Lect 11 - Line Balancing & EOQ
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Transcript of Lect 11 - Line Balancing & EOQ
7 – 1
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
7 – 3Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 4Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 5Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 6Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 7Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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%
7 – 8Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 9Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
A Line ProcessA Line Process
The theoretical minimum number of stations is
TM =tc
wheret =total time required to assemble each unit
7 – 10Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
A Line ProcessA Line Process
Idle time, efficiency, and balance delay
Idle time = nc – t
wheren =number of stations
Efficiency (%) = (100)tnc
Balance delay (%) = 100 – Efficiency
7 – 11Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 12Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Solved Problem 2Solved Problem 2
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
7 – 13Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Solved Problem 2Solved Problem 2
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.
7 – 14Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Solved Problem 2Solved Problem 2
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
7 – 15Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 16Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 17Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Solved Problem 2Solved Problem 2
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%
7 – 18Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 19Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
K
In classIn class - Example - Example
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
7 – 20Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
In classIn class - Example - Example
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
7 – 21Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
In classIn class - Example - Example
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
7 – 22Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
Station
Work Elements Assigned Cumulative Time
Idle Time(c = 120)
1
2
3
4
5
In classIn class - Example - Example
Using trial and error, one possible solution is shown below.
7 – 23Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
In classIn class - Example - Example
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
7 – 24Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.
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
7 – 25
Inventory Inventory Management & the Management & the Economic Order Economic Order Quantity (EOQ)Quantity (EOQ)
7 – 26
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
7 – 30
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)
7 – 31
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.
7 – 32
7 – 33
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
7 – 34
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
7 – 36
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
7 – 37
Frequently used inventory termsFrequently used inventory terms
Inventory lot sizeReplenishment Lead timeStock outReorder PointSafety stock
7 – 38
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
7 – 39
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
7 – 40
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)
7 – 41
7 – 42
7 – 43
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
AverageAveragecyclecycleinventoryinventory
QQ——22
Cycle-Inventory LevelsCycle-Inventory Levels
7 – 44
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
7 – 45
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:
7 – 46
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:
7 – 47
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
7 – 48
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:
7 – 49
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
7 – 50
In Class ExampleIn Class Example
7 – 51
In Class ExampleIn Class Example
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In Class Example (In Class Example (continued)continued)
7 – 53
In Class ExampleIn Class Examplecontinuedcontinued
7 – 54
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?