Inventory Management 101 Basic Principles SmartOps Corporation. All rights reserved Copyright 2005 TeknOkret Services. All Rights Reserved.

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1 Inventory Management 101 Basic Principles 1

2 Agenda Basic Concepts Simple Inventory Models Batch Size 2

3 Supply Chain Building Blocks SKU: Stocking keeping unit Stocking Point: Inventory storage Item A Loc 1 Location where inventory is held for strategic reasons Customer: External demand source Supplier: Provider of inventory or raw material Internal Demand: Propagated demand from downstream Process Point: plant or other assembly point Path: logistics connection C S 3

4 Tandem or Series Supply Chain S Simplest model Node vs Stocking Point Single vs Multi-Stage (Echelon) Upstream vs Downstream S Item A Loc 1 Item A Loc 3 Item A Loc 2 C Item A Loc 1 C 4

5 Distribution Supply Chain S Warehouse or Distribution Center Multi-sourcing Item A Loc 3 Item A Loc 2a Item A Loc 2b Item A Item A Item A Item A Loc 1a Loc 1b Loc 1c Loc 1d C 5

6 Process Supply Chain S Bill of Material (BOM): Matching of input to outputs Item X Loc 2 Item Y Loc 2 Item A Loc 2 Item A Loc 1 C 6

7 Insight 1 An Order-Up-To replenishment policy simplifies the replenishment decision process by providing a simple rule to trigger a reorder upon review When inventory position (on-hand (possibly negative), and pipeline inventory) at the beginning of the period is less than the Target Inventory Position (TIP), then Order must be placed, and Order quantity must be enough to bring inventory position back to the target inventory position 7

8 Computing Target Inventory Position The right Target Inventory Position depends on the answer to three questions How much inventory do I need to meet current demand? How much inventory do I need to meet future demand until the next order can be placed? How much inventory do I need to hedge against uncertainty? 8

9 Sequence of Events In any periodic (discrete-time) model, one must assume that events within a period have a precedence order There is no right or wrong assumption, it is just a choice Any inventory decision made using one assumption can be translated to a situation using a different assumption One common sequence of events assumption is Receive shipments due to arrive within the period Make replenishment decision and execute orders to upstream supply (Plan) Observe demand and satisfy downstream demand (React) Period 1 Period 2 Period 3 Period 4 Average demand Time 9

10 Agenda Basic Concepts Simple Inventory Models Service Level Basic Multi-Stage Logic 10

11 Impact of PBR When demand is certain, how much inventory is needed for a single item/location? Suppose that you can get inventory immediately upon ordering, but cannot reorder until the next review period 11

12 Impact of Lead Times When demand is certain, how much inventory is needed for a single item/location? Suppose that you cannot get inventory immediately upon ordering 12

13 Computing Target Inventory Position (Known Demand) Let Demand be m Let Period Between Review be PBR Let Lead Time be LT Average Cycle Stock (CS) = Demand for All Periods Until Next Review = ½ PBR x m Average Pipeline Stock (PS) = Demand for All Other Periods During Lead Time = LT x m Target Inventory Position (TIP) = CS + PS 13

14 Example A Demand: 100 +/- 0 Lead Time: 1 PBR: 2 Initial On-Hand: 100 units Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events First period is a review period 14

15 Example A Table and Diagram Demand: 100 +/- 0 Lead Time: 1 PBR: 2 Initial On-Hand: 100 units Other Assumptions: Period Avg Cycle Stock Beg of Per End of Per Avg Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events First period is a review period Safety Stock OnHand Stock Beg of Per End of Per Avg Pipeline Stock Target Inv Position Orders Planned Receipts 15

16 Steps for Computing TIP and Other Inventory Components 1. Examine PBR and LT values 2. Mark on the table when the periods where review occurs 3. Mark on the table when review doesn t occur since neither TIP nor orders are calculated 4. Calculate TIP 5. Place TIP whenever review occurs 16

17 Steps for Computing TIP and Other Inventory Components (cont d) 6. For each period from the first to the last Compute order needed to order up to TIP Order = TIP Beginning-of-Period On Hand All Inventory in Pipeline (before ordering) Translate order into scheduled receipt in the bucket LT away from the current period Increase On Hand inventory by the Schedule Receipt due in the period Compute End-of-Period On Hand by deducting the demand from the Beginning-of-Period On Hand Compute Average On Hand Compute the Beginning-of-Period, End-of-Period, and Average Cycle Stock by subtracting safety stock from the On Hand 17

