Scaling a recipe and cooking times.

So I've got a recipe I want to make for a crowd. As written, the recipe says it serves 4. I need it to serve 18. I can handle the math when it comes to increasing the quantities, but is there any formula for calculating the new cooking time, or should I just resign myself to cooking them in separate batches? (If you're curious, the recipe will be for the braised short ribs for Alton Brown's Good Eats Beef Stew.)

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