Inventory Management and Control 2

AMAZON.com Jeff Bezos, in 1995, started AMAZON.com as a “virtual” retailer – no inventory, no warehouses, no overhead; just a bunch of computers. Growth forced AMAZON.com to excel in inventory management! AMAZON is now a worldwide leader in warehouse management and automation.

Order Fulfillment at AMAZON (1 of 2) You order items; computer assigns your order to distribution center [closest facility that has the product(s)] Lights indicate products ordered to workers who retrieve product and reset light. Items placed in crate with items from other orders, and crate is placed on conveyor. Bar code on item is scanned 15 times – virtually eliminating error.

Order Fulfillment at AMAZON (2 of 2) Crates arrive at a central point where items are boxed and labeled with new bar code. Gift wrapping done by hand (30 packages per hour) Box is packed, taped, weighed and labeled before leaving warehouse in a truck. Order appears on your doorstep within a week

Inventory Defined Inventory is the stock of any item or resource held to meet future demand and can include: raw materials, finished products, component parts, supplies, and work-in-process 3

Inventory Classifications Process stage Demand Type Number & Value Other Raw Material WIP Finished Goods Independent Dependent A Items B Items C Items Maintenance Operating

Independent vs. Dependent Demand Independent Demand (Demand for the final end-product or demand not related to other items; demand created by external customers) Finished product Independent demand is uncertain Dependent demand is certain A Dependent Demand (Derived demand for component parts, subassemblies, raw materials, etc- used to produce final products) B(4) C(2) D(1) E(1) E(2) B(1) E(3) Component parts

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

Types of Inventories (1 of 2) Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories (manufacturing firms) or merchandise (retail stores)

Types of Inventories (2 of 2) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

The Material Flow Cycle (1 of 2)

The Material Flow Cycle (2 of 2) Wait Time Move Time Queue Time Setup Time Run Time Input Output Cycle Time Run time: Job is at machine and being worked on Setup time: Job is at the work station, and the work station is being "setup." Queue time: Job is where it should be, but is not being processed because other work precedes it. Move time: The time a job spends in transit Wait time: When one process is finished, but the job is waiting to be moved to the next work area. Other: "Just-in-case" inventory.

Performance Measures Inventory turnover (the ratio of annual cost of goods sold to average inventory investment) Days of inventory on hand (expected number of days of sales that can be supplied from existing inventory)

Functions of Inventory (1 of 2) To “decouple” or separate various parts of the production process, ie. to maintain independence of operations To meet unexpected demand & to provide high levels of customer service To smooth production requirements by meeting seasonal or cyclical variations in demand To protect against stock-outs

Functions of Inventory (2 of 2) 5. To provide a safeguard for variation in raw material delivery time 6. To provide a stock of goods that will provide a “selection” for customers 7. To take advantage of economic purchase-order size 8. To take advantage of quantity discounts 9. To hedge against price increases

Disadvantages of Inventory Higher costs Item cost (if purchased) Ordering (or setup) cost Holding (or carrying) cost Difficult to control Hides production problems May decrease flexibility

Inventory Costs Holding (or carrying) costs Costs for storage, handling, insurance, etc Setup (or production change) costs Costs to prepare a machine or process for manufacturing an order, eg. arranging specific equipment setups, etc Ordering costs (costs of replenishing inventory) Costs of placing an order and receiving goods Shortage costs Costs incurred when demand exceeds supply 5

Holding (Carrying) Costs Obsolescence Insurance Extra staffing Interest Pilferage Damage Warehousing Etc.

Inventory Holding Costs (Approximate Ranges) Cost as a % of Inventory Value 6% (3 - 10%) 3% (1 - 3.5%) (3 - 5%) 11% (6 - 24%) (2 - 5%) 26% Category Housing costs (building rent, depreciation, operating cost, taxes, insurance) Material handling costs (equipment, lease or depreciation, power, operating cost) Labor cost from extra handling Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, scrap, and obsolescence Overall carrying cost

Ordering Costs Supplies Forms Order processing Clerical support etc.

Setup Costs Clean-up costs Re-tooling costs Adjustment costs etc.

