If your problem is not the sheer quantity of work, but poor organisation, then your problem is your boss or the system that he or she has to work within. Of course there are some jobs where you are simply reacting to external events or crises that cannot be planned. But even here there should still be sufficient cover to cope with all but really exceptional events.
First is your boss aware of the problem? Managers are often promoted because they are good at their job, not because they are any good at managing. And of course if their idea of a treat is to get a fascinating report to write at 4:30pm on a Friday afternoon, they may not quite understand that some people have a life.
It is therefore worth raising the problem directly – not in the heat of the moment when it can look like a challenge to authority, but at another time. If there are some better ways of organising work, then suggest changes in a way that doesn't threaten your boss's authority. Or suggest a working party or time at a team meeting to talk through the issue.
This might start with a simple audit of how people spend their time, though be careful to do it in a way that doesn't look like you are trying to find out who's wasting time. The emphasis should be on tracing work through the system. Are there bottlenecks? Do tasks get lost, and then suddenly reappear only when they are urgent.
A likely cause may be poor communication, possibly made worse by people hoarding information or using it as power. While workplaces need their proper procedures, gateways are often a hold up.
Or perhaps your boss needs some time management training, or perhaps to understand that not everybody is quite like him or her. A common mistake in managers is that they concentrate on the parts of their job that they do directly, and neglect planning and allocating work for other people. Managing your manager is an important workplace skill!
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