There are many problems that will occur,
The most important you will no the able to scale your company. One of the main reasons behind putting these systems and automating everything is to handle large volumes, if you cannot integrate them properly it defeats the purpose. So naturally you will have to have manual steps to keep all these in synch, which will be every expensive and error prone. So it is a bad idea, if it is temporary situation it is probably okay, but in the long run you want to integrate all these.
Here are some of the problems I have seen consistently occur
1 - The orders will not hit the Warehouse Management System, sometimes nobody will even know that the orders have not made it to the Warehouse and everyone realizes only when the customer calls to check on the order
2 - You need to have very thorough reporting in place just to cross check everything against all the three systems, it is painful. You will end up paying employees to do hard and painful work to jeep these three systems in synch
3 - The money is better spent by integrating these systems, in the long run, or least you could integrate the Accounting and the WMS first then do the EDI as Phase II.
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