I get asked this question a lot in my seminars. There are three basic ways to time your strategic planning around your annual cycles. First, you can schedule your planning process so that it precedes the budget cycle. This is useful if you feel it's important to get the money for strategic projects into your budget. This means you will have to complete and review your action plans before starting your budgeting, but it has the advantage of giving you some pretty detailed information about the expected cost of new strategic projects.
The second way to schedule your strategic planning process is to do it just after your year end. The main advantage of this is to give you the most complete, accurate and up-to-date data on your company's strategic performance. If your financial data gives you key insights about what strategies are working well for you (and it should), this approach might give you the best information for your strategic planning. One possible disadvantage is that it might not allow for inclusion of the action plan expenditures into your budgets, requiring a second look at your budget at the end of the strategic planning process.
The third scheduling approach is to time your strategic planning for a low point in management activity for the year. The main advantage of this is that you won't overload your executive team with the additional burden of planning meetings and homework. For construction, this might be the Fall or Winter, while for schools this is most likely the summer.
All of these approaches have pros and cons, and - of course - there are hybrid approaches that combine these approaches to scheduling strategic planning. I'd suggest you try one and see how it works for your team, understanding that it's always possible to change the timing of your strategic planning in the future. And, of course, a short discussion with an experienced, qualified strategic planning consultant can really help you find the timing that is right for your organization.