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**Types of Inventory Transit stock or pipeline inventory Cycle stock**

Safety stock (buffer inventory) Anticipation inventory Others Smoothing inventories Hedge inventories ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Four Inventory Drivers**

Demand and Capacity Mismatches Smoothing inventories Demand and Process Volume Mismatches Cycle stocks Demand and Supply Uncertainties Safety stocks Demand and Process Lead-Time Mismatches Anticipation inventories ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Independent Demand Demand from outside the organization**

Unpredictable usually forecasted Demand for tables . . . ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**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? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Two “Classic” Systems for Independent Demand Items**

Periodic review systems Continuous (perpetual) review systems Fixed order quantity (Q) Reorder point (R) ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Periodic Review System (Orders at regular intervals)**

Inventory level 2 4 6 Time ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Continuous Review System (Orders when inventory drops to R)**

How is the reorder point R established? Q Inventory level R Time L-T lead time to get a new order in ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Comparison of Periodic and Continuous Review Systems**

Periodic Review Fixed order intervals Variable order sizes Convenient to administer Orders may be combined Inventory position only required at review Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Order Quantity Q and Average Inventory Level**

As the order quantity doubles so does the average inventory (= Q/2) Q2 Q2 2 Q1 Q1 2 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**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? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Economic Order Quantity (EOQ) Model**

Cost Minimizing “Q” Assumptions: Uniform and known usage rate Fixed item cost Fixed ordering cost Constant lead time ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**What are the Total Relevant Annual Inventory Costs?**

Consider: D = Total demand for the year S = Cost to place a single order H = Cost to hold one unit in inventory for a year 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? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Holding Cost $ Holding cost increases as Q increases . . . (Q/2)×H Q**

©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Ordering costs per year decrease as Q increases**

$ Ordering costs per year decrease as Q increases (why?) (Q/2)×H (D/Q)×S Q ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Total Annual Costs and EOQ**

EOQ at minimum total cost ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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EOQ Solution When the order quantity = EOQ, the holding and setup costs are the same ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Sample Problems Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers 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 TricoFlexers doubles to 32,000. Does the EOQ also double? Explain what happens. Answers: EOQ = 800; 1,131 (goes up as the square root of 2) ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**EOQ tells us how much to order...**

…but when should we order? Reorder point and safety stock analysis ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Safety Stock When both lead time and demand are constant, you know exactly when your reorder point is ... Q R L ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**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 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Safety Stock III (Uncertainties)**

But what happens when either demand or lead time varies? Q R L1 L2 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Safety Stock IV What causes this variance? Average demand**

during lead time ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Safety Stock V Additional inventory beyond amount needed to meet “average” demand during lead time Protects against uncertainties in demand or lead time Balances the costs of stocking out against the cost of holding extra inventory ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Shown Graphically … Now, what is the chance of a stockout? 93% 7%**

©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Recalculating the Reorder Point to include Safety Stock**

©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Determining “z” I 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? Average inventory plus safety stock level ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Determining “z” II Typical choices for z: z = 90% service level z = 95% service level z = 99% service level What do we mean by “service level”? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Reorder Point 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? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Problems I One of the products stocked by Sam’s Club is SamsCola.**

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 SamsCola is $12. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Problems II According to the EOQ formula:**

How many cases of SamsCola should be ordered at a time during the slow season? How many cases of SamsCola should be ordered during the busy season? Slow season: 81 cases Busy season: 114 cases ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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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 SamsCola before the next order arrives. Use the following data to calculate the reorder point for SamsCola. 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 Answer: 245 cases ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Volume Discounts I What effect will volume discounts have on the EOQ?**

D = 1,200 units (100×12 months) K = 12% of unit cost S = $8.00 ordering cost Order Size Price $35.00 75 and up $32.50 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Volume Discounts II 1. Calculate the EOQ for the lowest price:**

2. If we can order this quantity AND get the lowest price, we’re done. Otherwise ... ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Volume Discounts III 3. Calculate EOQ at the next lowest price, and keep repeating until you find an EOQ that is “feasible”: We could order 68 at $35.00 each ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Volume Discounts IV 4. 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? ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Volume Discounts V Total costs at an order quantity of 75:**

(75/2)×(12%)×$ (1200/75)×$ ×$32.50 = $ $ $39,000 = ?? Total costs at an order quantity of 68: (68/2)×(12%)×$ (1200/68)×$ ×$35.00 = $ $ $42,000 = ?? Quantity 75: $39,274.25 Quantity 68: $42,283.98 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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Conclusions: When all costs are considered, it is cheaper to order 75 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. Hence, more detailed analysis is required. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**ABC Classification Method**

IDEA Companies have thousands of items to track Methods like EOQ only justifiable for most important items. ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**ABC Method Determine annual $ usage for each item**

Rank the items according to their annual $ usage Let: Top 20% “A” items roughly 80% of total $ Middle 30% “B” items roughly 15% of total $ Bottom “50% “C” item roughly 5% of total $ ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**ABC Analysis Example Total $ Usage = $98,500 Item Cost Demand $ Usage**

$46 200 $9,200 B2 $40 10 $400 C3 $5 6680 $33,400 D4 $81 100 $8,100 E5 $22 50 $1,100 F6 $6 $600 G7 $176 250 $44,000 H8 150 $900 I9 $10 $100 J10 $14 $700 Total $ Usage = $98,500 ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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**Ranking by Annual $ Usage**

Item $ Usage Cumulative $ Usage % of Total $ Usage Class G7 $44,000 44.67% A C3 $33,400 $77,400 78.58% A1 $9,200 $86,600 87.92% B D4 $8,100 $94,700 96.14% E5 $1,100 $95,800 97.26% H8 $900 $96,700 98.17% C J10 $700 $97,400 98.88% F6 $600 $98,000 99.49% B2 $400 $98,400 99.90% I9 $100 $98,500 100.00% ©2006 Pearson Prentice Hall — Introduction to Operations and Supply Chain Management — Bozarth & Handfield

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