Try making cleaning into an afterschool game. Sure it takes some time on your part, but it will be fun, the job will get done, and there won't be any yelling for a short while. Children love gadgets. Ever since I got my cordless small vacuum cleaner and cordless carpet cleaner, my kids volunteer to use them. Of course, you have to control their use of it because once they realize it's only another cleaning tool and not a fun toy, that'll be the end of that.
Children also love schedules.
Children love earning money. These are chores of mine which I don't want to do, like weeding or mopping the bathroom floors. All games and puzzles must be returned to this one spot, with any spare parts or pieces put into the basket for sorting later. This is so much easier than having games spread out and stored in every room, plus I've found my kids like knowing where everything is and clean up quicker and with no fuss. After selecting him carefully, my next secret to having a more helpful spouse is compromise.