Integrated safety stock optimization for multiple sourced stockpoints facing variable demand and lead time Hany Osman a,n , Kudret Demirli b,1 a Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd.W., EV13.119, Montreal, Quebec, Canada H3G 1M8 b Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd.W., EV4.187, Montreal, Quebec, Canada H3G 1M8 article info Article history: Received 16 March 2011 Accepted 2 August 2011 Available online 7 August 2011 Keywords: Supply chain Safety stock Order statistics Variable demand and lead time Benders decomposition technique abstract The safety stock placement problem of a multi-stage supply chain comprising multiple sourced stockpoints is addressed in this paper. Each stockpoint faces variability in its downstream demand and suppliers’ lead time. The maximum among these suppliers’ lead time is determined by employing concepts of order statistics. It is required to find the fill rate and safety stocks at each stockpoint that leads to satisfying the end customer service level at minimum safety stock placement cost. Hence, the fill rates and the safety amounts are decided from a global supply chain perspective. Two models are proposed; a decentralized safety stock placement model and a centralized consolidation model. The decentralized model finds the safety amounts at each stockpoint required to face its underlying lead time demand variability. The consolidation model finds the consolidated safety amounts that will be kept in the relevant consolidation center at each stage. A Benders decomposition technique is developed to handle the nonlinearity and binary restrictions involved in the safety stock consolidation model. Strategies proposed by the consolidation model achieve 45.2–62% reduction in safety amounts that results in a cost savings ranging between 22.2–44.2% as compared to the strategies proposed by the decentralized model. & 2011 Elsevier B.V. All rights reserved. 1. Introduction In this paper, the safety stock placement (SSP) problem of a supply chain including multiple sourced stockpoints is tackled. Each existing member in this supply chain faces variability in the upstream lead time and in the downstream demand. A graphical representation of the supply chain under consideration is depicted in Fig. 1. The chain is composed of an assembly facility at the most downstream stage, Tier1-suppliers at the intermedi- ate stage, and Tier2-suppliers at the initial stage. The supplying and inventory strategies, currently employed throughout the supply chain, failed to satisfy the promised delivery dates of the end items. The primary reason behind this shortfall is the existence of unreliable suppliers that are unable to deliver materials on time. The secondary reason concerns the inventory systems employed throughout the chain. These systems are established based on random ordering decisions, which often lead to a stockout occurrence. Moreover, each member of the chain does not employ a proper safety stock policy to face the fluctuation of customer demand and suppliers’ lead time. A three-stage research is conducted to resolve this problem. In the first stage, the supply chain is reconfigured and materials are redistributed to the highly reliable and coordinated suppliers (Osman and Demirli, 2010). In the second stage, a joint supply chain inventory–production system is proposed based on the deterministic assumptions of customer demand and supplier’s lead time (Osman, 2011). At the third stage, presented in this paper, the variability of downstream demand and upstream lead time is considered while developing a safety stock placement policy through the supply chain. Such an integrated policy, established from a supply chain perspective, should specify sufficient safety amounts and fill rate at each stockpoint to achieve a prespecified end customer service level at minimum cost. Two SSP models are developed to establish two different SSP policies. The decentralized policy, characterizing the first model, allows each stockpoint to independently handle the variability of its lead time demand. The centralized policy, characterizing the second model, aims at reducing the variability of lead time demand at each stage by pooling this variability at one stockpoint. Order statistics concepts are applied to determine the parameters of the lead time probability distribution at each multiple sourced stock- point. The two policies can be implemented after deciding on cycle time and order amount of deterministic inventory systems. The decentralized model is solvable to optimality using the nonlinear commercial solver Minos, whereas a decomposition algorithm Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.08.004 n Corresponding author. Tel.: þ1 514 848 2424x7224; fax: þ1 514 848 3175. E-mail addresses: h_most@encs.concordia.ca (H. Osman), demirli@encs.concordia.ca (K. Demirli). 1 Tel.: þ1 514 848 2424x3160; fax: þ1 514 848 3175. Int. J. Production Economics 135 (2012) 299–307