Shortage Costs Backordering cost Cost of lost sales

Inventory Control System Defined An inventory system is the set of policies and controls that monitor levels of inventory and determine what levels should be maintained, when stock should be replenished and how large orders should be Answers questions as: When to order? How much to order?

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

Requirements of an 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

Inventory Counting (Control) Systems Periodic System Physical count of items made at periodic intervals; order is placed for a variable amount after fixed passage of time Perpetual (Continuous) Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item (constant amount is ordered when inventory declines to a predetermined level)

Inventory Models Single-Period Inventory Model One time purchasing decision (Example: vendor selling t-shirts at a football game) Seeks to balance the costs of inventory overstock and under stock Multi-Period Inventory Models Fixed-Order Quantity Models Event triggered (Example: running out of stock) Fixed-Time Period Models Time triggered (Example: Monthly sales call by sales representative) 7

Single-Period Inventory Model

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 Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

Single Period Model Continuous stocking levels Identifies optimal stocking levels Optimal stocking level balances unit shortage and excess cost Discrete stocking levels Service levels are discrete rather than continuous Desired service level is equaled or exceeded

Single-Period Model This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu 8

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

Single Period Example 1 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2) Service level = .75 Service Level = 75% Quantity Ce Cs Stockout risk = 1.00 – 0.75 = 0.25

Single Period Model Example 2 Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game? Cu = $10 and Co = $5; P ≤ $10 / ($10 + $5) = .667 Z.667 = .432 therefore we need 2,400 + .432(350) = 2,551 shirts

Multi-Period Inventory Models Fixed-Order Quantity Models (Types of) Economic Order Quantity Model Economic Production Order Quantity (Economic Lot Size) Model Economic Order Quantity Model with Quantity Discounts Fixed Time Period (Fixed Order Interval) Models

Fixed Order Quantity Models: Economic Order Quantity Model

Economic Order Quantity Model Assumptions (1 of 2): Demand for the product is known with certainty, is constant and uniform throughout the period Lead time (time from ordering to receipt) is known and constant Price per unit of product is constant (no quantity discounts) Inventory holding cost is based on average inventory

Economic Order Quantity Model Assumptions (2 of 2): Ordering or setup costs are constant All demands for the product will be satisfied (no back orders are allowed) No stockouts (shortages) are allowed The order quantity is received all at once. (Instantaneous receipt of material in a single lot) The goal is to calculate the order quantitiy that minimizes total cost 9

Basic Fixed-Order Quantity Model and Reorder Point Behavior 4. The cycle then repeats. 1. You receive an order quantity Q. R = Reorder point Q = Economic order quantity L = Lead time L Q R Time Number of units on hand (Inv. Level) 2. You start using them up over time. 3. When you reach down to a level of inventory of R, you place your next Q sized order.

Average Inventory (Q/2) EOQ Model Reorder Point (ROP) Time Inventory Level Average Inventory (Q/2) Lead Time Order Quantity (Q) Demand rate Order placed Order received

EOQ Cost Model: How Much to Order? By adding the holding and ordering costs together, we determine the total cost curve, which in turn is used to find the optimal order quantity that minimizes total costs Slope = 0 Total Cost Order Quantity, Q Annual cost ($) Minimum total cost Optimal order Qopt Carrying Cost = HQ 2 Ordering Cost = SD Q

Why Holding Costs Increase? More units must be stored if more are ordered Purchase Order Description Qty. Microwave 1000 Order quantity Purchase Order Description Qty. Microwave 1 Order quantity

Why Ordering Costs Decrease ? Cost is spread over more units Example: You need 1000 microwave ovens Purchase Order Description Qty. Microwave 1 1 Order (Postage $ 0.33) 1000 Orders (Postage $330) Order quantity 1000

Basic Fixed-Order Quantity (EOQ) Model Formula TC=Total annual cost D =Annual demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + + 12

EOQ Cost Model Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt TC = + S D Q H Q 2 = + Q2 H TC Q 0 = + Qopt = 2SD Deriving Qopt Annual ordering cost = S D Q Annual carrying cost = HQ 2 Total cost = + H Q Proving equality of costs at optimal point = S D Q H Q 2 Q2 = 2S D H Qopt = 2 S D

