Serial supply chain

A serial supply chain consists of a number of entities that work sequentially to deliver product. In a serial supply chain, any given node s supply is affected by the decisions of upstream entities, and that node s demand is generated by downstream entities. Serial supply chains provide a simple supply chain structure, but it often implies use of a one-size- fits-all strategy that can generate significant costs if products and customer segments 

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C. J. Corbett, U. Karmarkar, Competition and Structure in Serial Supply Chains with Deterministic Demand, Management Science, 47(7), 966-978 (2001). 

The example provided earlier in the book (Figure 1.11) described the supply chain for a medical device manufacturer. In that example, products flow from the manufacturer to a distributor to a health care provider to a health care professional and finally to the patient. This is a serial supply chain the product flows through a series of steps to reach the patient. 

Order Variability in a Serial Supply Chain The Bullwhip Effect... 

Consider a set of independent entities (nodes) in a serial supply chain, shown in Figure 2.4. Node 1 is closest to the customer, and Node 1 is supplied by Node 2, Node 2 is supplied by Node 3, and so on. Now suppose that Node 1 faces a demand of fi every period. Suppose each node faces a lead time L to get product from its supplier immediately upstream. Finally, suppose that each node carries a pipeline inventory (sum of all physical inventory, plus orders or material in transit) of (T 4- S) X DemandForecast, where S is the safety stock factor at that location. Thus, if every node passed along the demand forecast it faced, each node would have a pipeline inventory of (Z 4- 5) X DemandForecast. 

This increase reflects the exponential growth in orders in response to lack of information in a fragmented supply chain. As mentioned in Chapter 1, this is called the bullwhip effect. Thus, even in a serial supply chain, lack of transparency can create undesirable volatility even when each entity behaves optimally, thus generating the bullwhip effect. The consequences of such volatility are increased capacity, inventory, delivery lead time, and costs. 

Graves and Willems [50] describe an approach to set safety stocks in a supply chain in order to provide the desired customer lead time. Their approach provides a conceptual basis to consider location of service parts inventory across a supply chain to optimize overall performance. The data for a sample five-stage serial supply chain is shown in Figure 6.7, with the supply chain details in the stage description row. 

In fact, in the simple i.i.d. case, Lee and Whang (1999) discuss ways in which installation-based policies can be set, through an establishment of an appropriate performance measure, to yield the same performance as a centralized serial supply chain. 

The benchmark case is of greater stand-alone interest when the network exhibits complexities such as stochastic demand that is filtered through the inventory policies implemented at the successive echelons, intricate cost structures, lead times, and multiple time periods of activity. This is the theme of the bulk of multi-echelon inventory theory, dating back to the serial supply chain analysis of Clark and Scarf (1960). This literature also considers system architectures that move product from a manufacturer to end customers along, multiple parallel paths, such as a 1-depot N-warehouse network. 

Serial Supply Chain with Deterministic Demand and Fixed Ordering Costs... 

Consider a two-stage, serial supply chain where the annual demand at stage 2 is D = 10,000 units. Fixed ordering costs at stages 1 and 2 are Ai = 400/order and A2 = 50/order, and inventory holding costs are hi = 10/unit/year and Izj = 15/unit/year. 

Shang and Song demonstrate that approximate solutions can be found for each upstream echelon e 1,2,..., N - 1 in the serial supply chain from two easily computed newsvendor-type fractiles, Q] and 0 , which they prove to be... 

Recall also that, at the farthest downstream site in the serial supply chain, echelon inventory is the same as installation inventory. Thus, Example 3.15 prescribes an installation inventory position at stage 3 of S3 = 31 units. Thus, when the system is first seeded with inventory, we set inventory at the field warehouse to = 31 units. Similarly, we seed... 

Serial Supply Chain with Fixed Costs and Stochastic Demand... 

Note also that the last example in the chapter essentially entails determining the placement of safety inventory in the supply chain (since the reorder point specifies inventory carried over and above the level required to meet expected demand over the replenishment lead time), albeit a simple, serial supply chain. Magnanti et al. (2006) present a general formulation of fhis problem, specifically a non-linear optimization formulation subject to linear constraints, to solve for the optimal placement of safety stocks in a general supply chain network. Magnanti et al. actually generalize the problem... 

Shang, K. and J. Song. 2003. Newsvendor bounds and heuristic for optimal policies in serial supply chains. Management Science. 49(5) 618-638. 

Daniel, S. R. J., and Rajendran, C. 2006. Heuristic approaches to determine base-stock levels in a serial supply chain with a single objective and with multiple objectives. European Journal of Operational Research 175 566-592. 

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