11a-inventory eoq msi a&b

8/13/2019 11A-Inventory EOQ MSi a&B

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Independent-Demand

Inventory


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Outline

Introduction

Purpose of Inventories

Inventory Cost Structures Independent versus Dependent Demand

Economic Order Quantity

Continuous Review System

Periodic Review System

Using P and Q System in Practice

ABC Inventory Management


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Introduction

Definition of Inventory

The Flow and Stock of Inventory


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A Material-Flow Process

Work inprocess

Work in

process

Work in

process

Finished

goods

Work in

process

Custom

er

Productive Process


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Inventory

Definition--The stock of any item orresource used in an organization

Raw materials Finished products

Component parts

Supplies

Work in process


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Inventory System Defined

Inventoryis the stock of any item or resourceused in an organization. These items orresources can include: raw materials, finishedproducts, component parts, supplies, and work-in-process.

An inventory systemis the set of policies andcontrols that monitor levels of inventory anddetermines what levels should be maintained,when stock should be replenished, and howlarge orders should be.


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Purpose of Inventories

To protect against uncertainties

To allow economic production and

purchase To cover anticipated changes in demand

or supply

To provide for transit


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Inventory Cost Structures

Item cost

Ordering (or setup) cost

Carrying (or holding) cost:

Cost of capital

Cost of storage

Cost of obsolescence, deterioration, and loss

Stock out cost


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E(1)

Independent vs. Dependent Demand

Independent Demand

(Demand not related to other items)

Dependent Demand(Derived)


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Classifying Inventory Models

Fixed-Order Quantity Models

Event triggered

Fixed-Time Period Models

Time triggered


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Independent versusDependent Demand


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Economic Order Quantity (EOQ)

Assumptions

Demand rate is constant, recurring, and known.

Lead time is constant and known.

No stockouts allowed.

Material is ordered or produced in a lot or batch and thelot is received all at once

Unit cost is constant (no quantity discounts)

Carrying cost depends linearly on the average level of

inventory Ordering (setup) cost per order is fixed

The item is a single product


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EOQ Inventory Levels

Time

Lot size = Q

Order

Interval

Average I nventory

Level = Q/2


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Notations and measurement unitsin EOQ

D = Demand rate, units per year

S = Cost per order placed, or setup cost,

dollars per orderC = Unit cost, dollars per unit

i= Carrying interest rate, percent of

dollar value per year

Q = Lot size, units


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Total Cost of Inventory


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EOQ Example (1) Problem Data

Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50

Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ andreorder point?


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EOQ Example (1) Solution

Q =2DS

H =

2(1,000 )(10)

2.50 = 89.443 units orOPT 90 un its

d =

1,000 units / year

365 days / year = 2.74 units / day

R eo rd er p oin t, R = d L = 2 .7 4u nits / d ay (7 days) = 1 9.1 8 o r_

20 un its

In summary, you place an optimal order of 90 units. In thecourse of using the units to meet demand, when you onlyhave 20 units left, place the next order of 90 units.


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EOQ Example (2) Problem Data

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10

Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = $15

Determine the economic order quantity and the reorder point.


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EOQ Example (2) Solution

Q =2 D S

H=

2(10,000 ) (10)

1.50= 3 6 5 .1 4 8 u n its , o rO P T 366 un its

d = 10,000 units / year365 days / year

= 27.397 units / day

R = d L = 27.397 units / day (10 days) = 273.97 or_

274 u nits

Place an order for 366 units. When in the course ofusing the inventory you are left with only 274 units, placethe next order of 366 units.


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Continuous Review System

Assumption of constant demand is

relaxed.

Monitoring of on hand stock position in acontinuous system

Q system(another name for continuous

review system)


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A Continuous Review (Q) System

R = Reorder Point

Q = Order Quantity

L = Lead time


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Probability Distribution of Demand

over Lead Time

m= mean demand R= Reorder point s= Safety stock


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Periodic Review System

All assumption of EOQ (except thatdemand is constant and no stockout)

remains in effect.Also known as P System or Fixed-order-

Interval System


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A Periodic Review (P) System


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Time Between Orders (P) andTarget Level (T) Calculation

DCi

SP

2

'' smT Where:

m = average demand over P+L

s = safety stock


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Using P and Q System in Practice

Use P system when orders must beplaced at specified intervals.

