12 – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Inventory Management 12 For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education Homework: 1, 3(assume 250 working days/year), 5, 7, 10, 13, Milligan Workshop

12 – 2 Inventory Management  Concepts  Weeks of supply  Turns  ABC Analysis  Q System  Q Systems Total Costs  P System  Q System vs. P System

12 – 3 Inventory Management  Inventory is a stock of anything held to meet some future demand. It is created when the rate of receipts exceeds the rate of disbursements.  A stock or store of goods.  Inventory Turns (Turnover) COGS/Avg. Inventory Investment

12 – 4 Inventory Management  Weeks of supply = Average aggregate Inventory Value / Weekly Sales (at cost)  IT = COGS / Average aggregate inventory value  The Eagle Machine Company averaged $2M in inventory last year, and the COGS was $10M. If the company has 52 business weeks per year, how many weeks of supply are held in inventory? What is the inventory turnover rate?

12 – 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Percentage of SKUs Percentage of dollar value 100 — 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 — Class C Class A Class B ABC Analysis Figure 12.1 – Typical Chart Using ABC Analysis

12 – 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 Booker’s Book Bindery divides SKUs into three classes, according to their dollar usage. Calculate the usage values of the following SKUs and determine which is most likely to be classified as class A. SKU NumberDescription Quantity Used per Year Unit Value ($) 1Boxes Cardboard (square feet) 18, Cover stock10, Glue (gallons) Inside covers20, Reinforcing tape (meters) 3, Signatures150,

12 – 7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 SKU Number Description Quantity Used per Year Unit Value ($) Annual Dollar Usage ($) 1Boxes500  3.00=1,500 2Cardboard (square feet) 18,000  0.02=360 3Cover stock10,000  0.75=7,500 4Glue (gallons)75  40.00=3,000 5Inside covers20,000  0.05=1,000 6Reinforcing tape (meters) 3,000  0.15=450 7Signatures150,000  0.45=67,500 Total81,310

12 – 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1

12 – 9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1

12 – 10 Outline, Two Major Models Fixed Quantity Model, Q Continuous Review System Order a fixed amount Order cycle (time between orders) varies EOQ, C (holding and ordering costs) R - Constant demand, constant lead time - Variable demand~N, constant lead time Fixed Interval Model, P Periodic Review System Order various amounts Order cycle is fixed or constant

12 – 11 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Inventory Control Systems Continuous review ( Q ) system  Reorder point system (ROP) and fixed order quantity system  For independent demand items  Tracks inventory position (IP)  Includes scheduled receipts (SR), on-hand inventory (OH), and back orders (BO) Inventory position =On-hand inventory + Scheduled receipts – Backorders IP = OH + SR – BO

12 – 12 Some Terms Constant demand, constant lead time. EOQ=Economic Order Quantity Q=Order Quantity D=Annual demand S=Order cost per order H=Annual holding cost per unit TC=Total annual costs TBO=Time between orders, order cycle time R=Reorder Point, used when LT>0 d=demand rate, dbar mean demand rate L=Lead time Constant means fixed or non-fluctuating.

12 – 13 Continuous Review System Constant demand, constant lead time. On-hand inventory (units) Time Average cycle inventory QQ—2QQ—2 1 cycle Receive order Inventory depletion (demand rate)

12 – 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Selecting the Reorder Point Time On-hand inventory TBO L L L Order placed Order placed Order placed IP R OH Order received Order received Order received Order received Figure 12.6 – Q System When Demand and Lead Time Are Constant and Certain

12 – 15 Continuous Review Systems – Total Costs Constant demand, constant lead time.

12 – 16 Ex: Find EOQ, TBO, and make cost comparisons Constant demand, constant lead time, LT=0. Suppose that you are reviewing the inventory policies on an item stocked at a hardware store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional information given: D = 60 units per week, or 3120 units per year S = $30 per order H = 25% of selling price, or $20 per unit per year

12 – 17 Ex: Determine ROP Constant demand, constant lead time, LT>0. Q=300 units, LT=8 days, TBO=30 days.

12 – 18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Continuous Review Systems Time On-hand inventory TBO 1 TBO 2 TBO 3 L1L1 L2L2 L3L3 R Order received Order placed Order placed Order received IP Order placed Order received Order received 0 IP Figure 12.7 – Q System When Demand Is Uncertain

12 – 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand During Lead Time Average demand during lead time Cycle-service level = 85% Probability of stockout (1.0 – 0.85 = 0.15) z σ dLT R Figure 12.9 –Finding Safety Stock with a Normal Probability Distribution for an 85 Percent Cycle-Service Level

12 – 20 Ex: Determine EOQ, ROP Q System Variable demand~N, constant lead time, LT>0. The Discount Appliance Store uses a fixed order quantity model. One of the company’s items has the following characteristics: Demand = 10 units/wk (assume 52 weeks per year, normally distributed) Ordering and setup cost (S) = $45/order Holding cost (H) = $12/unit/year Lead time (L) = 3 weeks Standard deviation of demand = 8 units per week Service level = 70%

12 – 21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Periodic Review System ( P ) PP T LLL Protection interval Time On-hand inventory IP 3 IP 1 IP 2 Order placed Order placed Order placed Order received Order received Order received IP OH Q1Q1 Q2Q2 Q3Q3 Figure – P System When Demand Is Uncertain

12 – 22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Application 12.6, P system The on-hand inventory is 10 units, and T is 400. There are no back orders, but one scheduled receipt of 200 units. Now is the time to review. How much should be reordered?

12 – 23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating P and T EXAMPLE 12.7 Again, let us return to the bird feeder example. Recall that demand for the bird feeder is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units. The lead time is 2 weeks, and the business operates 52 weeks per year. The Q system developed in Example 12.4 called for an EOQ of 75 units and a safety stock of 9 units for a cycle-service level of 90 percent. What is the equivalent P system? Answers are to be rounded to the nearest integer.

12 – 24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating P and T SOLUTION We first define D and then P. Here, P is the time between reviews, expressed in weeks because the data are expressed as demand per week: D = (18 units/week)(52 weeks/year) = 936 units P = (52) = EOQ D (52) = 4.2 or 4 weeks With d = 18 units per week, an alternative approach is to calculate P by dividing the EOQ by d to get 75/18 = 4.2 or 4 weeks. Either way, we would review the bird feeder inventory every 4 weeks.

12 – 25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Calculating P and T We now find the standard deviation of demand over the protection interval ( P + L ) = 6: Before calculating T, we also need a z value. For a 90 percent cycle-service level z = The safety stock becomes Safety stock = zσ P + L = 1.28(12.25) = or 16 units We now solve for T : = (18 units/week)(6 weeks) + 16 units = 124 units T = Average demand during the protection interval + Safety stock = d ( P + L ) + safety stock

12 – 26 Ex: P System, Determine the Amount to Order d=30 units per day  d =3 units per day LT=2 days Service level 99% P=7 days A=71 units

12 – 27 Q Model vs. P Model

12 – 28 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. IM in Action Video