Lect 11 - Line Balancing & EOQ

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Line Balancing..Line Balancing..

Purpose is to minimize the number of people and/or machines on an assembly line that is required to produce a given number of units

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

7 – 2Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Line Balancing ExampleLine Balancing Example

EXAMPLEGreen Grass’s plant manager just received marketing’s latest forecasts of fertilizer spreader sales for the next year. She wants its production line to be designed to make 2,400 spreaders per week. The plant will operate 40 hours per week.

a. What should be the line’s cycle time or throughput rate per hour be?Throughput rate/hr = 2400 / 40 = 60 spreaders/hrCycle Time = 1/Throughput rate= 1/60 = 1 minute = 60 seconds


Line balancing Example continued:Line balancing Example continued:

Assume that in order to produce the new fertilizer spreader on the assembly line requires doing the following steps in the order specified:

b.What is the total number of stations or machines required?TM (total machines) = total production time / cycle time = 244/60 = 4.067 or 5

Work Element Description Time

(sec)Immediate

Predecessor(s)

A Bolt leg frame to hopper 40 NoneB Insert impeller shaft 30 AC Attach axle 50 AD Attach agitator 40 BE Attach drive wheel 6 BF Attach free wheel 25 CG Mount lower post 15 CH Attach controls 20 D, EI Mount nameplate 18 F, G

Total 244


Draw a Precedence DiagramDraw a Precedence Diagram

SOLUTIONThe figure shows the complete diagram. We begin with work element A, which has no immediate predecessors. Next, we add elements B and C, for which element A is the only immediate predecessor. After entering time standards and arrows showing precedence, we add elements D and E, and so on. The diagram simplifies interpretation. Work element F, for example, can be done anywhere on the line after element C is completed. However, element I must await completion of elements F and G.

D

40

I

18

H

20

F

25

G

15

C

50

E

6

B

30

A

40

Precedence Diagram for Assembling the Big Broadcaster


Allocating work or activities to Allocating work or activities to stations or machinesstations or machines

The goal is to cluster the work elements into workstations so that 1. The number of workstations required is minimized2. The precedence and cycle-time requirements are not

violated The work content for each station is equal (or

nearly so, but less than) the cycle time for the line Trial-and-error can be used but commercial

software packages are also available


Finding a SolutionFinding a Solution

The minimum number of workstations is 5 and the cycle time is 60 seconds, so Figure 5 represents an optimal solution to the problem

Firtilizer Precedence Diagram Solution

D

40

I

18

H

20

F

25C

50

E

6

B

30

A

40

G

15


Calculating Line EfficiencyCalculating Line Efficiency

c. Now calculate the efficiency measures of a five-station solution:

Efficiency = (100) =tnc

2445(60)

= 81.3%

Idle time = nc – t = 5(60) – 244 = 56 seconds

Balance delay (%) = 100 – Efficiency = 100% - 81.3% = 18.7%


A Line ProcessA Line Process

The desired output rate is matched to the staffing or production plan

Line Cycle Time is the maximum time allowed for work at each station is

c =1r

wherec = cycle time in hoursr = desired output rate



The theoretical minimum number of stations is

TM =tc

wheret =total time required to assemble each unit



Idle time, efficiency, and balance delay

Idle time = nc – t

wheren =number of stations

Efficiency (%) = (100)tnc

Balance delay (%) = 100 – Efficiency


Solved Problem 2Solved Problem 2

A company is setting up an assembly line to produce 192 units per 8-hour shift. The following table identifies the work elements, times, and immediate predecessors:

Work Element Time (sec) Immediate Predecessor(s)

A 40 None

B 80 A

C 30 D, E, F

D 25 B

E 20 B

F 15 B

G 120 A

H 145 G

I 130 H

J 115 C, I

Total 720



a. What is the desired cycle time (in seconds)?b. What is the theoretical minimum number of stations?c. Use trial and error to work out a solution, and show your

solution on a precedence diagram.d. What are the efficiency and balance delay of the solution

found?

SOLUTIONa. Substituting in the cycle-time formula, we get

c = =1r

8 hours192 units

(3,600 sec/hr) = 150 sec/unit



b. The sum of the work-element times is 720 seconds, so

TM =tc = = 4.8 or 5 stations720 sec/unit

150 sec/unit-station

which may not be achievable.



c. The precedence diagram is shown in Figure 7.6. Each row in the following table shows work elements assigned to each of the five workstations in the proposed solution.

J

115

C

30

D

25

E

20

F

15

I

130H

145

B

80

G

120

A

40

Figure 7.6 – Precedence Diagram

Work Element

Immediate Predecessor(s)

A NoneB AC D, E, FD BE BF BG AH GI HJ C, I


Station Candidate(s) Choice Work-Element Time (sec)

Cumulative Time (sec)

Idle Time(c= 150 sec)

S1

S2

S3S4

S5

Solved Problem 2Solved Problem 2J

115

C

30

D

25

E

20

F

15 I

130H

145

B

80

G

120

A

40


Solved Problem 2Solved Problem 2J

115

C

30

D

25

E

20

F

15 I

130H

145

B

80

G

120

A

40

A A 40 40 110

B B 80 120 30D, E, F D 25 145 5

E, F, G G 120 120 30E, F E 20 140 10F, H H 145 145 5F, I I 130 130 20F F 15 145 5C C 30 30 120J J 115 145 5

Station Candidate(s) Choice Work-Element Time (sec)

Cumulative Time (sec)

Idle Time(c= 150 sec)

S1

S2

S3S4

S5



d. Calculating the efficiency, we get

Thus, the balance delay is only 4 percent (100–96).

