... Scrum team members need a single, well formed, sequenced list of Product Backlog Items that allows them to focus on maximizing value delivery. Without it they can generate features that are never or rarely used, deliver features at the wrong time which suboptimizes revenue, or become confused and disoriented and unable to deliver anything (see ScrumMaster Gets Fired).
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One person needs to be responsible for this backlog. This person needs deep domain knowledge, business insight to determine revenue impact of feature delivery, understanding of technical dependencies, and the authority to force rank the backlog to maximize business value.
Too many organizations try to put several bosses in charge of charting product rollout. Sometimes they can't even agree what the product is. While it takes up a staff position, and therefore a cost, a good product owner will increase a product revenue stream or product value delivered by at least 20% in the first year. Without someone to explicitly lead product development, it's almost impossible to make this work without a single focal point.
You can maximize revenue by continuously using your users as beta sites (where the deliverables are the beta deliveries) but customers can be made much more comfortable if a person on the vendor side takes responsibility for some up-front planning and thinking. Lean says that it is important to line up the decisions early on, so that the decisions are easy to make once the time comes to make them.
Get a Product Owner to order the Product Backlog and to take responsibility for the vision of the product, and for the value that emanates from the delivery of that vision.
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The best Product Owner is as close to value delivery as possible. There are multiple stakeholders — the end user, the organization deriving revenue from end user use of the product, persons concerned with regulatory authorities, legal issues, or standards bodies, etc. Often stakeholders cannot be Product Owners because they have limited knowledge, a conflict of interest, or lack of authority to make decisions. (Picture - "The One" from the matrix). One of the Product Owner's primary KPIs is revenue generation from the product — the business plan.
There is no Customer in Scrum. The Customer role is present in many real-world value streams. Scrum tends to reflect the Lean vision of partnership between the business and end user, rather than a relationship of animosity or of at-arms-length or over-the-wall communication. Customers can contribute paths to market, but the enterprise should be mindful that they are an additional handoff that can introduce delay and waste. These often are impediments to be removed.
It is often difficult to find a Product Owner. The domain knowledge may reside in a business expert (sometimes the CEO) who does not have enough time to fully form the Product Backlog. The domain expert may become a Chief Product Owner or you may need to find a Surrogate Product Owner.
If the creation of the Product Backlog takes too much time or expertise for one person, a Product Owner Team needs to be formed with a Chief Product Owner that has final control over the sequencing of the Product Backlog.
Anyone can put anything on the Product Backlog. They own it and must provide support for fully forming the Product Backlog Item. The Product Owner Team sequences that item in the global Product Backlog.