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12 Inventory Management

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Learning Objectives Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management. Discuss the nature and importance of service inventories Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful.

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Learning Objectives Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems.

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**Independent demand is uncertain. Dependent demand is certain.**

Inventory Independent Demand A B(4) C(2) D(2) E(1) D(3) F(2) Dependent Demand Independent demand is uncertain. Dependent demand is certain. Inventory: a stock or store of goods

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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

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**Types of Inventories Raw materials and purchased parts**

Partially completed goods called work-in-process (WIP) Finished-goods inventories (manufacturing firms) or merchandise (retail stores)

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**Types of Inventories Replacement parts, tools, and supplies**

Goods-in-transit to warehouses or customers

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**Functions of Inventory**

To meet anticipated demand To smooth production requirements To decouple operations To protect against stockouts

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**Functions of Inventory**

To take advantage of order cycles To help hedge against price increases To permit operations To take advantage of quantity discounts

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**Objectives 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 Inventory turnover is the ratio of the annual cost of goods sold to the average inventory investment.

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**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

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**Inventory Counting Systems**

Periodic System Physical count of items made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

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**Inventory Counting Systems**

Two-bin system: Two containers of inventory; reorder when the first is empty 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

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Key Inventory Terms Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Ordering costs: costs of ordering and receiving inventory Shortage costs: costs when demand exceeds supply of inventory

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**ABC Classification System**

Figure 12.1 Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - moderately important C - least important Annual $ value of items A B C High Low Percentage of Items

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**Cycle Counting A physical count of items in inventory**

Cycle counting management How much accuracy is needed? When should cycle counting be performed? Who should do it?

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**Economic Order Quantity Models**

Economic order quantity (EOQ) model The order size that minimizes total annual cost Economic production model Quantity discount model

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**Assumptions of EOQ Model**

Only one product is involved Annual demand requirements 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

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**Profile of Inventory Level Over Time**

The Inventory Cycle Figure 12.2 Profile of Inventory Level Over Time Quantity on hand Q Receive order Place Lead time Reorder point Usage rate Time

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**Total Cost Annual carrying cost Annual ordering cost Total cost = + Q**

2 H D S + TC = Q = Order quantity in units H = Holding (carrying) cost per unit D = Demand, usually in units per year S = Ordering cost

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**Cost Minimization Goal**

Figure 12.4C The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity)

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Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

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Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S = Q

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**Economic Production Quantity (EPQ)**

Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

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**Economic Production Quantity Assumptions**

Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

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**Economic Run Size Q0 = Order quantity in units**

H = Holding (carrying) cost per unit D = Demand, usually in units per year S = Ordering cost p = Production or delivery rate u = Usage rate

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**Total Costs with Purchasing Cost**

Annual carrying cost Purchasing TC = + Q 2 H D S ordering PD

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**Total Costs with PD Figure 12.7 Cost**

EOQ TC with PD TC without PD PD Quantity Adding purchasing cost doesn’t change EOQ

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**Total Cost with Constant Carrying Costs**

OC EOQ Quantity Total Cost TCa TCc TCb Decreasing Price CC a,b,c Figure 12.9A

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**When to Reorder with EOQ Ordering**

Reorder Point: When the quantity on hand of an item drops to this amount, the item is reordered 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

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**Determinants of the Reorder Point**

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

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Reorder Point If demand and lead time are both constant, the reorder point is simply ROP = d X LT Where d = Demand rate (units per day or week) LT = Lead times in days or weeks

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**Safety Stock Figure 12.12 Quantity Maximum probable demand**

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

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**Reorder Point Figure 12.13 The ROP based on a normal**

Risk of a stockout Service level Probability of no stockout Expected demand Safety stock z Quantity z-scale The ROP based on a normal distribution of lead time demand

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**Fixed-Order-Interval Model**

Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory levels Risk of stockout Fill rate: the percentage of demand filled by the stock on hand

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**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

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**Fixed-Interval Disadvantages**

Requires a larger safety stock for given risk of stockout Increases carrying cost Costs of periodic reviews

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Single Period Model Single period model: model for ordering of perishables and other items with limited useful lives Shortage cost: unrealized profits per unit (generally) Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

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**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 matched or exceeded

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**Optimal Stocking Level**

Figure 12.16 Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit Ce Cs Service Level Quantity So Balance point

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**Example 15 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

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**Operations Strategy Too much inventory Wise strategy**

Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain Wise strategy Reduce lot sizes Reduce safety stock Accurate and up-to-date inventory records

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