I also highly recommend Thom's advice - there is a huge concentration of distribution warehouses and also a large railroad yard along Lamar (US 78) between Memphis and Olive Branch, his bypass via I-55 is an excellent route. You won't hit construction until after crossing the Miss River, but there is about a 5 mile stretch in West Memphis where both I-40 and I-55 share a common roadway. The construction zone is single lane on each side with a 45mph speed limit, but currently it moves ok, with only occasional backups. The I-40 Mississippi bridge has it's own construction project, and has lane reductions on/near the bridge in downtown Memphis. Just stay on I-55 in West Memphis until you get to where I-40 splits off from I-55.