J Intell Manuf DOI 10.1007/s10845-010-0423-2 Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process Yesser Yedes · Anis Chelbi · Nidhal Rezg Received: 26 October 2009 / Accepted: 7 June 2010 © Springer Science+Business Media, LLC 2010 Abstract In this paper we deal with the integrated supply chain management problem in the context of a single vendor- single buyer system for which the production unit is assumed to randomly shift from an in-control to an out-of-control state. At the end of each production cycle, a corrective or preven- tive maintenance action is performed, depending on the state of the production unit, and a new setup is carried out. Two different integrated production, shipment and maintenance strategies are proposed to satisfy the buyer’s demand at min- imum total cost. The first one suggests that the buyer orders batches of size nQ and the vendor produces nQ and makes equal shipments of size Q. The second policy proposes that to satisfy the same ordered quantity, the vendor produces sepa- rately smaller batches of size Q, n times. The total integrated average cost per time unit corresponding to each strategy is considered as the performance criterion allowing choosing the best policy for any given situation. Keywords Supply chain management · Production · Inventory · Maintenance · Quality · Single-vendor single-buyer Introduction In integrated supply chains, vendors and buyers or suppliers and purchasers seek to exploit the least opportunity to make Y. Yedes CEREP/LGIPM, Tunis, Tunisia A. Chelbi CEREP, Tunis, Tunisia N. Rezg (B ) LGIPM/INRIA, Metz, France e-mail: rezg@univ-metz.fr more competitive the whole supply chain. In this case, all strategic tactic and operational decisions made jointly by all actors involve different types of resources and tools depend- ing on the complexity of the supply chain configuration. The related models are based on the integration of diverse activities. The role of such integration grows continuously, from the era of individual models to the appearance of the joint tendency, but still with the same main objective: an efficient management of all integrated activities providing considerable cost reductions. Basically, the Economic Ordering Lot sizing (or Eco- nomic Production Lot sizing) problem have been widely and differently treated in the literature in both single and joint context. The models proposed, since Harris’s classic square root economic order quantity (EOQ) model, have been improved relaxing assumptions and/or taking into account more factors and parameters. Many of these models related to the case of imperfect pro- duction process. Individual models such as those developed by Rosenblatt and Lee (1986), Cheng (1991) and Khouja and Mehrez (1994) assumed that the production process shifts to an out-of-control state after a random period of time but didn’t suggest any solution to counter this unreliabil- ity problem. On the other hand, Lee and Srinivason (2001), Ben-Daya and Khursheed (2002) and Ben-Daya (2002) considered integrated production-inventory and preventive maintenance models. Later on, Sheu and Chen (2004) made a lot-sizing model to determine the level of preventive main- tenance for an imperfect process control. Aghezzaf et al. (2006) proposed a combined production and maintenance strategy in a batch production system context. Their model allows determining an integrated production and mainte- nance plan that satisfies the demand over the entire hori- zon without backlogging, and which minimizes the expected total production and maintenance costs. Yang et al. (2008) 123