Deriving the EOQ How much to order?: When to order? We also need a reorder point to tell us when to place an order 13

EOQ Model Equations = × Q* D S H N T d ROP L 2 Optimal Order Quantity Expected Number of Orders Expected Time Between Orders Working Days / Year = × Q* D S H N T d ROP L 2

EOQ Example 1 (1 of 3) Given the information below, what are the EOQ and reorder point? Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15 14

EOQ Example 1(2 of 3) In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units. 15

EOQ Example I(3 of 3) Order cycle time= 365/(D/Qopt) = 365/11 Orders per year = D/Qopt = 1000/90 = 11 orders/year Order cycle time= 365/(D/Qopt) = 365/11 = 33.1days TCmin = SD Q HQ 2 (10)(1,000) 90 (2,5)(90) TCmin = $ 111 + $111 = 22 $ + +

EOQ Example 2(1 of 2) Annual Demand = 10,000 units Determine the economic order quantity and the reorder point given the following… Annual Demand = 10,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = 10% of cost per unit Lead time = 10 days Cost per unit = $15 16

EOQ Example 2(2 of 2) Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units. 17

EOQ Example 3 H = $0.75 per yard S = $150 D = 10,000 yards Qopt = 2(150)(10,000) (0.75) Qopt = 2,000 yards TCmin = + S D Q H Q 2 TCmin = + (150)(10,000) 2,000 (0.75)(2,000) TCmin = $750 + $750 = $1,500 Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Order cycle time =311 days/(D/Qopt) = 311/5 = 62.2 store days

When to Reorder with EOQ Ordering ? Reorder Point – is the level of inventory at which a new order is placed ROP = d . L 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 (probability that inventory available during lead time will meet demand) 1 - Probability of stockout

Reorder Point Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 yards

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

Probabilistic Models Answer how much & when to order Allow demand to vary Follows normal distribution Other EOQ assumptions apply Consider service level & safety stock Service level = 1 - Probability of stockout Higher service level means more safety stock More safety stock means higher ROP

Safety Stock Quantity Maximum probable demand Expected demand LT Time Expected demand during lead time Maximum probable demand ROP Quantity Safety stock Safety stock reduces risk of stockout during lead time

Variable Demand with a Reorder Point point, R Q LT Time Inventory level

Reorder Point with a Safety Stock point, R Q LT Time Inventory level Safety Stock

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

Reorder Point for Service Level Probability of meeting demand during lead time = service level a stockout R Safety stock dL Expected Demand zd L The reorder point based on a normal distribution of LT demand

Reorder Point for Variable Demand (Example) 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 = 1.65 R = dL + z d L = 30(10) + (1.65)(5)( 10) = 326.1 yards Safety stock = z d L = (1.65)(5)( 10) = 26.1 yards

Fixed Order Quantity Models: -Noninstantaneous Receipt- Production Order Quantity (Economic Lot Size) Model

Production Order Quantity Model Production done in batches or lots Capacity to produce a part exceeds that part’s usage or demand rate Allows partial receipt of material Other EOQ assumptions apply Suited for production environment Material produced, used immediately Provides production lot size Lower holding cost than EOQ model Answers how much to order and when to order

EOQ POQ Model When To Order Time Inventory Level Both production and usage take place Usage only takes place Maximum inventory level

EOQ POQ Model When To Order Inventory Level Average Inventory Optimal Order Quantity (Q*) Reorder Point (ROP) Time Lead Time

POQ Model Inventory Levels (1 of 2) Time Supply Begins Supply Ends Production portion of cycle Demand portion of cycle with no supply Maximum inventory level

POQ Model Inventory Levels (2 of 2) Time Inventory Level Production Portion of Cycle Max. Inventory Q·(1- u/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply Average inventory Q/2(1- u/p)

