An information-content based measure of proliferation as a proxi for structural complexity

In this article we propose the use of an information-content based measure as a proxy for supply chain complexity. The focus of our research is the problem of structural complexity in the supply chain, i.e. the complexity emanating from the proliferation of products, channels and markets. Notwithstanding it is widely agreed among practitioners that this proliferation damages supply chains, rendering them less efficient, there is still need for a mechanism for measuring structural complexity and evaluating its impact on the firm's performance. In an attempt to filling this void, we propose a definition that originates from the firm's business strategy and, based on it, suggest the direct use of entropy as a more austere measure for structural complexity than other available alternatives, which rely heavily in the use of typically hard to acquire data. We show that the suggested measure has some interesting mathematical properties (to which we refer to as internal consistency) together with the capability of reproducing certain empirical regularities observed in supply chain management (external consistency). Moreover, the proposed measure has attributes that are not present in other measures: it requires a limited and easily accessible amount of data, it allows direct comparison between firms or business units, and it is a useful tool for assessing the impact on structural complexity of alternative managerial decisions (the look-ahead property). Numerical examples are provided.