Having an in-house customer service call center surely does have its benefits. It allows you to maintain a working business relationship with your clients at any time of the day. Going 24/7 shows them that you are committed to providing them with the service they seek and require of you.
Customers are constantly looking for service and when they need more from you, they won't hesitate to instantly pick up a phone and make contact with your company. Purchasing orders should be acknowledged immediately; you need to keep your sales flowing. Clients will constantly be placing purchase orders from you and it's your job to make sure that they are addressed. Giving your clients assurance that you meet their expectations and deliver proper service is a big benefit to your business relationship with them.
Your order processing service should be quick to keep those purchase orders liquid and flowing. Providing customers with such a reliable and convenient service is sure to keep you in long-term business deals with them. However, if you're thinking of the overall cost of the whole thing, then you should consider outsourcing. It's still a good way to keep your customers in contact with you and you still provide clients with the professional service they want to be receiving from you. This way, doing 24/7 business is very achievable.