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Inventory Management. 12-2 Lecture Outline   Elements of Inventory Management   Inventory Control Systems   Economic Order Quantity Models   Quantity.

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Presentation on theme: "Inventory Management. 12-2 Lecture Outline   Elements of Inventory Management   Inventory Control Systems   Economic Order Quantity Models   Quantity."— Presentation transcript:

1 Inventory Management

2 12-2 Lecture Outline   Elements of Inventory Management   Inventory Control Systems   Economic Order Quantity Models   Quantity Discounts   Reorder Point   Order Quantity for a Periodic Inventory System

3 12-3 What Is Inventory?   Stock of items kept to meet future demand   Purpose of inventory management how many units to order when to order

4 12-4 Types of Inventory   Raw materials   Purchased parts and supplies   Work-in-process (partially completed) products (WIP)   Items being transported   Tools and equipment

5 12-5 Inventory and Supply Chain Management  Bullwhip effect demand information is distorted as it moves away from the end-use customer demand information is distorted as it moves away from the end-use customer higher safety stock inventories to are stored to compensate higher safety stock inventories to are stored to compensate  Seasonal or cyclical demand  Inventory provides independence from vendors  Take advantage of price discounts  Inventory provides independence between stages and avoids work stop-pages

6 12-6 Two Forms of Demand  Dependent  Demand for items used to produce final products   Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers   Cars, appliances, computers, and houses are examples of independent demand inventory

7 12-7 Inventory and Quality Management   Customers usually perceive quality service as availability of goods they want when they want them   Inventory must be sufficient to provide high-quality customer service in TQM

8 12-8 Inventory Costs  Carrying cost  cost of holding an item in inventory  Ordering cost  cost of replenishing inventory  Shortage cost  temporary or permanent loss of sales when demand cannot be met

9 12-9 Inventory Control Systems  Continuous system (fixed- order-quantity)  constant amount ordered when inventory declines to predetermined level  Periodic system (fixed-time- period)  order placed for variable amount after fixed passage of time

10 12-10 ABC Classification  Class A 5 – 15 % of units 5 – 15 % of units 70 – 80 % of value 70 – 80 % of value  Class B 30 % of units 30 % of units 15 % of value 15 % of value  Class C 50 – 60 % of units 50 – 60 % of units 5 – 10 % of value 5 – 10 % of value

11 12-11 ABC Classification: Example 1$ PARTUNIT COSTANNUAL USAGE

12 12-12 ABC Classification: Example (cont.) Example $ PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE , , , , , , $85,400

13 12-13 Economic Order Quantity (EOQ) Models   EOQ optimal order quantity that will minimize total inventory costs   Basic EOQ model   Production quantity model

14 12-14 Assumptions of Basic EOQ Model  Demand is known with certainty and is constant over time  No shortages are allowed  Lead time for the receipt of orders is constant  Order quantity is received all at once

15 12-15 Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0

16 12-16 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = Annual carrying cost = Total cost = +

17 12-17 EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = Deriving Q opt Proving equality of costs at optimal point = Q 2 = Q opt =

18 12-18 EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Slope = 0 Minimum total cost Optimal order Q opt Q opt

19 12-19 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc Q opt = yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 TC min = = Orders per year =D/Q opt = = orders/year Order cycle time = days/(D/Q opt ) = = store days

20 12-20 Production Quantity Model   An inventory system in which an order is received gradually, as inventory is simultaneously being depleted   AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed   p - daily rate at which an order is received over time, a.k.a. production rate   d - daily rate at which inventory is demanded

21 12-21 Production Quantity Model (cont.) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

22 12-22 Production Quantity Model (cont.) p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qp dp Average inventory level = 1 - Q2 dp TC = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

23 12-23 Production Quantity Model: Example C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = = yards 2C o D C c 1 - dp TC = = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = = days per order Qp

24 12-24 Production Quantity Model: Example (cont.) Number of production runs = = = runs/year DQDQ Maximum inventory level =Q 1 - = = yards dpdp

25 12-25 Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

26 12-26 Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE $ – ( d 1 ) ( d 2 )

27 12-27 Quantity Discount: Example QUANTITYPRICE $1, , C o =$2,500 C c =$190 per computer D =200 Q opt = = = PCs 2CoD2CoDCcCc2CoD2CoDCcCc TC = + + PD = C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

28 12-28 Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

29 12-29 Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = yards/day Lead time = L = 10 days R = dL = = yards

30 12-30 Safety Stocks  Safety stock  buffer added to on hand inventory during lead time  Stockout  an inventory shortage  Service level  probability that the inventory available during lead time will meet demand

31 12-31 Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

32 12-32 Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

33 12-33 Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

34 12-34 Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

35 12-35 Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 yards per day L= 10 days  d = 5 yards per day For a 95% service level, z = R= dL + z  d L = = yards Safety stock= z  d L = = yards

36 12-36 Order Quantity for a Periodic Inventory System Q = d(t b + L) + z  d t b + L - I where d= average demand rate t b = the fixed time between orders L= lead time  d = standard deviation of demand z  d t b + L= safety stock z  d t b + L= safety stock I= inventory level

37 12-37 Fixed-Period Model with Variable Demand d= 6 bottles per day  d = 1.2 bottles t b = 60 days L= 5 days I= 8 bottles z= 1.65 (for a 95% service level) Q= d(t b + L) + z  d t b + L - I = = bottles


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