1. MGT 657 operations management Lecture 6b

2. Managing Constraints Constraints are factors that limit performance
Three types of constraints
Physical (e.g. machine, labor, material shortages)
Market (e.g. demand is less than capacity)
Management (e.g. policy, metrics, mind-sets etc)
A bottleneck is any resource whose capacity limits the organization’s ability to meet volume, mix, or fluctuating demand requirements

3. Managing Constraints
Bottlenecks can both be internal or external to the firm and are typically a process or step with the lowest capacity
Throughput time is the total elapsed time from the start to the finish of a job or a customer being processed at one or more work-centers
A bottleneck can be identified in several different ways
If it has the highest total time per unit processed
If it has the highest average utilization and total workload
If a reduction of processing time would reduce the average throughput time for the entire process

4. Bottleneck Analysis and the Theory of Constraints
The bottleneck time is the time of the slowest workstation (the one that takes the longest) in a production system
The throughput time is the time it takes a unit to go through production from start to end
2 min/unit
4 min/unit
3 min/unit A B C

5. Capacity Analysis Two identical sandwich lines
Lines have two workers and three operations
All completed sandwiches are wrapped
Wrap/
Deliver
37.5 sec/sandwich
Order
30 sec/sandwich
Bread
Fill
15 sec/sandwich
20 sec/sandwich
Toaster

6. Capacity Analysis
Wrap/
Deliver
37.5 sec
Order
30 sec
Bread
Fill
15 sec
20 sec
Toaster
The two lines each deliver a sandwich every 20 seconds
At 37.5 seconds, wrapping and delivery has the longest processing time and is the bottleneck
Capacity per hour is 3,600 seconds/37.5 seconds/sandwich = 96 sandwiches per hour
Throughput time is = seconds

7. Capacity Analysis Standard process for cleaning teeth
Cleaning and examining X-rays can happen simultaneously
Check out
6 min/unit
Check in
2 min/unit
Develops X-ray
4 min/unit
8 min/unit
Dentist
Takes X-ray
5 min/unit
X-ray exam
Cleaning
24 min/unit

8. Capacity Analysis All possible paths must be compared
Check out
6 min/unit
Check in
2 min/unit
Develops X-ray
4 min/unit
8 min/unit
Dentist
Takes X-ray
5 min/unit
X-ray exam
Cleaning
24 min/unit
All possible paths must be compared
Bottleneck is the hygienist at 24 minutes
Hourly capacity is 60/24 = 2.5 patients
X-ray exam path is = 27 minutes
Cleaning path is = 46 minutes
Longest path involves the hygienist cleaning the teeth, patient should complete in 46 minutes

9. Bottleneck Management
Release work orders to the system at the pace of set by the bottleneck
Lost time at the bottleneck represents lost time for the whole system
Increasing the capacity of a non-bottleneck station is a mirage
Increasing the capacity of a bottleneck increases the capacity of the whole system

10. Theory of Constraints
Five-step process for recognizing and managing limitations
Step 1: Identify the constraints (bottlenecks)
Step 2: Develop a plan for overcoming the constraints
Step 3: Focus resources on accomplishing Step 2
Step 4: Reduce the effects of constraints by offloading work or expanding capability
Step 5: Once overcome, go back to Step 1 and find new constraints

11. Identifying the Bottleneck
EXAMPLE 1 Managers at the First Community Bank are attempting to shorten the time it takes customers with approved loan applications to get their paperwork processed. The flowchart for this process, consisting of several different activities, each performed by a different bank employee, is shown in Figure 1. Approved loan applications first arrive at activity or step 1, where they are checked for completeness and put in order. At step 2, the loans are categorized into different classes according to the loan amount and whether they are being requested for personal or commercial reasons. While credit checking commences at step 3, loan application data are entered in parallel into the information system for record-keeping purposes at step 4. Finally, all paperwork for setting up the new loan is finished at step 5. The time taken in minutes is given in parentheses.

12. Identifying the Bottleneck
Check for credit rating (15 min)
Complete paperwork for new loan (10 min)
Check loan documents and put them order (15 min)
Categorize loans (20 min)
Enter loan application into the system (12 min)
Processing Credit Loan Applications at First Community Bank
Which single step is the bottleneck? The management is also interested in knowing the maximum number of approved loans this system can process in a 5-hour work day.

