Inventory Management. Copyright 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Independent demand items

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1 Chapter 12 Inventory Management McGraw-Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Inventory Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used (Dependent demand -> MRP) 12-2 Inventory Management 1

2 Types of Inventory Raw materials and purchased parts Work-in-process or Semi-Finished Goods Finished goods inventories or merchandise Maintenance and repairs (MRO) inventory, tools and supplies Goods-in-transit to warehouses or customers (pipeline inventory) 12-3 Inventory Functions Inventories serve a number of functions such as: 1. To meet anticipated customer demand 2. To smooth production requirements 3. To decouple operations 4. To protect against stockouts 5. To take advantage of order cycles 6. To hedge against price increases 7. To permit operations 8. To take advantage of quantity discounts 12-4 Inventory Management 2

3 Inventory Management Management has two basic functions concerning inventory: 1. Establish a system for tracking items in inventory 2. Make decisions about When to order( ROP,FOI) How much to order (Q,S) 12-5 Effective Inventory Management Requires: 1. A system keep track of inventory 2. A reliable forecast of demand 3. Knowledge of lead time and lead time variability 4. Reasonable estimates of holding costs ordering costs shortage costs 5. A classification system for inventory items 12-6 Inventory Management 3

4 Inventory Counting Systems Periodic System Physical count of items in inventory made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item Two-bin system Two containers of inventory; reorder when the first is empty 12-7 A B Inventory Management 4

5 Inventory Counting Technologies Universal product code (UPC) Bar code printed on a label that has information about the item to which it is attached Radio frequency identification (RFID) tags A technology that uses radio waves to identify objects, such as goods in supply chains 12-9 Demand Forecasts and Lead Time Forecasts Inventories are necessary to satisfy customer demands, so it is important to have a reliable estimates of the amount and timing of demand Lead time Time interval between ordering and receiving the order Point-of-sale (POS) systems A system that electronically records actual sales Such demand information is very useful for enhancing forecasting and inventory management Inventory Management 5

6 ABC Classification System A-B-C approach Classifying inventory according to some measure of importance, and allocating control efforts accordingly A items (very important) 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value B items (moderately important) High C items (least important) 50 to 60 percent of the number of items in inventory but only A Annual $ value about 10 to 15 percent of the of items annual dollar value B Low Few C Number of Items Many Example 1 page 563 Item Annual Demand Unit Cost Annual Dollar Value Classification Inventory Management 6

7 Item Annual Demand Unit Cost Annual Dollar Value Classification Series1 Inventory Management 7

8 Annual Annual Item Demand Unit Cost Dollar Value Classification A A B B B C C C C C C C Cycle Counting Cycle counting A physical count of items in inventory (reduce discrepancies..) Cycle counting management How much accuracy is needed? (APICS recommended) A items: ± 0.2 percent B items: ± 1 percent C items: ± 5 percent When should cycle counting be performed? Who should do it? Inventory Management 8

9 How Much to Order: EOQ Models The basic economic order quantity model The economic production quantity model The quantity discount model Basic EOQ Model The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs q y y Assumptions Only one product is involved Annual demand requirements are 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 Inventory Management 9

10 The Inventory Cycle Q=350 Usage Quantity rate = 50 on hand units/day s Profile of Inventory Level Over Time Reorder point = 100 units Receive order Place order Receive order Place order Receive order Time Lead time = 2 days Total Annual Cost Total Cost where = = Annual Holding Cost Q H 2 Q = Order quantity in units + Annual Ordering Cost + H = Holding (carrying) cost per unit D = Demand, usually in unit per year S = Ordering cost D S Q Inventory Management 10

11 Goal: Total Cost Minimization Annu ual Cost The Total-Cost Curve is U-Shaped Q D TC = H + S 2 Q Holding Costs Ordering Costs Q * (optimal order quantity) Order Quantity (Q) Deriving EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q * = 2DS H = 2(annual demand)(order d)( d cost) annual per unit holding cost Inventory Management 11

12 Example 2 page 568 A local distributor for a national tire company expects to sell approximately 9,600 steel belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75.The distributor operates 288 days a year. a. What is the EOQ? b. How many times per year does the store reorder? c. What is the length of an order cycle? d. What is the total annual cost if the EOQ quantity is ordered? D = 9,600 tires per year H = $16 per unit per year S = $75 a. 2DS 2(9,600)75 Q0 = = = 300 tires H 16 b. Number of orders per year: D/Q = 9,600 tires/300 tires = 32 c. Length of order cycle: Q/D = 300 tires/ 9,600 tires/yr =1/32 year = 288*1/32 = 9 workdays d. TC = Carrying cost + Ordering cost = (Q/2)H + (D/Q)S = (300/2)16 + (9,600/300)75 = $2,400 + $ 2,400 = $4,800 Inventory Management 12

