How does your sponsor want value measured? Your question indicates that the driver for your project was to measure (and presumably reduce) call duration. That would seem to be the likely first metric.
Aside: Based on years of cynical experience, I'd suggest that you also measure rework - the number of calls that need to be re-opened or reworked. My current call center closes tickets on any excuse whatsoever, and prohibits the customer from re-opening a ticket; this generates very short call duration and very high ticket completion rates, but very low customer satisfaction. "My printer doesn't work" "OK, reboot your PC; ticket closed", "My printer still doesn't work, and I've rebooted", "OK, reboot the printer; ticket closed", etc. Never discovering that the printer is out of toner.
I'd further suggest that you measure the total cost of ownership of the software and calculate the cost/minute of reduced duration. If the call duration is reduced by an average of 30s, but the total cost of ownership is $100,000, what is the payback period? When will the investment break even?
It is likely you'll have to make some assumptions (it would be great if you could somehow pilot the project and get good numbers, but it is likely that you're going to have to model the change with extensive assumptions)
It may also be worth measuring re-use - can the software store solutions in a format that makes it easier for other call center analysts to consult/reference prior? Has this customer had this problem before? Has another customer had this problem? Is this ticket potentially related to another ticket? Does this ticket indicate that there is an enterprise wide problem? Can we speed ticket resolution faster by providing references to other tickets? Can this software help to triage tickets for escalation to a higher tier? Does it help find the right analyst to solve a problem? (Analysts are not fungible; they each bring unique expertise to the table - is it worth waiting for the expert on this type of problem, or is it better to assign to the next available analyst?)
Can the proposed solution analyze longer duration calls to determine the cause? What do all calls where the duration is greater than 1 standard deviation above the average have in common? Is it the analyst? the problem type? the customer? Day of week? etc.?
You seem to indicate that you're considering two different solutions - one which manages all call center operations and the other which takes a different approach to the goal. If I were interested in managing call center operations, I'd need to measure a bit more than call duration. How many escalations to resolution? total time to resolution? amount of knowledge created by the call center (capital improvement).
The short summary is that I'd measure the benefits in terms of the sponsor's desired goals. You hint that this is call duration, but I'd listen carefully for other desired benefits.
Those are some ideas, but I'm not sure they address the core of your question. Can you confirm that this is what you're looking for, or refine my understanding of the question?
