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OMG 402 - Operations Management Spring 1997

Learn how to make the safety stock decision in a supply chain to balance cost and service level. Calculate the reorder point and safety stock to avoid stockouts while waiting for orders to arrive.

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OMG 402 - Operations Management Spring 1997

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

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

  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. 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-iceclears build-up and inhibits ice formation • Stock-out of fluid grounds planes

  6. demand (gallons/wk.) 35,000 gal. weeks 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. 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. inventory position inventory on-hand inventory (gallons) Q Q re-order point (R) order received order placed weeks lead time The Safety Stock Decision Note: both demand during lead time and lead time itself can be variable

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

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

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

  12. Calculating Reorder Point and Safety Stock • R = E[DL]+ 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. Calculating Reorder Point and Safety Stock • Assume: • L = 2 weeks, Dt = 35,000 gal, st = 4,000 gal • Then: • E[DL] = • sL = • R = E[DL] + s but what should s be ??

  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{DL > R } = 0.01, i.e., Pr{DL – E[DL] > R – E[DL] } = 0.01 Pr{DL – E[DL] > s } = 0.01 Pr{Z > s/sL} = 0.01, or s/sL = z0.99 R = E[DL] + s = E[DL] + z0.99sL = how many stockouts can we expect (on average) per week?

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

  16. Calculating Reorder Point and Safety Stock: Variable Lead Times di = demand during week i (a random variable) with mean E[di] = mt and variance var(di) = st2 n = number of weeks in lead time. Given: E[n] and var(n) = sn2 demand during lead time = DL = d1 + d2 + … + dn We wish to find: E[DL] = expected demand during lead time sL2 = variance of demand during lead time

  17. Calculating Reorder Point and Safety Stock: Variable Lead Times E[DL] = E[n] mt sL2 = E[n] st2 + mt2sn2 Then, find R as before: s = zsLR = E[DL] + s Note that management must control many contributors to safety stock: • randomness of demand, st2 • length of lead time, E[n] • randomness of lead time, sn2

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

  19. plant echelon warehouse echelon r1 r2 r3 r4 r5 r6 r7 r8 r9 Echelon Management in a Supply Chain plant wh1 wh2 wh3 Manage your own level and those below you - your echelon.

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

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

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

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

  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. 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

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