13 Example 3page 568 Economic Production Quantity (EPQ) Assumptions Only one product is involved Annual demand requirements are known Usage rate is constant Usage occurs continually, but production occurs periodically The production rate is constant Lead time does not vary There are no quantity discounts Inventory Management 13

14 EPQ: Inventory Profile Q Q * Production Usage Production Usage Production and usage only and usage only and usage Cumulative production I max Amount on hand Time EPQ Total Cost TC = Carrying Cost + Setup Cost I = 2 where I max max D H + S Q = Maximum inventory Q = p ( p u) p = Production or delivery rate u = Usage rate Inventory Management 14

15 EPQ * Q p DS = 2 H p p u Example 4 page 571 A toy manufacturer uses 48,000 rubber wheels per year fir its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year.carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. the firm operates 240 days per year. Determine the a. Optimal run size. b. Minimum total annual cost for carrying and setup. c. Cycle time for the optimal run size. d. Run time. D = 48,000 wheels per year S = $45 H = $1 per wheel per year p = 800 wheels per day u = 48,000 wheels per 240 days, or 200 wheels per day Inventory Management 15

16 2DS p 2(48,000) a. Q0 = = = 2400 wheels H p u I b. TCmin = Carrying cost + Setup cost = 2 First compute I max : I Q p 0 max = u 2, ( p ) = ( ) max D H + S Q 0 = 1,800 wheels 1,800 48,000 TC = $1 + $45 = $900 + $900 = $1, ,400 c. d. Q0 2,400 wheels Cycle time = = = 12 days u 200 wheels per day Q0 2,400 wheels Run time = = = 3 days p 800 wheels per day Quantity Discount Model Quantity discount Price reduction offered to customers for placing large orders Total Cost = Carrying Cost + Ordering Cost + Purchasing Cost where Q = H + 2 P = Unit price D Q S + PD Inventory Management 16

17 Quantity Discounts Quantity Discounts Inventory Management 17

18 Example 5 page 575 The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost. D = 816 cases per year S = $12 H = $4 per case per year Range Price 1 to 49. $20 50 to to or more. 16 Range Price 1 to 49. $20 50 to to or more. 16 $20/Case $18/Case $17/Case $16/Case Inventory Management 18

19 2DS 2(816)12 1. EOQ = = = cases H cases can be bought at $18 per case TC 70 = Carrying cost + Order cost + Purchase cost = (Q/2)H + (D/Q0)S + PD = (70/2)4 + (816/70) (816) = $14,968 TC 50 = (50/2)4 + (816/50) (816) = $16,616 TC 80 = (80/2)4 + (816/80) (816) = $14,154 TC 100 = (100/2)4 + (816/100) (816) = $13, ***** When to Reorder Reorder point When the quantity on hand of an item drops to this amount, the item is reordered. Determinants of the reorder point 1. The rate of demand 2. The lead time 3. The extent of demand and/or lead time variability 4. The degree of stockout risk acceptable to management Inventory Management 19

20 Reorder Point: Under Certainty ROP = d LT where d = Demand rate (units per period, per day, per week) LT = Lead time (in same time units as d) Reorder Point: Under Uncertainty Demand or lead time uncertainty creates the possibility that demand will be greater than available supply ppy To reduce the likelihood of a stockout, it becomes necessary to carry safety stock Safety stock Stock that is held in excess of expected demand due to variable demand and/or lead time Expected demand ROP = + Safety Stock during lead time Inventory Management 20

21 Safety Stock Quant ity Maximum probable demand during lead time Expected demand during lead time ROP LT Safety stock Time Q ROP 0 lead time Shortage or back order Inventory Management 21

22 0 μ σ safety stock? Safety Stock? As the amount of safety stock carried increases, the risk of stockout decreases. This improves customer service level Service level The probability that demand will not exceed supply during lead time Service level = 100% - Stockout risk Inventory Management 22

23 How Much Safety Stock? The amount of safety stock that is appropriate for a given situation depends upon: 1. The average demand rate and average lead time 2. Demand and lead time variability 3. The desired service level Expected demand ROP + zσ during lead time where = dlt z = Number of standard deviations σ dlt = The standard deviation of lead time demand Reorder Point The ROP based on a normal Distribution of lead time demand Service level Risk of stockout Expected demand Safety stock ROP 0 z Quantity ty z-scale Inventory Management 23

