Many authors have highlighted the gap between the supply side and the demand side of the order fulfilment process. Generally, the latter tends primarily to be “agile” by maximising responsiveness and flexibility while the former tends to be “lean” by maximising efficiency. However, the most fundamental trade-offs in supply chain management are between these two properties. This is the “leagile” objective. In stock-out situation, the delivery options that would minimize the customers’ dissatisfaction while reconciling the conflicting objectives of the different actors of the supply network must be defined. Today, no particular method seems to allow managing bulk within this leagile ambition. This paper proposes a non-sequential Advanced Available-to-promise model to tackle this question. The model is applied to a numerical example and the results obtained are used to illustrate the most representative delivery strategies.