Use P systems when multiple items areordered from the same supplier (joint-replenishment).

Use P system for inexpensive items.


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Service Level versus Inventory Level

1.1

2.5

2.42.32.22.12.01.91.81.7

1.6

1.51.3

1.2

1.0

1.4

75%

80%

85%

90%

95%

100%

105%

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

Average Inventory Level

ServiceLevel(%)

z values

100

100

Q


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Special Purpose Model:

Price-Break Model Formula

CostHoldingAnnual

Cost)SetuporderDemand)(Or2(Annual=

iC

2DS=QOPT

Based on the same assumptions as the EOQ model,the price-break model has a similar Qoptformula:

i = percentage of unit cost attributed to carrying inventoryC = cost per unit

Since C changes for each price-break, the formula above willhave to be used with each price-break cost value.


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Price-Break Example Problem Data

(Part 1)

A company has a chance to reduce their inventory orderingcosts by placing larger quantity orders using the price-breakorder quantity schedule below. What should their optimal orderquantity be if this company purchases this single inventory itemwith an e-mail ordering cost of $4, a carrying cost rate of 2% ofthe inventory cost of the item, and an annual demand of 10,000units?

Order Quantity(units) Price/unit($)0 to 2,499 $1.202,500 to 3,999 1.004,000 or more .98


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Price-Break Example Solution (Part 2)

units1,826=0.02(1.20)

4)2(10,000)(=

iC

2DS=QOPT

Annual Demand (D)= 10,000 unitsCost to place an order (S)= $4

First, plug data into formula for each price-break value of C.

units2,000=0.02(1.00)

4)2(10,000)(=iC

2DS=QOP T

units2,020=0.02(0.98)

4)2(10,000)(=

iC

2DS=QOP T

Carrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, theQoptvalue is feasible.

Interval from 2500-3999, theQoptvalue is not feasible.

Interval from 4000 & more, theQoptvalue is not feasible.

Next, determine if the computed Qoptvalues are feasible or not.


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Since the feasible solution occurred in the first price-break,it means that all the other true Qoptvalues occur at thebeginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Total

annual

costs

So the candidatesfor the price-breaks

are 1826, 2500,and 4000 units.

Because the total annual cost function is au shaped function.


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iC

2

Q+S

Q

D+DC=TC

Next, we plug the true Qoptvalues into the total cost annual cost functionto determine the total cost under each price-break.

TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)= $12,043.82

TC(2500-3999)= $10,041TC(4000&more)= $9,949.20

Finally, we select the least costly Qopt, which is this problem occurs in the4000 & more interval. In summary, our optimal order quantity is 4000units.

Mi ll S t


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Miscellaneous Systems

Optional Replenishment System

Maximum Inventory Level, M

MActual Inventory Level, I

q = M - I

I

Q = minimum acceptable order quantity

If q > Q, order q, otherwise do not order any.


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Miscellaneous SystemsBin Systems

Two-Bin System

Full Empty

Order One Bin of

Inventory

One-Bin System

Periodic Check

Order Enough to

Refill Bin


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ABC Inventory Management

Based on Pareto concept (80/20 rule)

Classification of items as A, B, or C

Example (See Table)


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Annual Usage of Items by Dollar Value

Item

Annual Usage in

Units Unit Cost Dollar Usage

Percentage ofTotal Dollar

Usage

1 5,000 1.50$ 7,500$ 2.9%

2 1,500 8.00 12,000 4.7%

3 10,000 10.50 105,000 41.2%4 6,000 2.00 12,000 4.7%

5 7,500 0.50 3,750 1.5%

6 6,000 13.60 81,600 32.0%

7 5,000 0.75 3,750 1.5%

8 4,500 1.25 5,625 2.2%9 7,000 2.50 17,500 6.9%

10 3,000 2.00 6,000 2.4%

Total 254,725$ 100.0%


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ABC Chart

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

3 6 9 2 4 1 10 8 5 7

Item No.

PercentUsage

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

Cumulative%U

sage

Percentage of Total Dollar Usage Cumulative Percentage

A B C


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Inventory Accuracy and CycleCounting

Inventory accuracy

Do inventory records agree with physical count?

Cycle Counting

Frequent counts

Which items? When?

By whom?

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