' forcing him/her for strategy change on the system efficiency. We show that a `black' scenario of the system stacking in a `jammed phase' (with all agents preferring unloyal strategy and having plenty tasks scheduled for realization) may be avoided when return to loyalty is allowed and either i) the number of agents chosen for task realization, or ii) the number of assigned tasks, or iii) the threshold value of assigned tasks, which force the agent to conversion from loyal strategy to unloyal one, or iv) the threshold value of tasks assigned to unloyal agent, which force him/her to task redistribution among his/her neighbors, are smartly chosen.