Most of the budgets get consumed addressing poorly addressed previous problems. Focus on root cause analysis, and prevention of recurrence. Test your Root Cause Analysis - did you change the process , the technology or work practice - if not root cause was not done. This thinking slowly leads to non linear staffing. If your contract is locked both in staffing and SLA there is little scope for cost improvement as automation will only add cost.

Another factor is working with your vendor during contracting. There may be lower cost options you hadn't considered. One example is replacing penalties with exit clauses. Another is less strict SLAs. 4 9s is way more expensive than 3 9s. The difference is not significant for most workloads, but the savings can be dramatic.

Define the work scope very clearly. Choose low cost destinations to support. Define the support team structure very optimally. Automate as much as possible. Self service capabilities can be very cost effective

Outsourcing budgets are always tight as part of their nature. It is key not to waste money without value added e.g. a quick win this year but having to spend exponential money next year. Prioritize vendors with long-term potential, because exiting one relationship and entering the next is the most stupid way to burn money. Take a closer look at the history and character of a potential vendor's leaders, especially their willingness to develop together with their customers in a long-term perspective. Listen to the solution approach of a potential vendor from a short-, medium-, and long-term perspective as they know their business better than you do. Think in bonus-/malus-rules, as vendor-driven improvements will not occur if not appreciated.