Any tips for how to reduce  end-to-end supply chain costs while not sacrificing quality?

Question really is: what is the reason why you want to reduce costs? If you can answer this without the knee-jerk reaction of "because our margins aren't where they should be" then you also have your answer.
Many times companies pursue cost reduction ad noseum, without actually checking if it makes sense under the given circumstances...as shareholders get greedy....then they shoot themselves in the foot and spend more on restoring where they were before than what they actually saved.

We recommend looking into the system and identifying where the most touches occur- are they value added or required? If not, it may be time to Lean out the process and some businesses overlook the cost of the supply chain in the last mile, where a good amount of Total Cost of Ownership can be mitigated through the supply chain impacting other parts of the business.

The key thing in supply chains is to look at overall system costs while dealing with individual elements. That is why integrated business planning is so essential because it is all about the tradeoffs. Do you want to minimize unit cost in manufacturing with long runs, then be prepared to lock up cash in inventory. It is always good to find the right balance. You can source at the lowest cost and then pay for quality and delivery delays that hold up production and result in missed sales orders. Local optimization vs. system wide tradeoffs is something that needs to be considered and SC technology now gives that e2e visibility to enable those tradeoffs.

I'd not add much as there are many good answers in the thread already.
What I usually do are:
1. know what your cost drivers are and why - always (collaborate with your CFO to have these)
2. know which one of these add value to your customers and why
3. know which one of these are driving quality & efficiency and why
4. know which ones of these are making your team happy (they are talented and love working for you) and why

5.The rest can be cut. Supply chains are in constant move and change. This drives up/down cost elements, even if you have cost reduction initiatives in place.

Keep your eyes on the stability vs the flow of the business in terms of costs and cut those "sprouts" of costs which come from temporarily unsupervised elements coming from change (new processes that were put in place or process/system changes, people changes etc.).

If you keep these, you cannot go wrong.

Great question and responses here. Thank you for sharing. 

To reduce cost without sacrificing quality is where the art and science of balancing it out or trade off play the key role. 

Cost and quality often has a negative correlation. But there is a space to consider, different customers perceive quality in different ways. 

If we can identify and match the quality needs for each group of customers, we can see more ways to reduce cost in overall end-to-end supply chains. 

Using careful supply chain segmentations can help those balancing act and trade off become more effective, resulting in reduce cost but not sacrificing quality and customer satisfaction.