Can I reuse cedar grilling planks?
I will generally reuse a plank on two conditions:


The bottom isn't completely charred. Sometimes, the bottom ends up complete black. I find that this won't start to smoke a second time. It's also a mess to store anywhere. 
The top isn't a mess of food. This is largely dependent on what you cook. Fish skin sometimes gets cooked on, glaze bubbles and chars, oil lights on fire and the top surface chars. Something like shrimp, tomato, or sausage will be fairly clean though, and nothing will cook on to the top. 


In order to reuse the plank, I clean it with soap and water, the same way I'd clean a wooden chopping board. I've never managed to use a plank more than twice and I usually just toss them after a single use. 

Keep in mind that a dried cedar plank is a dried cedar plank. Cost is generally more based on the store that you buy it in than the product you're buying. A hardware super store (like Home Depot) will generally have these quite cheap.