Inventory Management Learning Objectives Define the term inventory

Inventory Management

Learning Objectives § § § Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss the nature and importance of service inventories Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful. 2

Learning Objectives § § § Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the singleperiod model would be appropriate, and solve typical problems. 3

Inventory: a stock or store of goods Dependent Demand A C(2) B(4) D(2) Independent Demand E(1) D(3) F(2) Independent demand is uncertain. Dependent demand is certain. 4

Inventory Models § Independent demand – finished goods, items that are ready to be sold § E. g. a computer § Dependent demand – components of finished products § E. g. parts that make up the computer 5

Types of Inventories § Raw materials & purchased parts § Partially completed goods called work in progress § Finished-goods inventories § (manufacturing firms) or merchandise (retail stores) 6

Types of Inventories (Cont’d) § Replacement parts, tools, & supplies § Goods-in-transit to warehouses or customers 7

Functions of Inventory § To meet anticipated demand § To smooth production requirements § To decouple operations § To protect against stock-outs 8

Functions of Inventory (Cont’d) § To take advantage of order cycles § To help hedge against price increases § To permit operations § To take advantage of quantity discounts 9

Objective of Inventory Control § To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds § Level of customer service § Costs of ordering and carrying inventory Inventory turnover is the ratio of average annual cost of goods sold to average inventory investment. 10

Effective Inventory Management § A system to keep track of inventory § A reliable forecast of demand § Knowledge of lead times § Reasonable estimates of § Holding costs § Ordering costs § Shortage costs § A classification system 11

Inventory Counting Systems § Periodic System Physical count of items made at periodic intervals § Perpetual Inventory System that keeps track of removals from inventory continuously, thus monitoring current levels of each item 12

Perpetual Inventory System § Two-Bin System - Two containers of inventory; reorder when the first is empty § Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached 0 214800 232087768 13

Key Inventory Terms § Lead time: time interval between ordering and receiving the order § Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year § Ordering costs: costs of ordering and receiving inventory § Shortage costs: costs when demand exceeds supply 14

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A – 10 -20% items, 60 -70% value B – 30 -40% items, 20 -30% value C – 50 -60% items, High A 10 -15% value Annual Value of items B C Low High Percentage of Items 15

Cycle Counting § A physical count of items in inventory § Cycle counting management § How much accuracy is needed? § When should cycle counting be performed? § Who should do it? 16

Cycle Counting Example 5, 000 items in inventory, 500 A items, 1, 750 B items, 2, 750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item Class Quantity A 500 Each month B 1, 750 Each quarter C 2, 750 Every 6 months Cycle Counting Policy Number of Items Counted per Day 500/20 = 25/day 1, 750/60 = 29/day 2, 750/120 = 23/day 77/day 17

Economic Order Quantity Models § Economic order quantity (EOQ) model § The order size that minimizes total annual cost § Economic production model § Quantity discount model 18

Assumptions of EOQ Model § Only one product is involved § Annual demand requirements known § Demand is even throughout the year § Lead time does not vary § Each order is received in a single delivery § There are no quantity discounts 19

The Inventory Cycle Q Quantity on hand Profile of Inventory Level Over Time Usage rate Reorder point Receive order Place Receive order Time Lead time 20

Total Cost Annual Total cost = carrying + ordering cost TC = Q H 2 + DS Q Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost 21

Cost Minimization Goal Annual Cost The Total-Cost Curve is U-Shaped Ordering Costs QO (optimal order quantity) Order Quantity (Q) 22

Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. 23

Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q H 2 = DS Q 24

Reorder Points þ þ EOQ answers the “how much” question The reorder point (ROP) tells when to order Lead time for a Demand ROP = per day new order in days =dx. L D d = Number of working days in a year 25

Inventory level (units) Reorder Point Curve Q* Slope = units/day = d ROP (units) Lead time = L Time (days) 26

Economic Production Quantity (EPQ) § Production done in batches or lots § Capacity to produce a part exceeds the part’s usage or demand rate § Assumptions of EPQ are similar to EOQ except orders are received incrementally during production 27

Economic Production Quantity Assumptions § § § § Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts 28

Inventory level Production Order Quantity Model Part of inventory cycle during which production (and usage) is taking place Demand part of cycle with no production Maximum inventory t Time 29

Economic Run Size Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost p = Production rate or Delivery rate u = Usage rate 30

Quantity discount model Annual Purchasing + TC = carrying + ordering cost Q H TC = 2 + DS Q + PD 31

Quantity discount model Cost TC 1 TC 2 TC 3 Unit price 1 Unit price 2 Unit price 3 Quantity 32

When to Reorder with EOQ Ordering § Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered § Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time. § Service Level - Probability that demand will not exceed supply during lead time. 33

Determinants of the Reorder Point § § The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock) 34

Stock-out Cost can be determined þ Used when demand is not constant or certain þ Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the {units short x the probability x the stockout cost/unit x the number of orders per year} 35