Maximum inventory level POQ Model Equations 2*D*S Production Order Quantity = Q * = ( ) p u H* 1 - p ( ) - u p Maximum inventory level * = 1 Q D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day D = * S Setup Cost Q ( ) u = Holding Cost 1/2 * H * Q 1 - p

Production Order Quantity Example (1 of 2) H = $0.75 per yard S = $150 D = 10,000 yards u = 10,000/311 = 32.2 yards per day p = 150 yards per day POQopt = = = 2,256.8 yards 2 S D H 1 - u p 2(150)(10,000) 0.75 1 - 32.2 150 TC = + 1 - = $1,329 u p S D Q H Q 2 Production run = = = 15.05 days per order Q p 2,256.8 150

Production Quantity Example (2 of 2) H = $0.75 per yard S = $150 D = 10,000 yards u= 10,000/311 = 32.2 yards per day p = 150 yards per day Number of production runs = = = 4.43 runs/year D Q 10,000 2,256.8 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 yards u p 32.2 150 Qopt = = = 2,256.8 yards 2CoD Cc 1 - d p 2(150)(10,000) 0.75 1 - 32.2 150 TC = + 1 - = $1,329 CoD Q CcQ 2 Production run = = = 15.05 days per order 2,256.8

Fixed-Order Quantity Models: Economic Order Quantity Model with Quantity Discounts

Quantity Discount Model Answers how much to order & when to order Allows quantity discounts Price per unit decreases as order quantity increases Other EOQ assumptions apply Trade-off is between lower price & increased holding cost Total cost with purchasing cost TC = + + PD S D Q iC Q 2 Where P: Unit Price

Price-Break Model Formula Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula: i = percentage of unit cost attributed to carrying inventory C = cost per unit Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value

Total Costs with PD Cost Adding Purchasing cost doesn’t change EOQ TC with PD TC without PD PD Quantity Adding Purchasing cost doesn’t change EOQ

Total Cost with Constant Carrying Costs OC EOQ Quantity Total Cost TCa TCc TCb Decreasing Price CC a,b,c

Quantity Discount – How Much to Order?

Price-Break Example 1 (1 of 3) ORDER SIZE PRICE 0 - 99 $10 100 - 199 8 (d1) 200+ 6 (d2) For this problem holding cost is given as a constant value, not as a percentage of price, so the optimal order quantity is the same for each of the price ranges. (see the figure)

Price Break Example 1 (2 of 3) Qopt Carrying cost Ordering cost Inventory cost ($) Q(d1 ) = 100 Q(d2 ) = 200 TC (d2 = $6 ) TC (d1 = $8 ) TC = ($10 )

Price Break Example 1 (3 of 3) Qopt Carrying cost Ordering cost Inventory cost ($) Q(d1 ) = 100 Q(d2 ) = 200 TC (d2 = $6 ) TC (d1 = $8 ) TC = ($10 ) The lowest total cost is at the second price break

Price Break Example 2 QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 1 - 49 $1,400 50 - 89 1,100 90+ 900 S = $2,500 H = $190 per computer D = 200 Qopt = = = 72.5 PCs 2SD H 2(2500)(200) 190 TC = + + PD = $233,784 SD Qopt H Qopt 2 For Q = 72.5 TC = + + PD = $194,105 SD Q H Q 2 For Q = 90

Price-Break Example 3 (1 of 4) A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of $4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? Order Quantity(units) Price/unit($) 0 to 2,499 $1.20 2,500 to 3,999 1.00 4,000 or more .98

Price-Break Example (2 of 4) First, plug data into formula for each price-break value of “C” Annual Demand (D)= 10,000 units Cost to place an order (S)= $4 Carrying cost % of total cost (i)= 2% Cost per unit (C) = $1.20, $1.00, $0.98 Next, determine if the computed Qopt values are feasible or not Interval from 4000 & more, the Qopt value is not feasible Interval from 2500-3999, the Qopt value is not feasible Interval from 0 to 2499, the Qopt value is feasible

Price-Break Example 2 (3 of 4) Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why? Because the total annual cost function is a “u” shaped function Total annual costs So the candidates for the price-breaks are 1826, 2500, and 4000 units 0 1826 2500 4000 Order Quantity