13. Identifying the Bottleneck
SOLUTION We define the bottleneck as step 2, where a single-minute reduction in its time reduces the average throughput time of the entire loan approval process. The throughput time to complete an approved loan application is max(15, 12) + 10 = 60 minutes. Although we assume no waiting time in front of any step, in practice such a smooth process flow is not always the case. So the actual time taken for completing an approved loan will be longer than 60 minutes due to nonuniform arrival of applications, variations in actual processing times, and the related factors.
The capacity for loan completions is derived by translating the “minutes per customer” at the bottleneck step to “customer per hour.” At First Community Bank, it is 3 customers per hour because the bottleneck step 2 can process only 1 customer every 20 minutes (60/3).

14. Identifying the Bottleneck
Services may not have simple line flows and demand may vary considerably
Bottlenecks can be identified by using average utilization
Variability creates floating bottlenecks
Variability increases complexity

15. Identifying the Bottleneck
EXAMPLE 2 Two types of customers enter Barbara’s Boutique shop for customized dress alterations. After T1, Type A customers proceed to step T2 and then to any of the three workstations at T3, followed by steps T4 and T7. After step T1,Type B customers proceed to step T5 and then steps T6 and T7. The numbers in the parentheses are the minutes it takes that activity to process a customer.
a. What is the capacity per hour of Type A customers?
b. If 30 percent of the customers are Type A customers and 70 percent are Type B customers, what is the average capacity?
c. When would Type A customers experience waiting lines, assuming there are no Type B customers in the shop? Where would Type B customers have to wait, assuming no Type A customers?

16. Identifying the Bottleneck
(12) T7
(10) T4
(18)
T3-a
(14)
T3-c
(11)
T3-b
Type
A or B?
Type A
Type B T2
(13) T6
(22) T5
(15)
a. For Type A customers, step T2 can process (60/13) = 4.62 customers per hour. T3 has three work stations and a capacity of (60/14) + (60/10) + (60/11) = customer per hour. Step T4 can process (60/18) = 3.33 customers per hour. The bottleneck for type A customers is the step with the highest processing time per customer, T4.

17. Identifying the Bottleneck
(12) T7
(10) T4
(18)
T3-a
(14)
T3-c
(11)
T3-b
Type
A or B?
Type A
Type B T2
(13) T6
(22) T5
(15)
b. The bottleneck for Type B customers is T6 since it has the longest processing time per customer. The capacity for Type B customers is (60/22) = 2.73 customers per hour. Thus the average capacity is 0.3(3.33) + 0.7(2.73) = 2.9 customers per hour

18. Identifying the Bottleneck
(12) T7
(10) T4
(18)
T3-a
(14)
T3-c
(11)
T3-b
Type
A or B?
Type A
Type B T2
(13) T6
(22) T5
(15)
c. Type A customers would wait
before T2 and T4 because the activities immediately preceding them have a higher rate of output.
Type B customers would wait
before steps T5 and T6 for the same reason. This assumes there are always new customers entering the shop.

19. Identifying the Bottleneck
EXAMPLE 3 Diablo Electronics manufactures four unique products (A, B, C, and D) that are fabricated and assembled in five different workstations (V, W, X, Y, and Z) using a small batch process. Each workstation is staffed by a worker who is dedicated to work a single shift per day at an assigned workstation. Batch setup times have been reduced to such an extent that they can be considered negligible. Figure 1 is a flowchart of the manufacturing process. Diablo can make and sell up to the limit of its demand per week, and no penalties are incurred for not being able to meet all the demand. Which of the five workstations (V, W, X, Y, or Z) has the highest utilization, and thus serves as the bottleneck for Diablo Electronics?

20. Identifying the Bottleneck
Product A $5
Raw materials
Purchased parts
Product: A
Price: $75/unit
Demand: 60 units/wk
Step 1 at workstation V (30 min)
Finish with step 3 at workstation X (10 min)
Step 2 at workstation Y (10 min)
Product B
Raw materials
Purchased parts
Product: B
Price: $72/unit
Demand: 80 units/wk
Finish with step 2 at workstation X (20 min)
Step 1 at workstation Y (10 min) $3 $2
Product C
Raw materials
Purchased parts
Product: C
Price: $45/unit
Demand: 80 units/wk
Finish with step 4 at workstation Y (5 min)
Step 2 at workstation Z (5 min)
Step 3 at workstation X (5 min)
Step 1 at workstation W (5 min) $2 $3
Product D
Raw materials
Purchased parts
Product: D
Price: $38/unit
Demand: 100 units/wk $4
Step 2 at workstation Z (10 min)
Finish with step 3 at workstation Y (5 min)
Step 1 at workstation W (15 min) $6
Figure 1 Flowchart for Products A, B, C, and D

