Managing Inventory throughout the Supply Chain Chapter Objectives

Managing Inventory throughout the Supply Chain

Chapter Objectives Be able to: q Describe the various roles of inventory, including the different types of inventory and inventory drivers. q Distinguish between independent demand inventory. q Calculate the restocking level for a periodic review system. q Calculate the economic order quantity (EOQ) and reorder point (ROP) for a continuous review system. q Determine the best order quantity when volume discounts are available. q Calculate the target service level and target stocking point for a singleperiod inventory system. q Describe how inventory decisions affect other areas of the supply chain. In particular, be able to describe the bullwhip effect, inventory positioning issues, and the impact of transportation, packaging, and material handling considerations. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 2

Inventory Management • Functions, forms, and drivers of inventory • Inventory cost issues • Tools: Economic order quantity (EOQ) Reorder point (ROP) and safety stock Dealing with quantity discounts © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 3

Types of Inventory • • Cycle stock Safety stock (buffer inventory) Anticipation inventory Others – Hedge inventories – Transportation inventory (pipeline) – Smoothing inventories © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 4

Four Inventory Drivers 1. Demand Supply Uncertainties Safety stock, hedge inventory 2. Demand Process Volume Mismatches Cycle stock 3. Demand Capacity Mismatches Smoothing inventory 4. Demand Supply Lead-Time Mismatches Anticipation inventory, transportation inventory © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 5

Independent Demand • Demand from outside the organization • Unpredictable usually forecasted Demand for tables. . . © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 6

Dependent Demand • Tied to the production of another item • Relevant mostly to manufacturers Once we decide how many tables we want to make, how many legs do we need? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 7

Two “Classic” Systems for Independent Demand Items • Periodic review systems • Continuous (perpetual) review systems Factors – Order quantity (Q) – Restocking level (R) – Inventory level when reviewed (I) © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 8

Restocking Levels • Periodic Review • Continuous Review © 2008 Pearson Prentice Hall ---

Periodic Review System (Orders at regular intervals) Inventory level 2 4 © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 6 Time 10

Continuous Review System (Orders when inventory drops to R) How is the reorder point ROP established? Q Inventory level R L-T Time lead time to get a new order in © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 11

Comparison of Periodic and Continuous Review Systems Periodic Review Continuous Review • Fixed order intervals • Varying order intervals • Variable order sizes • Fixed order sizes (Q) • Allows individual review • Convenient to frequencies administer • Possible quantity • Orders may be discounts combined • Lower, less-expensive • Inventory position safety stocks only required at review © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply 12 Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036

Order Quantity Q and Average Inventory Level As the order quantity doubles so does the average inventory (= Q/2) Q 2 Q 1 © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 Q 2 2 Q 1 2 13

What is the “Best” Order Size Q? Determined by: • Inventory related costs – Order preparation costs and setup costs – Inventory carrying costs – Shortage and customer service costs • Other considerations – Out of pocket or opportunity cost? – Fixed, variable, or some mix of the two? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 14

Economic Order Quantity (EOQ) Model • Cost Minimizing “Q” • Assumptions: Uniform and known demand rate Fixed item cost Fixed ordering cost Constant lead time © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 15

What are the Total Relevant Annual Inventory Costs? Consider: Ø D = Total demand for the year Ø S = Cost to place a single order Ø H = Cost to hold one unit in inventory for a year Ø Q = Order quantity Then: Total Cost = Annual Holding Cost + Annual Ordering Cost = [(Q/2) × H] + [(D/Q) × S] How do these costs vary as Q varies? Why isn’t item cost for the year included? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 16

Holding Cost $ (Q/2)×H Holding cost increases as Q increases. . . Q © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 17

Ordering Costs $ Ordering costs per year decrease as Q increases (why? ) (Q/2)×H (D/Q)×S Q © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 18

