PurposeThere is a view that firms should decide between a lean or agile approach to supply management primarily on the basis of whether their product offering is “functional” (predictable demand, low variety and a long life cycle) or “innovative” (unpredictable demand, high variety and a short life cycle). This paper aims to present and test the proposition that this dichotomy is less useful in complex, one‐off project environments, such as shipbuilding or construction, because projects typically require the assembly of many different, largely functional, products in a unique or innovative configuration.Design/methodology/approachThe paper reports a case study focusing on one of the supply chains serving a major UK shipyard. The case study data were gathered by means of semi‐structured face‐to‐face interviews with key personnel (procurement, sales, production, materials management and engineering/design) from each company within the defined supply chain.FindingsThe case study reveals that the design and build process used in the shipyard introduces radical unpredictability into the demand for “functional” components of naval vessels.Originality/valueThe paper raises important questions as to the conceptual robustness and the empirical generalisability of some of the extant literature on supply strategy selection. In particular, the case study suggests that a core assumption – that the demand for functional products is relatively predictable – is not sustainable in the context of project specific supply chains where the ultimate demand is generated by an active organisational buyer.