Efficiency (%) = (100)tnc = 720 sec/unit

5(150 sec/unit)

= 96%


In classIn class - Example - Example

A plant manager needs a design for an assembly line to assembly a new product that is being introduced. The time requirements and immediate predecessors for the work elements are as follows:

Work Element Time (sec) Immediate Predecessor

A 12 ―B 60 AC 36 ―D 24 ―E 38 C, DF 72 B, EG 14 ―H 72 ―I 35 G, HJ 60 IK 12 F, J

Total = 435


K


Draw a precedence diagram, complete I, F, J, and K

Work Element Time (sec) Immediate

Predecessor

A 12 ―

B 60 A

C 36 ―

D 24 ―

E 38 C, D

F 72 B, E

G 14 ―

H 72 ―

I 35 G, H

J 60 I

K 12 F, J

Total = 435

F

J

B

E

I

A

C

G

H

D



If the desired output rate is 30 units per hour, what are the cycle time and theoretical minimum?

c = =1r

130

(3600) = 120 sec/unit

TM =tc = = 3.6 or 4 stations435

120



Suppose that we are fortunate enough to find a solution with just four stations. What is the idle time per unit, efficiency, and the balance delay for this solution?

Idle time = nc – t

Efficiency (%) = (100)tnc

Balance delay (%) = 100 – Efficiency

= 4(120) – 435 = 45 seconds

= 100 – 90.6 = 9.4%

= (100) = 90.6%435480


Station

Work Elements Assigned Cumulative Time

Idle Time(c = 120)

1

2

3

4

5


Using trial and error, one possible solution is shown below.



Using trial and error, one possible solution is shown below.

H, C, A 120 0

B, D, G 98 22

E, F 110 10

I, J, K 107 13

A fifth station is not needed

Station

Work Elements Assigned Cumulative Time

Idle Time(c = 120)

1

2

3

4

5


Managerial ConsiderationsManagerial Considerations

Pacing is the movement of product from one station to the next

Behavioral factors such as absenteeism, turnover, and grievances can increase after installing production lines

The number of models produced complicates scheduling and necessitates good communication

Cycle times are dependent on the desired output rate

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Inventory Inventory Management & the Management & the Economic Order Economic Order Quantity (EOQ)Quantity (EOQ)

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Lecture todayLecture today

Why is inventory so bad?Why hold inventory?Where to hold inventory?What are types of inventory to keep?What are the inventory costs?How much inventory to keep?When to order & how much to order?What do I need to know to make those

decisions?

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Inventory ManagementInventory Management

Inventory management is the planning and controlling of inventories in order to meet the competitive priorities of the organization.

Inventory management requires information about expected demands, amounts on hand and amounts on order for every item stocked at all locations.

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Inventory BasicsInventory Basics

Inventory is created when the receipt of materials, parts, or finished goods exceeds their disbursement.

Inventory is depleted when their disbursement exceeds their receipt.

An inventory manager’s job is to balance the advantages and disadvantages of both low and high inventories.

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Inventory CostsInventory Costs Cost of capital ObsolescenceStorage InsuranceTaxesSecurityTheftDamageLocatingMeasurementManagement & Labor

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Why hold Inventory?Why hold Inventory?

Customer Sales & Service: Avoid Retail stock outs and thus customer goodwill (Retailing)

Seasonal sales (Xmas trees)Take advantage of quantity discountsBalance process flow timeUncertainty in supply and demandLead TimeSpeculative inventory (wine, gold)

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Inventory at Inventory at WALWAL--MARTMART

Making sure the shelves are stocked with tens of thousands of items at their 5,379 stores in 10 countries is no small matter for inventory managers at Wal-Mart.

Knowing what is in stock, in what quantity, and where it is being held, is critical to effective inventory management.

With inventories in excess of $29 billion, Wal-Mart is aware of the benefits from improved inventory management.

They know that effective inventory management must include the entire supply chain.

The firm is implementing radio frequency identification (RFID) technology in its supply chain.

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Macro Inventory DecisionsMacro Inventory Decisions

Where do we hold inventory?◦ Manufacturers and suppliers◦ warehouses and distribution centers◦ retailers

Types of Inventory to keep?◦ raw materials◦ WIP◦ finished goods

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Micro Inventory DecisionsMicro Inventory Decisions

When to order items?How much of each item to order?How much safety stock to keep?

Objective: minimize overall cost of keeping inventory!