Total Annual Costs and EOQ at minimum total cost © 2008 Pearson Prentice Hall

EOQ Solution When the order quantity = EOQ, the holding and setup costs are equal © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 20

Sample Problems • Pam runs a mail-order business for gym equipment. Annual demand for the Trico. Flexers is 16, 000. The annual holding cost per unit is $2. 50 and the cost to place an order is $50. What is the economic order quantity? • Using the same holding and ordering costs as above, suppose demand for Trico. Flexers doubles to 32, 000. Does the EOQ also double? Explain what happens. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 21

EOQ tells us how much to order. . . …but when should we order? Reorder point and safety stock analysis © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 Chapter 8, Slide

Safety Stock When both lead time and demand are constant, you know exactly when your reorder point is. . . Q R L © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 23

Safety Stock II Under these assumptions: Reorder point = total demand during the lead time between placement of the order and its receipt. ROP = d × L, where d = demand per unit time, and L = lead time in the same time units © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 24

Safety Stock III (Uncertainties) But what happens when either demand or lead time varies? Q R L 1 © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 L 2 25

Safety Stock IV What causes this variance? Average demand during lead time © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 26

Uncertainty Drivers 1) 2) 3) 4) The variability of demand The variability of lead time The average length of lead time The desired service level 2) and 3) are determined by a company’s choice of supply chain partners © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 27

Safety Stock • Additional inventory beyond amount needed to meet “average” demand during lead time • Protects against uncertainties in demand or lead time • Balances the costs of stockouts against the cost of holding extra inventory © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 28

Shown Graphically … Now, what is the chance of a stockout? 7% 93% © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 29

Recalculating the Reorder Point to include Safety Stock © 2008 Pearson Prentice Hall ---

Determining “z” z = number of standard deviations above the average demand during lead time The higher z is: § The lower the risk of stocking out § The higher the average inventory level What is the average inventory level when we include safety stock? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 31

Determining “z” Typical choices for z: z = 1. 28 z = 1. 65 z = 2. 33 90% service level 95% service level 99% service level What do we mean by “service level”? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 32

Reorder Point + Safety Stock Formula: § § What happens if lead time is constant? What happens if the demand rate is constant? What happens if both are constant? If you wanted to reduce the amount of safety stock you hold, what is your best option? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 33

Problems I One of the products stocked by Sam’s Club is Sams. Cola. · During the slow season, the demand rate is approximately 650 cases a month, which is the same as a yearly demand rate of 650× 12 = 7, 800 cases. · During the busy season, the demand rate is approximately 1, 300 cases a month, or 15, 600 cases a year. · The cost to place an order is $5, and the yearly holding cost for a case of Sams. Cola is $12. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 34

Problems II According to the EOQ formula: q How many cases of Sams. Cola should be ordered at a time during the slow season? q How many cases of Sams. Cola should be ordered during the busy season? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 35

Problems III During the busy season, the store manager has decided that 98 percent of the time, he does not want to run out of Sams. Cola before the next order arrives. Use the following data to calculate the reorder point for Sams. Cola. • • • Weekly demand during the busy season: 325 cases per week Lead-time: 0. 5 weeks Standard deviation of weekly demand: 5. 25 Standard deviation of lead-time: 0 (lead-time is constant) Number of standard deviations above the mean needed to provide a 98% service level (z): 2. 05 © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 36

Quantity Discounts I What effect will quantity discounts have on EOQ? D = 1, 200 units (100× 12 months) H = $10 per unit per year S = $30. 00 ordering cost Order Size 0 - 89 90 and up Price $35. 00 $32. 50 Note: When H is a cost based on a percent of the value of the item, these calculations become more complicated, but are done in the same way. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 37

Quantity Discounts II 1. Calculate the EOQ for the non discount price: 2. If we can order this quantity AND get the lowest price, we’re done. Otherwise. . . © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 38

Quantity Discounts III Compare total holding, carrying, AND item cost for the year at: Each price break The first feasible EOQ quantity Do you understand why we must now look at item cost for the year? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 39

