Most supervisors today realize that working from home doesn't mean goofing off. That doesn't mean they won't have concerns, voice objections, or resist your efforts. Supervisors might intellectually understand the importance of work/life balance or that happy employees are more productive and have lower absenteeism or turnover. But when faced with an actual request that reduces their control over a direct report they're likely to respond reflexively. The key is to make whatever concessions and compromises you must to get your supervisor to give the arrangement a try. Pitch it as a trial period. Promise higher productivity. Pledge to work longer hours. Whatever your reason for wanting to work from home, the only foolproof explanation is that you want to be more productive.
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