21. Identifying the Bottleneck
SOLUTION Because the denominator in the utilization ratio is the same for every workstation, with one worker per machine at each step in the process, we can simply identify the bottleneck by computing aggregate workloads at each workstation.
The firm wants to satisfy as much of the product demand in a week as it can. Each week consists of 2,400 minutes of available production time. Multiplying the processing time at each station for a given product with the number of units demanded per week yields the workload represented by that product. These loads are summed across all products going through a workstation to arrive at the total load for the workstation, which is then compared with the others and the existing capacity of 2,400 minutes.

22. Identifying the Bottleneck
Workstation
Load from Product A
Load from Product B
Load from Product C
Load from Product D
Total Load (min) V W X Y Z

23. Identifying the Bottleneck
Workstation
Load from Product A
Load from Product B
Load from Product C
Load from Product D
Total Load (min) V W X Y Z
60  30 = 1800
1,800
80  5 = 400
100  15 = 1,500
1,900
60  10 = 600
80  20 = 1,600
80  5 = 400
2,600
80  10 = 800
100  5 = 500
2,300
100  10 = 1,000
1,400
These calculations show that workstation X is the bottleneck, because the aggregate work load at X exceeds the available capacity of 2,400 minutes per week.

24. Identifying the Bottleneck
EXAMPLE 4 O’Neill Enterprises manufactures three unique products (A, B, C) that are fabricated and assembled in four different workstations (W, X, Y, Z) using a small batch process. Each of the products visits every one of the four workstations, though not necessarily in the same order. Batch setup times are negligible. A flowchart of the manufacturing process is shown below. O’Neill can make and sell up to the limit of its demand per week, and there are no penalties for not being able to meet all the demand. Each workstation is staffed by a worker dedicated to work on that workstation alone, and is paid $12 per hour. Variable overhead costs are $8000/week. The plant operates one 8-hour shift per day, or 40 hours/week. Which of the four workstations W, X, Y, or Z has the highest total workload, and thus serves as the bottleneck for O’Neill Enterprises?

25. Identifying the Bottleneck
Flowchart for Products A, B, and C
Product A
Raw materials
Purchased part
Product: A
Price: $90/unit
Demand: 65 units/wk
Finish with step 4 at workstation Z (16 min)
Step 2 at workstation Y (15 min)
Step 3 at workstation X (9 min)
Step 1 at workstation W (10 min) $7 $6
Product B
Raw materials
Purchased part
Product: B
Price: $85/unit
Demand: 70 units/wk
Finish with step 4 at workstation Z (13 min)
Step 2 at workstation W (10 min)
Step 3 at workstation Y (10 min)
Step 1 at workstation X (12 min) $9 $5
Product C
Raw materials
Purchased part
Product: C
Price: $80/unit
Demand: 80 units/wk
Finish with step 4 at workstation Z (10 min)
Step 2 at workstation X (10 min)
Step 3 at workstation W (12 min)
Step 1 at workstation Y (5 min)
$10 $5

26. Identifying the Bottleneck
SOLUTION Identify the bottleneck by computing total workload at each workstation. The firm wants to satisfy as much of the product demand in a week as it can. Each week consists of 2400 minutes of available production time. Multiplying the processing time at each station for a given product with the number of units demanded per week yields the capacity load. These loads are summed across all products going through that workstation and then compared with the existing capacity of 2400 minutes.

27. Identifying the Bottleneck
Work Station
Load from Product A
Load from Product B
Load from Product C
Total Load (minutes) W X Y Z

28. Identifying the Bottleneck
Work Station
Load from Product A
Load from Product B
Load from Product C
Total Load (minutes) W X Y Z
(65x10)= 650
(7010)= 700
(8012)= 960
2310
(659)= 585
(7012)= 840
(8010)= 800
2225
(6515)= 975
(70x10)= 700
(80x5)= 400
2075
(6516)= 1040
(7013)= 910
(8010)= 800
2750
These calculations show that workstation Z is the bottleneck, because the aggregate work load at Z exceeds the available capacity of 2400 minutes per week.

