How would you go about prioritising these requests and why?
1. Dev team really wants to build a new library, claiming that when it's done, any development will be much faster.
2. Call centre agent reported, that some business customers of the website experience difficulties when a lot of products are added to the basket - the website slows down massively and they are considering switching to competition. Some business customers already left.
3. Business stakeholders ask to implement a new form of payment for customers and claim that this will bring the business a lot of money.
A Product Owner can order the Product Backlog as he or she sees fit. A Product Owner is also responsible for maximizing product value. Which of the requests you cite would be most likely to have the greatest impact on value according to the available empirical evidence?
Ian's answer is just great. Try to understand and answer his question.
PS:
I'll assume you are a PO (have seen a PSPO badge on your profile). Without knowing anything about your business and the specifics, if I were you. I'd try to find out more about #2 - sounds like you have potentially critical production issues, but you & the team need to investigate more. And I'd start with it, production usually takes precedence.
Once more is learnt about what causes the performance problems, and the possible causes of the high load, you'd be in a position to determine the real severity and impact, so you may choose to tackle those first.
I totally agree with Eugene.
In my opinion, task #2 is most important as it is directly impacting the business in negative way. Anyways, the final call will be taken by Product Owner only from business point of view (how bad it impacts the business).
Task #3 and Task#1 are enhancement and improvement tasks respectively. Both things can divide into more Granuler form and work can start on both parallely depending on the Development teams bandwith.
Here too the final call will be taken by Product Owner only.
Thanks.