1. Quantitative Review II
ISQS Introduction to Production and Operations Management Spring 2014
Quantitative Review II

2. Taguchi Loss Function
Design the product or service so that it will not be sensitive to variations during the manufacturing or delivery process
For example, design a manufactured good with a smaller design tolerance = better quality

3. Taguchi Loss Function where L(x) = the monetary value of the loss
associated with deviating from the
target limit “T”
k = the constant that translates the
deviation into dollars
x = the actual value of the dimension
T = target limits

4. A quality characteristic has a specification (in inches) of 0. 200  0
A quality characteristic has a specification (in inches) of  If the value of the quality characteristic exceeds by the tolerance of on either side, the product will require a repair of $150. Develop the appropriate Taguchi loss function (k).

5. A quality engineer has a manufacturing specification (in cm) of 0
A quality engineer has a manufacturing specification (in cm) of plus or minus Historical data indicates that if the quality characteristic takes on values larger than .250 cm or smaller than .150 cm, the product fails and a cost of $75 is incurred. Determine the Taguchi Loss Function and estimate the loss for a dimension of cm.

6. Reliability Management
Series product components
Parallel product components

7. The manufacturing of compact disks requires four sequential steps
The manufacturing of compact disks requires four sequential steps. The reliability of each of the steps is 0.96, 0.87, 0.92, and 0.88 respectively. What is the reliability of the process?

8. Parallel/Redundancy B
.91 A C
.98
.97 B
.91

9. Given the diagram below, determine the system reliability if the individual component reliabilities are: A = 0.94, B = 0.92, C = 0.97, and D = 0.93. A D C B
RaRb = 1 - ( )( ) =
RcRd = 1 - ( )( ) =
RabRcd = (0.9952)(0.9979) =

10. The system reliability for a two-component parallel system is 0. 99968
The system reliability for a two-component parallel system is If the reliability of the first component is 0.99, determine the reliability of the second component.
= 1 – (1 – 0.99)(1 – p2)
= 1 – (0.01 – 0.01p2)
–1 = p2
p2 = 0.968

11. More Reliability Question
What is the reliability of this system? If you could add one process (must be one of the existing processes) to best improve reliability what would be the improved reliability? A
0.987 B
0.895 C
0.947 D
0.918

12. More Reliability Question -- Solution
0.987 B
0.895 C
0.947 D
0.918
Reliability = 0.987*0.895*0.947*0.918= 0.768 A
0.987 B
0.895 C
0.947 D
0.918
Parallel B Reliability = 1-( )*( ) = 0.989
System Reliability = 0.987*0.989*0.947*0.918 = 0.849
Improvement = – = 0.08

13. Kanban where: K = the number of Kanban cards
d = the average production rate OR demand of product
p = the processing time
w = the waiting time of Kanban cards
α = safety stock as a %, usually ranging from 0 to 1
C = the capacity of a standard container

14. Computing the number of kanbans: An aspirin manufacturer has converted to JIT manufacturing using Kanban containers. They wish to determine the number of containers at the bottle filling operation which fills at a rate of 400 per hour. Each container holds 35 bottles, it takes 30 minutes to receive more bottles (processing plus delivery time) and safety stock is set at 10%. d = 400 bottles per hour p+w = 30 minutes or 0.5 hour C = 35 bottles per container α = 0.10

15. Location Analysis Methods
Factor Rating Method:
Σ (Factor Weighti * Factor Scorei)
5*10=
2*10=
4*20=
2*20=
2*30=
5*30=
5*10=
3*10=
3*30=
5*30=

16. Location Analysis Methods
Center-of-Gravity Method:
where dix = x-coordinate of location i
diy = y-coordinate of location i
Qi = Quantity of goods moved to or from location i

17. Center-of-Gravity Method
Where would be the best place to put the warehouse?
Location X
coordinate Y
Number of Containers Shipped per Week
Chicago 30
120
2,000
Pittsburgh 90
110
1,000
New York
130
Atlanta 60 40

18. Question 3
A Plus Logistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are Chicago, Pittsburgh, and New York. Which town would be the best place to put the warehouse?

