Echelon stock

To analyze the warehouse, we foUow the standard notion of echelon stock. That is, we aggregate stage 0, along with stages i = 1,. . . , c, into a single system, indexed by E (for echelon). This aggregated system supplies the superposition of all c demand streams. Note that each demand process stiU has its own lead time L. Let... 

Axsater, S., K. Rosling. 1993. Notes Installation vs. echelon stock policies for multilevel inventory control. Management Sci. 39 (10) 1274-1280. 

To simplify this expression, we use echelon holding costs, defined as follows The echelon holding cost at echelon j is Hj = hj - hj y where, consistent with the earlier sections of the chapter, hj is per-unit cost of holding inventory per period. (Since ho = 0, = hi.) Thus, echelon stock at echelon j is valued at... 

Using the information given previously and a CSL target of 95% for each stage, we obtain installation reorder point levels of R2 = riiDLT,2 + csl 0011,2 = 82.2 + 1.645 X 14.2 = 106 and Rj = fliDLxi + csl Odlxi = 191.8 + 1.645 X 21.75 = 228. As discussed in Axsater (2006, Chapter 8), any installation-stock reorder point policy can be replaced by an equivalent echelon-stock reorder point policy that has... 

The resulting (centralized, echelon-stock) policies are (Q2, R2) = (Qir 2) = (44 106) and (Qj, Rj) = (894, 781). Therefore, whenever installation inventory at stage 2 (same as echelon inventory at echelon 2) falls below 106 imits, we place an order on stage 1 for 447 imits, and whenever echelon inventory at echelon 1 falls below 781 imits, stage 1 should place an order on its sup>plier for 894 units. 

Chen, E and Y. S. Zheng. 1994. Evaluating echelon stock (R,nQ) policies in serial pro-duction/inventory systems with stochastic demand. Management Science. 40 1262-1275. 

As for the echelon safety factor,, it can either be prespecified by the user or, if the stifety stock levels are to be set automatically based on target fill rates specified at the retail level, it can be obtained from the solution to ... 

To demonstrate the presence of waste in the supply chain, Mentzer and Moon describe a four-echelon supply chain retailer, wholesaler, manufacturer, and supplier. They assume that the retailer that sells directly to an end-user provides a sales forecast of 1000 units to its immediate partner, the wholesaler. The authors note that supply chain trading partners, including the retailer, often hedge their forecasts with safety stock. If each uses a 10 percent safety stock hedge, then the extra inventory that will accumulate over the supply chain is over 100 percent of the needed supply. So, to support final sales of 1000 units, there would be 1105 units in supply chain safety stock distributed along the chain. 

Cachon, G. 2001. Stock wars inventory competition in a two-echelon supply chain. Operations Research, Vol.49, 658-674. 

Retailer s echelon base-stock level Bl = t)[ H-Supplier s echelon base-stock level ... 

Echelon-based inventory systems. Consider next an echelon-based inventory system with a single decision-maker, that applies the base stock levels (10.27). For this setting Aviv (2002a) shows the following... 

In this section we describe a way for finding the pair of safety-stock parameters 7 and 7, that minimize the long-run average total supply chain cost. We assume that installation-based policies are used. The extension of the discussion to echelon-based policies is relatively easy, given the observations made in 6.1.2. We refer to a supply chain in which these optimal safety stocks are used, as a coordinated two-level inventory system. We assume that h < and set = 0. Aviv (2002b) shows the following ... 

The approximation developed by Shang and Song (2003) uses echelon holding costs, as defined earlier, and starts from the optimal echelon N base-stock level, which—by the authors reference to Chen and Zheng (1994)— is given by computing the critical fractile... 

It is helpful to develop an intuitive interpretation of these bounds on the optimal echelon base-stock levels. Note that 0y can be expressed as... 

This potential understatement of the optimal overage cost results in S being an upper bound on the system-optimal base-stock level at echelon j. 

Example 3.15 Multi-echelon base-stock policies... 

Compute the updated echelon base-stock levels for the Stage Three Incorporated example (Example 3.15) given the same distribution of demand at the field warehouse, but with a penalty cost that is 20% of the original value (i.e., b = 10) and a 50% increase in echelon holding costs (i.e., installation holding costs of = 3.00,= 2.25, and = 1.50). 

Phophoinositides are from Echelon (Salt Lake City, UT http //www. echelon-inc.com/) or from Matreya (State College, PA http //www. matreya.com). Stock solutions of pure lipids (0.5-20 mM) are stored and aliquoted in 2 ml glass vials under argon at -20°. 

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