What is the cost-effective way of doing product innovation?

For cost-effective innovation, you need to be clear on which aspect of your organisational asset you are making better, stronger and faster:

Product innovations can span all three organisational assets as you may be building products to re-sell, and products to improve the internal systems that help you work better, provide better partner experiences or make better decisions, faster.

Given we are looking to establish a basis on cost-effectiveness, we need to create a sense of ROI that balances the effort that needs to be done to achieve the desired outcome, and how it creates impact.

Follow this process:

Identify the business asset you will add value to (Core Products, Value Chain or Organisation).
Establish the nature of the value you want to improve, i.e. identify the Work Value Element (WaVE) you will allocate effort towards. If you are in software, you can use this to reference a potential set of WaVEs.
Determine the KPI you are going to make better for e.g. count of tickets processed per day, errors reported per day, average queue size per day.
Make sure you have an organisational agreement that this KPI is reflective of the value you are trying to improve (direct/proxy).
Determine your existing Cost-per-unit, i.e. Using a product support ticket as an example, this can be Total spend on support per year / Number of tickets per year = Cost-per-unit in support.
Be clear on how your innovation will improve this KPI (10%, 20% 10X, etc. ) Will you be able to do more tickets with the same costs? or will you decrease the count of support tickets that come in?
Be clear on how much you are willing to commit to improving this KPI. This is generally limited by a pre-set allocated budget limit or a budget you need to get executive support.

Either way, having a clear view of the KPI, Cost per unit and how each unit will be improved before and after will allow you to build an informed decision on whether to invest this effort or not. This means you can determine if it is cost-effective.

I suggest you involve cross-functional representation as an area of innovation that can increase the costs in another, nullifying the outcome desired. Engaging more people helps you increase your confidence in achieving a valuable return, optimisation, or innovation.

I also think you need a system to better your decisions around how to approach work and requests. I wrote more about this where I cover a framework around which you can decide how to approach work: How to determine what product opportunity to pursue next.