19. Question 3 (Continued)

20. Question 3 -- Solution
(130)(1000) = (130)(1000) =120 Therefore, the best place to put warehouse is Insanity!

21. Location Analysis Methods
Load Distance Model:
Find load distance score by: Calculate the rectilinear distance and multiply by the number of loads

22. Load Distance Score for AB = 45*4 = 180
Load Distance Model
Calculate Rectilinear Distance
Identify Loads, i.e., 4 loads from A to B
Load Distance Score for AB = 45*4 = 180

23. TT Logistics Co. has just signed a contract to deliver products to three locations, and they are trying to decide where to put their new warehouse. The three delivery locations are A, B, and C. The two potential sites for the warehouse are D and E. The total quantity to be delivered to each destination is: 200 to A, 100 to B, and 300 to C. The x, y coordinates for the delivery locations and warehouses are as follows: Where to locate warehouse, D or E?
Location X
coordinate Y
Location A 92 42
Location B 80 40
Location C 90 35
Warehouse D 45
Warehouse E

24. Load Distance Score Warehouse D Distance Loads Score
Location X
coordinate Y
Location A 92 42
Location B 80 40
Location C 90 35
Warehouse D 45
Warehouse E
Load Distance Score
Warehouse D
Distance Loads Score
Location A =
Location B 10+5=
Location C 0+10=
5500
Warehouse E
Location A =
Location B 10+0=
Location C 0+5=
3300

25. Designing Process Layouts
Step 1: Gather information
Space needed, space available, importance of proximity between various units
Step 2: Develop alternative block plans
Using trial-and-error or decision support tools
Step 3: Develop a detailed layout
Consider exact sizes and shapes of departments and work centers including aisles and stairways
Tools like drawing, 3-D models, and CAD software are available to facilitate this process.

26. Process Layout (Step 1: Gather information)
Recovery First Sports Medicine Clinic Layout
(total space 3750 sq.ft.) A
400 sq.ft. B
300 sq.ft. C D
800 sq.ft. E
900 sq.ft. F
1050 sq.ft.

27. Process Layout (Step 2: Develop a block layout)
Current Proposed A
400 sq.ft. B
300 sq.ft. C D
800 sq.ft. E
900 sq.ft. F
1050 sq.ft. A
400 sq.ft. D
800 sq.ft. C
300 sq.ft. E
900 sq.ft. B F
1050 sq.ft.
Proposed layout would require less walking.

28. Load Distance Problem A B C D E F 10 30 15 20 5 25
What is the load distance for this layout?
Trips between departments B A D C E F
Dept. A B C D E F 10 30 15 20 5 25

29. Load Distance Problem A B C D E F 10 30 15 20 5 25 Depts. Trips15 20 5 25
Depts.
Trips
Distance
Score AB 10 1 AC 30 2 60 AD AF 20 BD BE 15 BF 3 45 CD CE CF 5 EF 25
345

30. Assembly Line Balancing
Step 1: Identify task & immediate predecessors
Step 2: Calculate the cycle time
Step 3: Determine the output rate
Step 4: Compute the theoretical minimum number of workstations
Step 5: Assign tasks to workstations (balance the line)
Step 6: Compute efficiency, idle time & balance delay

31. Assembly Line Balancing (Step 1: Identify tasks & immediate predecessors)

32. Layout Calculation
Step 2: Determine cycle time (The amount of time each workstation is allowed to complete its tasks.)
Cycle time = Station A (50 seconds) -- the bottleneck
Step 3: Determine output rate
Step 4: Compute the theoretical minimum number of workstations (number of station needed to achieve 100% efficiency)

33. Assembly Line Balancing (Step 5: Balance the line)
3 Work Stations (A,B), (C,D,G), (E,F,H,I)
55 sec
55 sec
55 sec

34. Assembly Line Balancing (Step 6: Compute efficiency, idle time & balance delay)
Balance Delay = 1 – Assembly Line Efficiency

35. Line Balancing Problem
What is the bottleneck?
What is the maximum production per hour?
What is efficiency and balance delay?
How to minimize work stations?
How should they be groups?
New efficiency? A B C
4.1 mins D
1.6 mins E
2.7 mins F
3.3 mins G
2.6 mins
2.3 mins
3.4 mins

36. Line Balancing Problem
What is the bottleneck?
4.1 minutes
What is the maximum production per hour?
60/4.1 = units/hour
What is efficiency and balance delay?
Efficiency = 20/(7*4.1) = 69.69%
Balance Delay = = 30.31%
How to minimize work stations?
Should we use 4 or 5 work stations?

