Alternate approximation of concave cost functions for process design and supply chain optimization problems

• We present an alternate approximation of concave cost functions for economies of scale.
• We propose a logarithmic function that is exact and has bounded gradients at zero values.
• We illustrate the application and advantages of the proposed approximation.

This short note presents an alternate approximation of concave cost functions used to reflect economies of scale in process design and supply chain optimization problems. To approximate the original concave function, we propose a logarithmic function that is exact and has bounded gradients at zero values in contrast to other approximation schemes. We illustrate the application and advantages of the proposed approximation.