Optimizing raw materials and finished goods safety stocks in a production network under guaranteed service approach
The safety stock placement problem under the guaranteed service approach (GSA) determines the placement and amount of safety stocks to hold at different stocking locations of a supply chain. We consider a network of production facilities. Each facility includes a processing unit, inventory of raw materials, and inventory of produced items or finished goods. A facility may hold safety stocks for both raw materials and finished goods. The objective of this work is to identify the production stages that hold safety stocks, the allocation of safety stocks between raw materials and finished goods, and the release policy of raw materials to the processing unit in order to minimize systemwide inventory costs while meeting a target service level. We name this new problem as the safety stock placement and allocation (SSPA) problem. A spanning tree network of production facilities that serves an external demand of a single end product from stock is considered. Along the assumptions of GSA, demand over any period is bounded. We assume that demand interarrival times are independent and follow a general probability distribution. Replenishment of a production stage is triggered by finished goods inventory according to a periodic review base stock policy, with a common review period between stages. Supplier stages quote a guaranteed service time within which the goods must be shipped to the customers. After stipulated transportation times the goods arrive at the raw materials inventory, which are then released following a base stock policy with delay. The allocation of safety stocks within a stage influences the delay parameter of the base stock release policy. In fact, due to the variability of demand during the incoming service time (replenishment lead time) a stage must carry safety stocks or delay the release to ensure availability of required raw materials. When no raw material safety stocks are held, a delay is required between the occurrence of demand and the release of raw materials to the workstation. It follows that a key tactical planning decision is the release delay parameter. Based on these system settings and assumptions, a mathematical formulation of the SSPA is presented. Our analysis suggests that holdings for raw materials follow an all or nothing rule, where a facility either hedges raw materials for the demand during the entire incoming service time or holds no safety stock at all. Concerning the release policy, this translates to one of the two possibilities either an immediate release or a delay equal to the total incoming service time. We find that a facility may hold raw material safety stocks only under the following conditions a) if a facility procures raw materials from a supplier external to the supply chain under control, b) if it requires a positive transportation delay between shipment and receipt of raw materials, and c) if a stage rations its raw materials among several suppliers. In all other cases, it is optimal to hold safety stocks only in the form of finished goods. Furthermore, we find conditions on holding costs, production lead times and incoming service times that will determine the optimal allocation of raw materials and finished goods safety stocks when a stage may hold safety stocks in both the forms. Based on these findings, an existing dynamic programming algorithm for spanning tree networks is extended to so$\mlve SSPA. The algorithm is then used to test the propositions on a real sized instance with 31 production facilities. Experiments confirm the claims made in this paper. Further, we evaluate the savings yielded by employing safety stocks in the form of both raw materials and finished goods, as opposed to holding only finished goods safety stocks. Results show that the magnitude of savings depends on the value added at a stage, and also the transportation times between stages.