Price-Break Example 2 (4 of 4) Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-break TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12,043.82 TC(2500-3999)= $10,041 TC(4000&more)= $9,949.20 Finally, we select the least costly Qopt, which in this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units

Multi-period Inventory Models: Fixed Time Period (Fixed-Order- Interval) Models

Fixed-Order-Interval Model Orders are placed at fixed time intervals Order quantity for next interval? (inventory is brought up to target amount, amount ordered varies) Suppliers might encourage fixed intervals Requires only periodic checks of inventory levels (no continous monitoring is required) Risk of stockout between intervals

Inventory Level in a Fixed Period System Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum p Q1 Q2 Q3 Q4 Target maximum Time d Inventory

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

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

Fixed-Time Period Model with Safety Stock Formula q = Average demand + Safety stock – Inventory currently on hand

Fixed-Time Period Model: Determining the Value of sT+L The standard deviation of a sequence of random events equals the square root of the sum of the variances 20

Order Quantity for a Periodic Inventory System Q = d(tb + L) + zd T + L - I where d = average demand rate T = the fixed time between orders L = lead time  d = standard deviation of demand zd tb + L = safety stock I = inventory level z = the number of standard deviations for a specified service level

Fixed-Period Model with Variable Demand (Example 1) d = 6 bottles per day sd = 1.2 bottles tb = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) Q = d(tb + L) + zd tb + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles

Fixed-Time Period Model with Variable Demand (Example 2)(1 of 3) Given the information below, how many units should be ordered? Average daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The standard deviation of daily demand is 4 units. 21

Fixed-Time Period Model with Variable Demand (Example 2)(2 of 3) So, by looking at the value from the Table, we have a probability of 0.9599, which is given by a z = 1.75 22

Fixed-Time Period Model with Variable Demand (Example 2) (3 of 3) So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period 23

Miscellaneous Systems: Optional Replenishment System Maximum Inventory Level, M Actual Inventory Level, I q = M - I I M Q = minimum acceptable order quantity If q > Q, order q, otherwise do not order any. 24

ABC Classification System Demand volume and value of items vary Items kept in inventory are not of equal importance in terms of: dollars invested profit potential sales or usage volume stock-out penalties 26

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important Annual $ value of items A B C High Low Percentage of Items

ABC Analysis Classify inventory into 3 categories typically on the basis of the dollar value to the firm $ volume = Annual demand x Unit cost A class, B class, C class Policies based on ABC analysis Develop class A suppliers more carefully Give tighter physical control of A items Forecast A items more carefully

Classifying Items as ABC 20 40 60 80 100 50 % Annual $ Usage A B C Class % $ Vol % Items 70-80 5-15 15 30 5-10 50-60 % of Inventory Items

ABC Classification PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE

ABC Classification PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400

ABC Classification A B C PART UNIT COST ANNUAL USAGE 1 $ 60 90 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 A B C

ABC Classification A B C PART UNIT COST ANNUAL USAGE 1 $ 60 90 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 A B C % OF TOTAL % OF TOTAL CLASS ITEMS VALUE QUANTITY A 9, 8, 2 71.0 15.0 B 1, 4, 3 16.5 25.0 C 6, 5, 10, 7 12.5 60.0

ABC Classification C B A % of Value | | | | | | 0 20 40 60 80 100 100 – 80 – 60 – 40 – 20 – 0 – | | | | | | 0 20 40 60 80 100 % of Quantity % of Value A B C

Inventory Accuracy and Cycle Counting Inventory accuracy refers to how well the inventory records agree with physical count. Physically counting a sample of total inventory on a regular basis Used often with ABC classification A items counted most often (e.g., daily)

Advantages of Cycle Counting Eliminates shutdown and interruption of production necessary for annual physical inventories Eliminates annual inventory adjustments Provides trained personnel to audit the accuracy of inventory Allows the cause of errors to be identified and remedial action to be taken Maintains accurate inventory records

Last Words Inventories have certain functions. But too much inventory Tends to hide problems Costly to maintain So it is desired Reduce lot sizes Reduce safety stocks