Abstract This paper discusses some aspects of the centralised version of the supply chain coordination method that uses the so-called Alternating Direction Method (ADM) presented by Jeong (2012, A centralized/decentralized design of a full return contract for a risk-free manufacturer and a risk-neutral retailer under partial information sharing. International Journal of Production Economics 136 (1), 110–115). We show that the method requires both from the retailer and the manufacturer to faithfully follow the proposed algorithm, without any attempt to follow their own interests in gaining higher profits. We also warn that the condition of the information privacy is violated also in partial information sharing model. Furthermore, we correct an error in one of the equations.