Safety Stock Example ROP = 50 units Orders per year = 6 Stockout cost = $40 per units Carrying cost = $5 per units per year Demand (Units) ROP 30 40 50 60 70 Probability of demand level. 2. 2. 3. 2. 1 1. 0 36

Safety Stock Example ROP = 50 units Orders per year = 6 Safety Stock Additional Holding Cost 20 (20)($5) = $100 10 0 Stockout cost = $40 per frame Carrying cost = $5 per frame per year Total Cost Stockout Cost $0 $100 = $240 $290 $0 (10)(. 2)($40)(6) + (20)(. 1)($40)(6) = $960 (10)($5) = $50 (10)(. 1)($40)(6) A safety stock of 20 frames gives the lowest total cost ROP = 50 + 20 = 70 frames 37

Inventory level Probabilistic Demand Minimum demand during lead time Maximum demand during lead time Mean demand during lead time ROP Normal distribution probability of demand during lead time Expected demand during lead time Safety stock 0 Lead time Place order Receive order Risk Time 38

Probabilistic Demand Risk of a stockout (5% of area of normal curve) Probability of no stockout 95% of the time Mean demand ROP = ? units Quantity Safety stock 0 z Number of standard deviations Z=1. 65 39

Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + Zsdlt where Z = number of standard deviations sdlt = standard deviation of demand during lead time 40

Other Probabilistic Models When data on demand during lead time is not available, there are other models available 1. When demand is variable and lead time is constant 2. When lead time is variable and demand is constant 3. When both demand lead time are variable 41

Other Probabilistic Models Demand is variable and lead time is constant ROP = (average daily demand x lead time in days) + Zsdlt where sd = standard deviation of demand per day sdlt = sd lead time 42

Probabilistic Example Average daily demand (normally distributed) = 15 Standard deviation = 5 Lead time is constant at 2 days 90% service level desired Z for 90% = 1. 28 ROP = (15 units x 2 days) + Zsdlt = 30 + 1. 28(5)( 2) = 30 + 8. 96 = 38. 96 ≈ 39 Safety stock is about 9 units 43

Other Probabilistic Models Lead time is variable and demand is constant ROP = (daily demand x average lead time) + Zsdlt = Z x (daily demand) x σlt where slt = standard deviation of lead time in days 44

Probabilistic Example Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time = slt = 3 98% service level desired Z for 98% = 2. 055 ROP = (10 units x 6 days) + 2. 055(10 units)(3) = 60 + 61. 55 = 121. 65 Reorder point is about 122 units 45

Other Probabilistic Models Both demand lead time are variable ROP = (average daily demand x average lead time) + Zsdlt where sd = standard deviation of demand per day slt = standard deviation of lead time in days sdlt = (average lead time x sd 2) + (average daily demand) 2 slt 2 46

Probabilistic Example Average daily demand (normally distributed) = 150 Standard deviation = sd = 16 Average lead time 5 days (normally distributed) Standard deviation = slt = 1 days 95% service level desired Z for 95% = 1. 65 ROP = (150 packs x 5 days) + 1. 65 sdlt = (150 x 5) + 1. 65 (5 days x 162) + (1502 x 12) = 750 + 1. 65(154) = 1, 004 packs 47

Fixed-Order-Interval Model § Orders are placed at fixed time intervals § Order quantity for next interval? § Suppliers might encourage fixed intervals § May require only periodic checks of inventory levels § Risk of stockout 48

Fixed-Order-Interval Model On-hand inventory Target maximum (T) Q 4 Q 2 Q 1 Q 3 P P P Time 49

Fixed-Interval Benefits § Tight control of inventory items § Items from same supplier may yield savings in: § Ordering § Packing § Shipping costs § May be practical when inventories cannot be closely monitored 50

Fixed-Interval Disadvantages § Requires a larger safety stock § Increases carrying cost § Costs of periodic reviews 51

Single Period Model § Single period model: model for ordering of perishables and other items with limited useful lives § Shortage cost: generally the unrealized profits per unit = revenue per unit – Cost per unit § Excess cost: difference between purchase cost and salvage value of items left over at the end of a period = Original cost per unit – Salvage value per unit 52

Optimal Stocking Level Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit Ce Cs Service Level Quantity So Balance point 53

Example 15 § § Ce = $0. 20 per unit Cs = $0. 60 per unit Service level = Cs/(Cs+Ce) =. 6/(. 6+. 2) Service level =. 75 Ce Cs Service Level = 75% Quantity Stockout risk = 1. 00 – 0. 75 = 0. 25 54

Supermarket § Items used by many products are held in a common area often called a supermarket § Items are withdrawn as needed § Inventory is maintained using JIT systems and procedures § Common items are not planned by the MRP system 55

Operations Strategy § Too much inventory § Tends to hide problems § Easier to live with problems than to eliminate them § Costly to maintain § Wise strategy § Reduce lot sizes § Reduce safety stock 56