24 Reorder Point: Demand Uncertainty ROP = d + zσ where d LT z = Number of standard deviations d σ = d = Average demand per period (per day, per week) The stddev. of demand per period (same time units as d ) LT = Lead time (same time units as d ) Note : σ = σ dlt d LT Example 8 page 580 Suppose that the manager of a construction supply house determined from historical records that demand for sand during lead time average 50 metric tons. In addition, suppose the manager determined d that t demand during lead time could be described by a normal distribution that has a mean of 50 metric tons and a standard deviation of 5 metric tons. Answer these questions, assuming that the manager is willing to accept a stockout risk of no more than 3 percent: a. What value of z is appropriate? b. How much safety stock should be held? c. What reorder point should be used? Expected lead time demand = 50 metric tons σ dlt = 5 metric tons Risk = 3 percent Inventory Management 24

25 a. From table, using a service level of = obtain z = 1.88 b. Safety stock = σ dlt =1.88(5) = 9.4 metric tons c. ROP = Expected lead time demand + Safety stock = = 59.4 metric tons (order when ROP >= stock position = On hand + On order) *** Please read more for this example (page 580) please ***** Reorder Point: Lead Time Uncertainty average lead time Inventory Management 25

26 Reorder Point: Lead Time Uncertainty ROP = d LT + zdσ where LT z = Number of standard deviations d = σ LT Demand per period (per day, per week) = The stddev. of lead time (same time units as d) LT = Average lead time (same time units as d ) Example 9 page 580 A restaurant uses an average of 50 jars of a special sauce each week. Weekly usage of sauce has a standard deviation of 3 jars. the manager is willing to accept no more than a 10 percent risk of stockout lead time, which is two weeks. Assume the distribution of usage is normal. a. Determine the value of z. b. determine the ROP. d = 50 jars per week LT = 2 weeks σ d = 3 jars per week acceptable risk = 10 percent, service level =.90 a. from table service level of 0.90 z = 1.28 b. ROP = d LT + zσ d LT = (3) 2 = = Inventory Management 26

27 Shortages and Service Levels The expected number of units short in each order cycle is: E(n) = E(z)σ dlt where E(n) = Expected number of units short per order cycle E(z) = Standardized number of units short obtained from following table σ dlt = Standard deviation of lead time demand **Excel formula for E(Z)...A2 = cell contain value of z =(1/SQRT(2*PI()))*EXP(-0.5*A2*A2)-A2*(1-NORMSDIST(A2)) Z L(Z) Z L(Z) Z L(Z) Z L(Z) Z L(Z) Inventory Management 27

28 Z L(Z) Z L(Z) Z L(Z) Z L(Z) Z L(Z) !!! See Example 10 page 582 and Example 11 page 582 and Example 12 page 584 Inventory Management 28

29 How Much to Order: FOI Fixed-order-interval (FOI) model Orders are placed at fixed time intervals Reasons for using the FOI model Supplier s policy may encourage its use Grouping orders from the same supplier can produce savings in shipping costs Some circumstances do not lend themselves to continuously monitoring inventory position Fixed-Quantity vs. Fixed-Interval Ordering Inventory Management 29

30 FOI Model Target Inventory Inventory Position to Amount Order = Level at Time of Order where Q = T IP Q = Amount to order T = Target inventory level IP = Inventory position at time of order FOI Model T ( OI + LT) + zσ OI + LT = d d where OI = Order interval (length of time between orders) OI * Q = D * Time - frame of interest OI * represents the optimal time between orders. Time-frame of interest is an appropriate period (e.g., days or weeks). This is usually based on the timeframe expressed by the average demand rate, d-bar Inventory Management 30

31 Example 13 page 586 Given the following information, determine the amount to order.. d = 30 units per day Desired service level = 99 percent σ = 3 units per day d LT = 2 days OI = 7 days z = 2.33 for 99 percent service level Amount on hand at reorder time = 71 units Amount to order = d(oi + LT) + zσ d OI + LT - A = 30(7 + 2) (3) = 220 units Single-Period Model Single-period model Model for ordering gperishables and other items with limited useful lives Shortage cost Generally, the unrealized profit per unit C shortage = C s = Revenue per unit Cost per unit Excess cost Different between purchase cost and salvage value of items left over at the end of the period C excess = C e = Cost per unit Salvage value per unit Inventory Management 31

32 Single-Period Model The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs Two categories of problem: Demand can be characterized by a continuous distribution Demand can be characterized by a discrete distribution Stocking Levels Service level where C C s e C C + C = s = shortage cost per unit = excess cost per unit s e C s C e Service level S o Balance Point Quantity S o =Optimum Stocking Quantity Inventory Management 32