CHAPTER 12 PART A – INVENTORY MANAGEMENTSuman Niranjan

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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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

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TYPES OF INVENTORIES

Raw materials & purchased partsPartially completed goods called

work in progressFinished-goods inventories

(manufacturing firms) or merchandise (retail stores)

Replacement PartsPipeline Inventory

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FUNCTIONS OF INVENTORY

To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stock-outs

To take advantage of order cycles

To help hedge against price increases

To permit operations

To take advantage of quantity discounts6

LITTLE’S LAW

Little’s Law: The average amount of inventory in a system is

equal to the product of the average demand rate and the average time a unit spends in the system

Example If a unit is in system for an average of 10 days

and the demand for each day is 5 units, the average inventory: 5 units/day * 10 days = 50 units

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OBJECTIVE 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

Two fundamental decisions of inventory control When to order; how much to order

Days of inventory on-hand Higher – excess inventory; Lower – risk of running out

Inventory turnover is the ratio ofaverage cost of goods sold toaverage inventory investment.

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EFFECTIVE INVENTORY MANAGEMENT A system to keep track of inventory on-hand

and order A reliable forecast of demand and forecast

error Knowledge of lead times and lead time

variability Reasonable estimates of

Holding costs Ordering costs Shortage costs

A classification system of inventory items 9

INVENTORY COUNTING SYSTEMS

Periodic SystemPhysical count of items made at periodic intervals

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

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INVENTORY COUNTING SYSTEMS (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

RFID tags

0

214800 23208776811

ABC CLASSIFICATION SYSTEM

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

A - very important

B - mod. important

C - least important

Annual $ value of items

A

B

C

High

Low

Low HighPercentage of Items

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INVENTORY COUNTING

Increase Customer service

Improve Operations

Cycle Counting Purpose is to reduce the discrepancy amounts

indicated by the records and actual inventory

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? 13

ECONOMIC ORDER QUANTITY MODELS Basic 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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THE INVENTORY CYCLE

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 COST

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2

H DQ

S+

TC: Total CostQ: Order Quantity in UnitsH: Holding Cost Per UnitD: Demand, Usually in Units Per YearS: Ordering Cost

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COST MINIMIZATION GOAL

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al

Cost

(optimal order quantity)

TCQH

D

QS

2

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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.

O

2DS 2(Annual Demand)(Order or Setup Cost)Q = =

H Annual Holding Cost

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MINIMUM TOTAL COST

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

Q2

H DQ

S=

20

Number of orders per year =

length of the order cycle =

D

Q

Q

D

EXAMPLE 2

A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size 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 EOQ?b) How many times per year does the store

reorder?c) What is the length of an order cycle?d) What is the total annual cost if the EOQ

quantity is ordered?21

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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EOQ WITH INCREMENTAL INVENTORY REPLENISHMENT

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ECONOMIC RUN SIZE

02

p= Production or DeleveryRate

u= Usagerate

DS pQ

H p u

maxmin

0

max

carryingcost +setupcost2

Where Maximum Inventory

I DTC H S

Q

I

25

0 0

0

Cycle Time = Run Time =

Themaximum and average inventory are

2max

max average

Q Q

u p

Q II p u I

p

EXAMPLE 4

A toy manufacturer uses 48,000 rubber wheels 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 wheels is $45. The firm operates 240 days per year. Determine the Optimal run size. Minimum total annual cost for carrying and

setup. Cycle time for the optimal run size. Run time.

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