McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.

1212

Inventory Management

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Learning ObjectivesLearning Objectives

Define the term inventory and 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 ObjectivesLearning 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

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

InventoryInventory

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Inventory ModelsInventory 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 InventoriesTypes of Inventories

Raw materials & purchased parts Partially completed goods called

work in progress

Finished-goods inventories (manufacturing firms)

or merchandise (retail stores)

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Types of Inventories (Cont’d)Types of Inventories (Cont’d)

Replacement parts, tools, & supplies

Goods-in-transit to warehouses or customers

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Functions of InventoryFunctions of Inventory

To meet anticipated demand

To smooth production requirements (to build inventories during preseason period)

To decouple operations (in terms of operational difficulties)

To protect against stock-outs

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Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)

To take advantage of order cycles (to produce in economic lot size)

To help hedge against price increases

To permit operations (work in progress inventory)

To take advantage of quantity discounts

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Objective of Inventory ControlObjective 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 ofaverage cost of goods sold toaverage inventory investment.

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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

Effective Inventory ManagementEffective Inventory Management

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Inventory Counting SystemsInventory Counting Systems

Periodic SystemPhysical count of items made at periodic intervals (Manager periodically check the shelves)

Perpetual Inventory System (Continuous)

System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item

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Inventory Counting Systems Inventory Counting Systems (Cont’d)(Cont’d)

Two-Bin System - Two containers of inventory; reorder when the first is empty

Universal Bar Code - Bar code printed on a label that hasinformation about the item to which it is attached 0

214800 232087768

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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

Key Inventory TermsKey Inventory Terms

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ABC Classification SystemABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - mod. important

CC - least important

Figure 12.1

Annual $ value of items

AA

BB

CC

High

Low

Low HighPercentage of Items

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Economic order quantity (EOQ) model

The order size that minimizes total annual cost

Economic production model

Economic Order Quantity ModelsEconomic Order Quantity Models

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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

Assumptions of EOQ ModelAssumptions of EOQ Model

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The Inventory CycleThe Inventory CycleFigure 12.2

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

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Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2

H DQ

S+

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Cost Minimization GoalCost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQH

D

QS

2

Figure 12.4C

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Minimum Total CostMinimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q2

H DQ

S=

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Deriving the EOQDeriving 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.

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

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Example Example

A local distributor for a national tire company expects to sell approximately 9,600 steel belted radial tires of a certain cize 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 Economic Order Quantity? b)How many times per year does the store Re-order?c) What is the length of an order cycle? d)What is the total annual cost if the EOQ quantity is

ordered?

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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

Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)

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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

Economic Production Quantity Economic Production Quantity AssumptionsAssumptions

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Economic Run SizeEconomic Run Size

QDS

H

p

p u0

2

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A toy Manufacturing uses 48,000 rubber weels per year for 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 a wheels is $45. The firm operates 240 days per year. Determine the :-

a) Optimal run size (optimal quantity produced)

b) Minimum total annual cost for carrying cost and setup.

c) Cycle time for the optimal run size?

d) Run time

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Safety StockSafety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Figure 12.12

Safety stock reduces risk ofstockout during lead time

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