18 Example B Demand: 100 +/- 0 Lead Time: 3 PBR: 2 Initial On-Hand: 100 units Planned Receipts: 200 units (in the only period where a shipment ordered in the past can happen, namely in Period 2) Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events R R Now R

19 Example B Table and Diagram Demand: 100 +/- 0 Lead Time: 3 PBR: 2 Initial On-Hand: 100 units Planned Receipts: 200 units Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events Period Avg Cycle Stock Beg of Per End of Per Avg Safety Stock OnHand Stock Beg of Per End of Per Avg Pipeline Stock Target Inv Position Orders Planned Receipts 19

20 Impact of Demand Uncertainty When demand is uncertain, how much inventory is needed for a single item/location? Inventory level is based on: Demand Mean and Variability during Period Service Level Target 20

21 Normal Demand Model Based on Normal Distribution with a mean of μ and standard deviation of σ Z Factor: Number of standard deviations from mean Service level target (Type 1) is the probability that sufficient stock is available to meet demand Mathematically represented as Service Level = P(Inventory >= Demand) Service level converted to z factor using NORMSINV(Service Level) function Translates into following simple formulas for inventory in a single period: Inventory = μ + z x σ Normal(0,1) Service Level z -3σ -2σ -1σ μ 1σ 2σ 3σ -3σ -2σ -1σ μ 1σ 2σ 3σ 21

22 Z Factors Target Service Level z Factor 77% % % % % % % %

23 Computing Safety Stocks With Instantaneous Lead Time Assume planning for one product/one location/one period only Forecast: Normal(100, 25) units Service Level Target: 95% => NORMSINV(0.95) = z = Required Inventory = x 25 = 141 units Filled area represents 95% of total 141 units Cycle Stock Safety Stock 23

24 Example C Other Assumptions: Demand: 100 +/- 25 Service Level of 95% Lead Time: 0 (Instantaneous) PBR: 1 Initial On-Hand = 41 units Order-Up-To Replenishment Policy Review-Receive-Satisfy Sequence of Events 24

25 Example C Table and Diagram Demand: 100 +/- 25 Service Level of 95% Lead Time: 0 (Instantaneous) PBR: 1 Initial On-Hand = 41 units Other Assumptions: Order-Up-To Replenishment Policy Review-Receive-Satisfy Sequence of Events Period Cycle Stock Beg of Per End of Per Avg Safety Stock OnHand Stock Beg of Per End of Per Avg Pipeline Stock Target Inv Position Orders Planned Receipts 25

26 Saw Tooth Diagram On Hand Inventory Cycle Stock Period 1 Period 2 Period 3 Period Order Received Review/Order Placed Safety Stock Time Lead Time Periods Between Reviews 26

27 Insight 2 At time of review, the first step is to assess on-hand inventory and inventory left in the pipeline. The next step is to order the additional inventory needed Order placed at time of review will arrive LT periods later The next order will arrive PBR + LT periods Therefore, the next period most at risk of incurring stock out is the period right before the next order arrive. Order quantity must ensure that there is enough inventory to meet service level in that most-at-risk period and all previous periods. 27

28 Example - PBR=1, LT=1 Order Order placed at this review period arrives at the beginning of the next period Next order arrives only at the beginning of the third period CS SS SS 1 2 Current review period Because LT=1, there is nothing left in pipeline (since shipment just arrived) The next order will arrive at the beginning of period 3 Order placed at current review time must be enough so that OH + Order is able to meet service level for 2 periods worth of demand This is called Exposure-to-Risk Period 28

29 Computing Safety Stocks Let Demand Mean be m Let Demand Standard Deviation be s Let Period Between Review be PBR Let Lead Time be LT Let z be the z Factory corresponding to the Service Level z = NORMSINV(Service Level) Safety Stock = z x s x (LT + PBR) LT + PBR also referred to as the Exposure Period because it represents the amount of time before the next order could be received 29

30 Example D Demand: 100 +/- 25 Lead Time: 1 PBR: 1 Service Level = 95% Initial On-Hand = 158 units Planned Receipts = 100 units Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events 30

