You can, aside following indications on activity costs, conduct a classical analysis on variable and fixed costs - if you can solve the problem with a few variation on variable costs and maintain the fixed costs - only variable are relevant - and than, only these are important to decide...
Make or buy decisions are very basic questions that management accounting tries to solve.
A good management information system (MIS) will tell decision makers what the variable costs as well as some relevant fixed costs of manufacturing a certain good internally, i.e. within the company, are. If these preventable costs are higher than the procurement costs of that good from a supplier, then the company should consider its outsourcing options.
With variable costs I particularly mean direct material, direct labor, and variable overhead costs while with relevant fixed costs I mean overhead costs that can be directly assigned to the product in question and that would be eliminated if the product were made externally. E.g., salary for a shop floor supervisor (= fixed overhead cost) who’s assigned to only that one product and that could be potentially saved.
However, before making an outsourcing decision the company should consider its production capacity and capacity utilization before and after a possible outsourcing decision. When making outsourcing decisions, a company in general should not only consider quantitative management accounting Information, but also should take a look at the more qualitative impact the decision would have, such as the quality of the product.
Management accounting information therefore can help in the decision making process but you cannot rely on them alone.
You can also try Activity Based Costing - one of its aims is to identify activities that doesn´t bring an addition of value to the chain of production. This has lead to Activity Based Management, wich is a way to evaluate the profitability of all activities developed in the organization, in a way to make each one profitable or else, to outsource or disable that activity.