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3 Safety Stocks Used for Emergencies Finished Goods: Unexpected Demand (Level Related to Customer Service) Raw Materials: Orders Not Received Work-in-Process (WIP): Worker Unavailable or Machine Breakdown - Decoupling Inventory Also Known as Buffer or Fluctuation Inventory
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Inventory Control: Part 3 –Independent Demand Inventories
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Types of Inventories By Function
- Lot-Size (Cycle or Replenishment)- Instantaneous (Purchase)- Non-Instantaneous (Produce)
- Safety (Fluctuation or Buffer)- Anticipation (Seasonal)- Transportation (Pipeline)- Hedge (Beyond Scope of Class)
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Safety Stocks
Used for Emergencies Finished Goods: Unexpected Demand (Level
Related to Customer Service) Raw Materials: Orders Not Received Work-in-Process (WIP): Worker Unavailable or
Machine Breakdown - Decoupling Inventory Also Known as Buffer or Fluctuation Inventory
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Finished Goods Safety Stocks: Stored with Lot-Size Stocks
LT Time
Expected demandduring lead time (DDLT)
Maximum probable demandduring lead time
OP
Qua
ntity
Safety stock (SS)
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Safety Stocks
From Graph: OP = DDLT + SS where OP = Order Point DD = Forecast Demand LT = Lead Time SS = Safety Stock
So: SS = OP – DDLT by Algebra
OP Set from Customer Service Level (SL)
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Safety Stocks Example 1 The Frigid Corporation manufactures refrigerators. The probability distribution of demand during lead time is:
Demand Probability 10 .20 20 .20 30 .30 40 .20 50 .10
Suppose the customer service level is 70%. Determine the reorder point (consider only 10, 20, 30, 40, 50).
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Safety Stocks Example 1
Let SL = .7 (70%)Demand Probability CDF10 .2 .220 .2 .430 .3 .7 40 .2 .950 .1 1.0
OP = 30 (Meets Demand 70% of Time)
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Safety Stocks Example1
SS = OP – DDLT
DDLT= Expected Value of DemandDDLT= .2(10)+.2(20)+.3(30)+.2(40)+.1(50)DDLT= 28
SS = 30 – 28 = 2
If SL is 80%, What is OP and SS? If SL is 90%, What is OP and SS?
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Safety Stocks:Normal Demand
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Safety Stocks Example 2
The Inandout Production Company requires steel rods at the mean rate of 35 rods per day. This rate follows a normal distribution with a standard deviation of 3 per day. The service level has been set at 90%. If lead time for reordering is one day, what is the optimum safety stock?
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Safety Stocks:Example 2
Given: SL = .9 (90%), DDLT = 35, DDLT = 3
Z from Normal Table (text page 314) = 1.28( Z is also known as safety factor)Z = (OP – DDLT) / DDLT or
OP = DDLT + Z DDLT = 35 + (1.28)(3) 39
SS = OP – DDLT = 39 – 35 = 4
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Types of Inventories
Type Best Size 1. Lot-Sizea. Instantaneous Q*/2b. Non-Instantaneous IMAX*/22. Safety OP - DDLT3. Anticipation Guesstimate4. Transportation (Usage) (Time)5. Hedge Guesstimate
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Implementation ofInventory Control
Q* and N* Cannot Both be Fixed (E.g. Q* = 10, A= 100, N* = A/Q* = 100/10 = 10)
N Varies and Q* Fixed: Order Point System (AKA Fixed Order Quantity). Requires Two-Bin System, Kanban, or Perpetual Inventory. Order say Q* when Actual Inventory ≤ OP.
Q Varies and N* Fixed: Periodic Review System (AKA Fixed Order Cycle System)
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Periodic Review System Let T = D (R + LT) + SS Where
T = Target Inventory LevelD = Demand per Unit of TimeLT = Lead TimeR = Review Period (Fixed at 1/N*)SS = Safety Stock
Order Q = T – I WhereI = Inventory on Hand.
See Example on Page 321 of Text.
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