37. 4 Work Stations Efficiency = 20/(4*6) = 20/24 = 83.3%
Balance delay = = 16.7%
Maximum production/hour = 60/6 = 10 units/hour A B C
4.1 mins D
1.6 mins E
2.7 mins F
3.3 mins G
2.6 mins
2.3 mins
3.4 mins
5.7 mins
6 mins
2.6 mins
5.7 mins

38. 5 Work Stations Efficiency = 20/(5*5.7) = 20/28.5 = 70.18%
Balance delay = = 29.82%
Maximum production/hour = 60/5.7 = units/hour A B C
4.1 mins D
1.6 mins E
2.7 mins F
3.3 mins G
2.6 mins
2.3 mins
3.4 mins
5.7 mins
2.7 mins
4.1 mins
2.6 mins
4.9 mins

39. Should we use 4 or 5 or 7 work stations?
Efficiency = 83.3%
Balance delay = 16.7%
Maximum production/hour = 10 units/hour
5 Work Stations
Efficiency = 70.18%
Balance delay = 29.82%
Maximum production/hour = units/hour
7 Work Stations
Efficiency = 69.69%
Balance delay = 30.31%
Maximum production/hour = units/hour

40. Supply Chain Efficiency
Measuring Cash to Conversion Cycle
Inventory Turnover (IT)
Inventory Days’ Supply (IDS)
Accounts Receivable Turnover (ART)
Accounts Receivable Days’ Supply (ARDS)
Accounts Payable Turnover (APT)
Accounts Payable Days’ Supply (APDS)
Cash-to-Cash Conversion Cycle = IDS + ARDS - APDS

41. Inventory Ratios Inventory Turnover (IT):
# of times you turn your inventory annually
Inventory Days’ Supply (IDS):
how many days inventory you keep

42. Accounts Receivable Ratios
Accounts Receivable Turnover (ART):
# of times you turn your accts. rec. annually
Accounts Receivable Days’ Supply (ARDS):
how long it takes to get $ owed paid to you

43. Accounts Payable Ratios
Accounts Payable Turnover (APT):
# of times you turn your accts. payable annually
Accounts Payable Days’ Supply (APDS):
how long you take to pay your bills

44. Dell’s Financial data Revenue $35.40 billions
Cost of goods sold $29.10 billions
Average Inventory Value $0.306 billions
Average Accounts Receivable $2.586 billions
Average Accounts Payable $5.989 billions

45. Dell’s Example
Dell’s Inventory Turnover
Dell’s Inventory Days’ Supply

46. Dell’s Example Dell’s Accounts Receivable Turnover
Dell’s Accounts Receivable Days’ Supply

47. Dell’s Example Dell’s Accounts Payable Turnover
Dell’s Accounts Payable Days’ Supply

48. Dell’s Example Dell’s Cash-to-Cash Conversion Cycle
= IDS + ARDS – APDS
= 3.84 days days – days
= days
The negative value means that Dell receives customers’ payments (accounts receivable) days, on average, before Dell has to pay its suppliers (accounts payable).
This means that Dell’s value chain is a self-funding cash model.

49. Dell’s Negative Cash-to-Cash Conversion Cycle

50. Breakeven Analysis (Make/Buy Decision)
Total Cost of Outsourcing:
Total Cost of Insourcing:
Indifference Point:

51. The Bagel Shop Problem Jim & John plan to open a small bagel shop.
The local baker has offered to sell them bagels at 50 cents each. However, they will need to invest $2,000 in bread racks to transport the bagels back and forth from the bakery to their store.
Alternatively, they can bake the bagels at their store for 20 cents each if they invest $20,000 in kitchen equipment.
They expect to sell 80,000 bagels each year.
What should they do?

52. The Bagel Shop Problem
Indifference Point Calculation:

53. The Bagel Shop Problem Make vs Buy Decision at 80,000 bagels
Outsource (Buy) In House (Make)
$2,000+($.5*80,000) $20,000+($.2*80,000)
= $42, = $36,000
Make vs Buy Decision at 50,000 bagels
$2,000+($.5*50,000) $20,000+($.2*50,000)
= $27, = $30,000
If the demand is lower than the indifference point, outsourcing is a cheaper alternative, and vice versa.

54. That’s all, folks!
Good Luck!