1. OMG 402 - Operations Management Spring 1997 CLASS 14: Supply Chain Management Harry Groenevelt

2. 2 Agenda Recap The Safety Stock Decision: Living in an Uncertain World Echelon Management in a Supply Chain Supply Chain Performance Supply Chain Insights

3. 3 Recap Supply chains: balancing cost vs. service level Single Period Decisions: Trading off stockouts vs oversupply Pr{d < Q}  G/(L+G) Pr{Z  z  } = 

4. 4 The Safety Stock Decision: Living in an Uncertain World Safety Stock = buffer against unpredictable variation in supply and demand We will discuss: –how to ‘trigger’ an order (track inventory position, choose a reorder point) –how to calculate the reorder point and safety stock

5. 5 The Safety Stock Decision: Example De-icing fluid at Anchorage International Airport –Icing poses a constant threat to safety –Variant of glycol (antifreeze) used to de-ice clears build-up and inhibits ice formation –Stock-out of fluid grounds planes

6. 6 weeks demand (gallons/wk.) 35,000 gal. The Safety Stock Decision demand of 35,000 gallons/week standard deviation of demand during one week: st = 4,000 gal. it takes 2 weeks to receive an order goal: limit stock-outs while we wait for the order to arrive.

7. 7 The Safety Stock Decision Assume that we use an “order point-order quantity” inventory control system. Here’s how it works: –monitor inventory position: inventory position = inventory on-hand + scheduled receipts – backorders – inventory allocated –we re-order Q (often, Q = EOQ) when inventory position drops to R [see also: handout K&R Chapter 12, p. 549.]

8. 8 Note: both demand during lead time and lead time itself can be variable weeks inventory (gallons) Q Q re-order point (R) order placed order received inventory position inventory on-hand lead time The Safety Stock Decision

9. 9 Calculating Reorder Point and Safety Stock Quantities known: – lead time to receive order = L weeks (for now, assume this is constant) – D t = E[demand during one week] –  t = standard deviation of demand during one week

10. 10 Calculating Reorder Point and Safety Stock Find expected demand and variability during lead time: –E[demand during lead time] = E[D L ]= _______ –standard deviation of demand during lead time =  L = _________ Re-order point should be higher than E[D L ] The extra inventory is safety stock (s)

11. 11 weeks inventory (gallons) L L Q Q R safety stock ( s ) E[ D L ] what would happen if we set R = E[ D L ] ?? Calculating Reorder Point and Safety Stock

12. 12 Calculating Reorder Point and Safety Stock R = E[D L ]+ s. How large is safety stock, s? Safety stock size driven by variability of demand over lead time and specified service level: –Objective 1: Satisfy cycle service level, v Pr{stockout during lead time} < 1– v Pr{demand during lead time > R} < 1 – v –Objective 2: Satisfy fill rate, f proportion of orders not filled immediately < 1 – f –Objective 3: Balance expected holding costs vs. costs of stock-out

13. 13 Calculating Reorder Point and Safety Stock Assume: – L = 2 weeks, D t = 35,000 gal,  t = 4,000 gal Then: – E[D L ] = –  L = – R = E[D L ] + s but what should s be ??

14. 14 Calculating Reorder Point and Safety Stock Objective 1: Cycle service level v = 0.01 (99% of order cycles do not stock out) –Choose R so that Pr{D L > R } = 0.01, i.e., Pr{D L – E[D L ] > R – E[D L ] } = 0.01 Pr{D L – E[D L ] > s } = 0.01 Pr{Z > s/   } = 0.01, or s/  L = z 0.99 R= E[D L ] + s = E[D L ] + z 0.99  L = how many stockouts can we expect (on average) per week?

15. 15 Calculating Reorder Point and Safety Stock What happens when variability of demand increases? What happens when lead time increases?

16. 16 Calculating Reorder Point and Safety Stock: Variable Lead Times d i = demand during week i (a random variable) with mean E[d i ] =  t and variance var(d i ) =  t 2 n = number of weeks in lead time. Given: E[n] and var(n) =  n 2 demand during lead time = D L = d 1 + d 2 + … + d n We wish to find: E[D L ] = expected demand during lead time  L 2 = variance of demand during lead time

17. 17 Calculating Reorder Point and Safety Stock: Variable Lead Times E[D L ] = E[n]  t  L 2 = E[n]  t 2 +  t 2  n 2 Then, find R as before: s = z  L R = E[D L ] + s Note that management must control many contributors to safety stock: –randomness of demand,  t 2 –length of lead time, E[n] –randomness of lead time,  n 2

18. 18 which holds less safety stock as a % of demand? what factors may diminish these benefits? anchorage intl’ anchorage local anchorage intl’ anchorage local Calculating Reorder Point and Safety Stock: Economies of Scale

19. 19 warehouse echelon plant echelon plant wh1wh2wh3 r1r2r3r4r5r6r7r8r9 Manage your own level and those below you - your echelon. Echelon Management in a Supply Chain

20. 20 Echelon Management in a Supply Chain Each stocking point monitors its echelon inventory position Echelon inventory position = Total on-hand inventory + Total inventory in transit within echelon + Orders outstanding with echelon supplier – Backorders at echelon retailers – Inventory allocated to retail customers

21. 21 Echelon Management in a Supply Chain What are the advantages of this system? What are the barriers to implementation?

22. 22 Information and Material Flow Inventory Capacity Drivers of Supply Chain Performance Performance primarily driven by three attributes:

23. 23 Information and Material Flow Inventory Capacity demand variability and uncertainty supply variability and uncertainty supply lead time, order lead time pipeline information (how much stuff is out there?) bottleneck capacity set-up costs and times product flexibility volume flexibility (how much does it cost to ‘ramp up’?) safety stock pipeline stock (from Little’s Law!) cycle inventory (from batching) seasonal stock Drivers of Supply Chain Performance

24. 24 Drivers of Supply Chain Performance Information and Material Flow Inventory Capacity If you change one attribute, others must change as well to maintain performance.

25. 25 Supply Chain Insights Examined components of inventory: –Inventory due to batching (cycle stock) –Inventory as a buffer against variable demand during lead time (safety stock) Cycle stock is a response to order/setup costs, setup times, and capacity constraints; Safety stock guards against uncertain demand over lead times in the supply chain.

26. 26 Supply Chain Insights Methods to reduce safety stock: –reduce lead time –reduce variability of length of lead time –reduce demand variability –economies of scale In the long run, there are interactions between information, inventory and capacity