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Relevant Costs in an Inventory SystemRelevant Costs in an Inventory System

Procurement costs Ordering cost (administrative, inspection,

transportation etc.)Holding costs

Maintenance and Handling Taxes Obsolescence

Stock-outs costs Lost sales (Customer goodwill) Backorders

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Relevant information to any inventory Relevant information to any inventory decisiondecision

Knowing how much demand there isKnowing if this demand is fairly constant or

variesKnowing what is in stockKnowing where they exist in the supply chain Knowing how long it will take to replenishKnowing where it is going to be replenished from

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Frequently used inventory termsFrequently used inventory terms

Inventory lot sizeReplenishment Lead timeStock outReorder PointSafety stock

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Thousands of items are held in inventory by a typical organization, but only a small % of them deserves management’s closest attention and tightest control.

ABC analysis: The process of dividing items into three classes, according to their dollar usage, so that managers can focus on items that have the highest dollar value.

Knowing which Items are Critical

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ABC AnalysisABC Analysis

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100Percentage of itemsPercentage of items

Perc

enta

ge o

f dol

lar v

alue

Perc

enta

ge o

f dol

lar v

alue

100 100 —

90 90 —

80 80 —

70 70 —

60 60 —

50 50 —

40 40 —

30 30 —

20 20 —

10 10 —

0 0 —

Class C

Class A

Class B

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Economic Order Quantity (EOQ) is the lot size that minimizes total annual inventory holding and ordering costs.

Assumptions of EOQ1. The demand rate is constant and known with

certainty.2. There are no constraints on lot size.3. The only relevant costs are holding costs

and ordering/setup costs.4. Decisions for items can be made

independently of other items.5. Lead time is constant and known with

certainty.

Economic Order Quantity (EOQ)Economic Order Quantity (EOQ)

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Inventory depletion Inventory depletion (demand rate)(demand rate)

Receive Receive orderorder

1 cycle1 cycle

On-

hand

inve

ntor

y (u

nits

)O

n-ha

nd in

vent

ory

(uni

ts)

TimeTime

QQ

AverageAveragecyclecycleinventoryinventory

QQ——22

Cycle-Inventory LevelsCycle-Inventory Levels

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Ann

ual c

ost (

dolla

rs)

Ann

ual c

ost (

dolla

rs)

Lot Size (Lot Size (QQ))

Total Annual Cycle-Inventory CostsTotal Annual Cycle-Inventory Costs

Holding cost = (Holding cost = (HH))QQ22

Ordering cost = (Ordering cost = (SS))DDQQ

Total cost = (Total cost = (HH) + () + (SS))DDQQ

QQ22

Q = lot size; C = total annual cycle-inventory costH = holding cost per unit; D = annual demandS = ordering or setup costs per lot

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Costing out a Lot Sizing PolicyCosting out a Lot Sizing Policy

Bird feeder sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order (S) with the supplier is $45.

Annual holding cost (H) is 25% of a feeder’s value, based on operations 52 weeks per year.

Management chose a 390-unit lot size (Q) so that new orders could be placed less frequently.

What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size?

Museum of Natural History Gift Shop:

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Costing out a Lot Sizing PolicyCosting out a Lot Sizing Policy

What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size?

D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15

C = $2925 + $108 = $3033

C = (H) + (S) = (15) + (45) Q2

DQ

936390

3902

Museum of Natural History Gift Shop:

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3000 3000 —

2000 2000 —

1000 1000 —

0 0 —| | | | | | | |

5050 100100 150150 200200 250250 300300 350350 400400

Lot Size (Q)

Ann

ual c

ost (

dolla

rs)

Ann

ual c

ost (

dolla

rs) Total costTotal cost

Holding costHolding cost

Ordering costOrdering cost

Currentcost

CurrentQ

Lowestcost

Best Q (EOQ)

Lot Sizing at the MuseumLot Sizing at the Museumof Natural History Gift Shopof Natural History Gift Shop

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Computing the EOQComputing the EOQ

C = (H) + (S)Q2

DQ

EOQ = 2DSH

D = annual demandS = ordering or setup costs per lotH = holding costs per unit

D = 936 unitsH = $15S = $45

EOQ = 2(936)4515

= 74.94 or 75 units

C = (15) + (45)752

93675

C = $1,124.10

Bird Feeders:

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Time Between OrdersTime Between Orders

Time between orders (TBO) is the average elapsed time between receiving (or placing) replenishment orders of Q units for a particular lot size.

For the birdfeeder example, using an EOQ of 75 units.

TBOEOQ = EOQD

TBOEOQ = = 75/936 = 0.080 yearEOQD

TBOEOQ = (75/936)(12) = 0.96 months

TBOEOQ = (75/936)(52) = 4.17 weeks

TBOEOQ = (75/936)(365) = 29.25 days

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In Class ExampleIn Class Example

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In Class ExampleIn Class Example

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In Class Example (In Class Example (continued)continued)

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In Class ExampleIn Class Examplecontinuedcontinued

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Understanding the Effect of ChangesUnderstanding the Effect of Changes

What happens if there is a change in the Demand Rate (D)?

What happens if the Setup Costs (S) changes?

What happens if the holding Costs (H) change?

What happens if there are errors in estimating D, H, and S?

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Lect 11 - Line Balancing & EOQ