31 Example D Table and Diagram Demand: 100 +/- 25 Lead Time: 1 PBR: 1 Service Level = 95% Initial On-Hand = 158 units Planned Receipts = 100 units Other Assumptions: Period Cycle Stock Beg of Per End of Per Avg Safety Stock OnHand Stock Beg of Per End of Per Avg Pipeline Stock Target Inv Position Orders Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events Planned Receipts 31

32 Periodic Review Model with Pipeline Stock Inventory Pipeline Stock Period 1 Period 2 Period 3 Period On Order On Hand Cycle Stock Safety Stock 1 1 Order Received Review/Order Placed Time * Assumes not constrained by production capacity Lead Time Periods Between Reviews 32

33 Impact of Time-Varying Demand So far, all models have assumed that the demand was static over time, (e.g., 100 +/- 25 in every period). In many situations, the demand means and standard deviations will fluctuate over time The same logic used in the previous model applies. However, care must be used to use the demand in the periods e.g., m 1 = 100 units, m 2 = 200 units, m 3 = 100 units, etc rather than a static demand in the calculation e.g., m = 100 units, etc The TIP is based on the sum of the demands for the next PBR + LT periods 33

34 Safety Stocks With Time-Varying Demand The same care applies to using the demand in the different periods applies here as well. The TIP is based on the sum of the demands for the next PBR + LT periods plus the safety stock in the most-atrisk period Safety Stock in Most-At-Risk Period t+pbr+lt-1 z x ( s 2 t + s 2 t s 2 t+pbr+lt-1 ) 34

35 Example E Other Assumptions: Demand: 100 in every period +/- 10, 20, 10, 0, 40 respectively Lead Time: 1 PBR: 1 Initial On-Hand: 100 units Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events Service Level = 95% 35

36 Example E Table and Diagram Demand: 100 +/- 10, 20, 10, 0, 40 respectively Lead Time: 1 PBR: 1 Initial On-Hand: 100 units Period Demand Mean Demand SD Cycle Stock Beg of Per End of Per Safety Stock OnHand Stock Beg of Per End of Per Pipeline Stock Target Inv Position Orders Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events Service Level = 95% Planned Receipts 36

37 Updated Steps for Computing TIP 4. For each period from the first to the last Calculate TIP t = m t + m t m t+lt+pbr-1 + z x ( s 2 t + s 2 t s 2 t+lt+pbr-1 ) where SS t+lt+pbr-1 = z x ( s 2 t + s 2 t s 2 t+lt+pbr-1 ) Note: It is very important to remember that safety stock that goes in to the TIP at review period t is really the safety stock of the period most-atrisk in the exposure period, namely t+lt+pbr-1 37

38 Insight 3 Computing Target Inventory Position depends on a number of factors Period Between Review Lead Times Uncertainty and Desired Service Level Nature of Demand (Static or Time-Varying) Computing Expected Inventory and Orders depends on Target Inventory Position and Its Components Initial On-Hand and Planned Receipts in the Short Term 38

39 Agenda Basic Concepts Simple Inventory Models Batch Size Multi-Stage Logic 39

40 Batch Size Because of high cost of setup, changeover, and transportation, large batch size is common in manufacturing industries. Under batch size constraint, production/order quantity must be a multiple of batch size Q. Example: Q = 10, Order quantity can be 0, 10, 20, 30, No batch size, we will say Q = 0, which is more of a notation, does not mean order quantity will be 0. 40

41 Example D Revisited Demand: 100 +/- 0 Lead Time: 1 PBR: 1 Batch Size: 75 units Other Assumptions: Order-Up-To Replenishment Policy Receive-Review-Satisfy Sequence of Events Initial On-Hand is 100 units Period Cycle Stock Beg of Per End of Per Avg Safety Stock OnHand Stock Beg of Per End of Per Avg Pipeline Stock Target Inv Position Orders Planned Receipts

42 Insight 4 Q causes us produce/order more than needed. Therefore the total inventory will be higher. Also because of that, we can have a smaller safety stock requirement, with the extra order due to batch size serving as buffer. Again, it does not mean we have less total inventory. 42

43 Example D Revisited Demand: 100 +/- 25 Lead Time: 1 Period Between Review is 1 period Service Level = 95% Q =0 (no batch size constraint) Safety stock is 58 Q = 10 Safety stock is 54 43

44 Safety Stock Batch Size and Safety Stock Batch Size and Safety Stock Batch Size 44

45 THANK YOU 45