1. 1 Inventory Control: Part 3 – Independent Demand Inventories

2. 2 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)

3. 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

4. 4 Finished Goods Safety Stocks: Stored with Lot-Size Stocks LT Time Expected demand during lead time (DDLT) Maximum probable demand during lead time OP Quantity Safety stock (SS)

5. 5 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)

6. 6 Safety Stocks Example 1 The Frigid Corporation manufactures refrigerators. The probability distribution of demand during lead time is: DemandProbability 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).

7. 7 Safety Stocks Example 1 Let SL =.7 (70%) DemandProbabilityCDF 10.2.2 20.2.4 30.3.7  40.2.9 50.1 1.0 OP = 30 (Meets Demand 70% of Time)

8. 8 Safety Stocks Example1 SS= OP – DDLT DDLT= Expected Value of Demand DDLT=.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?

9. 9 Safety Stocks: Normal Demand Risk of a Stock Out Probability of No Stock Out (Service Level) Safety Stock MeanOP Quantity

10. 10 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?

11. 11 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

12. 12 Types of Inventories TypeBest Size 1.Lot-Size a. InstantaneousQ*/2 b. Non-InstantaneousIMAX*/2 2.SafetyOP - DDLT 3.AnticipationGuesstimate 4.Transportation(Usage) (Time) 5.HedgeGuesstimate

13. 13 Implementation of Inventory 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)

14. 14 Periodic Review System LetT = D (R + LT) + SS Where T= Target Inventory Level D = Demand per Unit of Time LT= Lead Time R = Review Period (Fixed at 1/N*) SS = Safety Stock Order Q = T – I Where I= Inventory on Hand. See Example on Page 321 of Text.

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