It would be helpful to know what kind of operation you are talking about. How many customer complaints do you have, how many people are handling these complaints and how long does it usually take for an issue to be resolved.
Depending on the size of your operation, there are multiple ways that technology can help.
1) Issue tracking software: Once you have more than two people handling complaints and these complaints cannot be immediately resolved, you should have some software that tracks these complaints. For every issue that cannot be immediately resolved, the people handling should document what the complaint was, what the response was and whether the customer was satisfied or not and the date for each of the steps. That way the customers do not have to retell their stories every time they get to a different representative and you can review the handling of individual cases and optimize your processes in order to provide the best response.
2) If you have a lot of customer complaints, you should force the people handling complaints to categorize the complaints as much as possible so that you can see which issues get resolved quickly and which get drawn out much longer than necessary.
3) If you have issues that arise frequently and have obvious solutions you could make a customer self-care portal where customers can choose their problem from a list and the solution is immediately triggered and can be tracked by the customers themselves. This requires quite a lot of effort and is only efficient if the operation is sufficiently large.
4) For very large organizations, you could even have a chatbot that interprets customer complaints and triggers solutions for them. But I guess if your organization is that large you should not ask on this forum but talk to an IBM representative or someone similar.