Quantity Discounts IV Total costs at an order quantity of 85: (85/2)×$10 + (1200/85)×$30 + 1200×$35. 00 = $425 + $423. 53 + $42, 000 = ? ? Total costs at an order quantity of 90: (90/2)×$10 + (1200/90)×$30 + 1200×$32. 50 = $450 + $400 + $39, 000 = ? ? © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 40

Conclusions: • When all costs are considered, it is cheaper to order 90 at a time and take the price discount. • When there are volume discounts, the EOQ calculation might be infeasible or might not result in lowest total cost. • If holding cost is a percentage of the item value (a common practice for more expensive items), analysis is more complex, but done the same way © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 41

Single-Period Inventory (When safety stock is not an option) • Inventory is perishable – Newspapers, periodicals – Fresh food, Christmas trees • Must balance costs of – Being short = profit lost – Having excess = item cost + disposal cost – salvage value • Requires a target service level that best balances shortage and excess costs © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 42

Target Service Level Sets expected shortage cost = expected excess cost Or (1–p) × Cshortage = p × Cexcess Where p = probability of enough units to meet demand, (1–p) = probability of shortage Hence solving for p where the top equation is true provides the target service level SLT = Cshortage / (Cshortage + Cexcess) © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 43

Target Stocking Point • Must know how demand is distributed – Is it roughly the same every day? – Are there different demand distributions? • In all cases, develop the cumulative probability distribution for the demand levels in order of increasing demand select demand level whose corresponding cumulative probability is nearest to the target service level. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 44

Text Example for SLT = 65% © 2008 Pearson Prentice Hall --- Introduction to

Inventory in the Supply Chain • Bullwhip Effect – Small demand changes large order variations • Inventory Positioning – Cost and value increases, flexibility decreases down the supply chain where do we hold inventory? • Transportation, Packaging, Material Handling – Physical size and quantity of lot, how it is packaged, handling equipment needed, and disposal of packaging are all factors in choosing appropriate supplier and distribution process © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 46

Demand versus Order Size (Bullwhip Effect) © 2008 Pearson Prentice Hall --- Introduction to

Case Study in Inventory Management Northcutt Bikes: The Service Department © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 Chapter 8, Slide

Supplement ABC Classification Method IDEA Companies have thousands of items to track Methods like EOQ only justifiable for most important items. © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 49

ABC Method 1. Determine annual $ usage for each item 2. Rank the items according to their annual $ usage 3. Let: Ø Top 20% “A” items roughly 80% of total $ Ø Middle 30% “B” items roughly 15% of total $ Ø Bottom “ 50% “C” item roughly 5% of total $ © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 50

ABC Analysis Example Item Cost Demand $ Usage A 1 $46 200 $9, 200 B 2 $40 10 $400 C 3 $5 6680 $33, 400 D 4 $81 100 $8, 100 E 5 $22 50 $1, 100 F 6 $6 100 $600 G 7 $176 250 $44, 000 H 8 $6 150 $900 I 9 $10 10 $100 J 10 $14 50 $700 Total $ Usage = $98, 500 © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 51

Ranking by Annual $ Usage Item $ Usage Cumulative $ % of Total $ Usage Class G 7 $44, 000 44. 67% A C 3 $33, 400 $77, 400 78. 58% A A 1 $9, 200 $86, 600 87. 92% B D 4 $8, 100 $94, 700 96. 14% B E 5 $1, 100 $95, 800 97. 26% B H 8 $900 $96, 700 98. 17% C J 10 $700 $97, 400 98. 88% C F 6 $600 $98, 000 99. 49% C B 2 $400 $98, 400 99. 90% C I 9 $100 $98, 500 100. 00% C © 2008 Pearson Prentice Hall --- Introduction to Operations and Supply Chain Management, 2/e --- Bozarth and Handfield, ISBN: 0131791036 52