estimating scope economies in the presence of semi-controllable and non-controllable costs

Measuring economies of scope is a significant aspect for firms and plays an important role in decision making. due to the presence of non-controllable and semi-controllable measures in many organizations, approaches based on data envelopment analysis (dea) are proposed in the current paper to estimate economies of scope with non-controllable and semi-controllable costs. a numerical example is used to illustrate the approaches proposed herein.