29. Product Mix Decisions
Example 4 cont. – Application of Theory of Constraints The senior management at O’Neill Enterprises wants to improve the profitability of the firm by accepting the right set of orders. Currently, decisions are made to accept as much of the highest contribution margin product as possible (up to the limit of its demand), followed by the next highest contribution margin product, and so on until no more capacity is available. Since the firm cannot satisfy all the demand, the product mix must be chosen carefully. Jane Hathaway, the newly hired production supervisor, is knowledgeable about the theory of constraints and bottleneck based scheduling. She believes that profitability can indeed be approved if bottleneck resources were exploited to determine the product mix. What is the change in profits if instead of the traditional method that O’Neill has used thus far; a bottleneck based approach advocated by Jane is used instead for selecting the product mix?

30. Product Mix Decisions
SOLUTION Decision rule 1: Traditional method - Select the best product mix according to the highest overall profit margin of each product.
Step 1: Calculate the profit margin per unit of each product as shown below A B C
Price
Raw Material & Purchased Parts
Labor
= Contribution Profit Margin

31. Product Mix Decisions
SOLUTION Decision rule 1: Traditional method - Select the best product mix according to the highest overall profit margin of each product.
Step 1: Calculate the profit margin per unit of each product as shown below A B C
Price
Raw Material & Purchased Parts
Labor
= Contribution Profit Margin
$90.00
$85.00
$80.00
–13.00
–14.00
–15.00
–10.00
–9.00
–7.40
$67.00
$62.00
$57.60
When ordering from highest to lowest, the profit margin per unit order of these products is ABC.

32. Product Mix Decisions
Step 2: Allocate resources W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation Z) is encountered. Subtract minutes away from 2400 minutes available for each week at each stage.
Work Center
Starting
After 65 A
After 70 B
Can Only Make 45 C W X Y Z

33. Product Mix Decisions
Step 2: Allocate resources W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation Z) is encountered. Subtract minutes away from 2400 minutes available for each week at each stage.
Work Center
Starting
After 65 A
After 70 B
Can Only Make 45 C W X Y Z
2400
1750
1050
510
2400
1815
975
525
2400
1425
725
500
1360
450
The best product mix is 65 A, 70 B, and 45 C

34. Product Mix Decisions
Step 3: Compute profitability for the selected product mix.
Profits
Revenue
Materials
Overhead
Labor
Profit

35. Product Mix Decisions
Step 3: Compute profitability for the selected product mix.
Profits
Revenue
Materials
Overhead
Labor
Profit
$15400
–$2500
–$8000
–$1920
$2980
Manufacturing the product mix of 65 A, 70 B, and 45 C will yield a profit of $2980.

36. Contribution Margin per minute
Product Mix Decisions
Decision rule 2: Bottleneck-based approach - Select the best product mix according to the dollar contribution per minute of processing time at the bottleneck workstation Z (get the most dollar benefit from the bottleneck).
Step 1: Calculate the contribution/minute of processing time at bottleneck workstation Z:
Product A
Product B
Product C
Contribution Margin
Time at Bottleneck
Contribution Margin per minute

37. Contribution Margin per minute
Product Mix Decisions
Decision rule 2: Bottleneck-based approach - Select the best product mix according to the dollar contribution per minute of processing time at the bottleneck workstation Z (get the most dollar benefit from the bottleneck).
Step 1: Calculate the contribution/minute of processing time at bottleneck workstation Z:
Product A
Product B
Product C
Contribution Margin
Time at Bottleneck
Contribution Margin per minute
$67.00
$62.00
$57.60
16 minutes
13 minutes
10 minutes
4.19
4.77
5.76
When ordering from highest to lowest contribution margin/minute at the bottleneck, the manufacturing sequence of these products is CBA, which is reverse of the traditional method order.

38. Product Mix Decisions
Step 2: Allocate resources W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation Z) is encountered. Subtract minutes away from 2400 minutes available for each week at each stage.
Work Center
Starting
After 80 C
After 70 B
Can Only Make 43 A W X Y Z

39. Product Mix Decisions
Step 2: Allocate resources W, X, Y, and Z to the products in the order decided in step 1. Satisfy each demand until the bottleneck resource (workstation Z) is encountered. Subtract minutes away from 2400 minutes available for each week at each stage.
Work Center
Starting
After 80 C
After 70 B
Can Only Make 43 A W X Y Z
2400
1440
740
310
2400
1600
760
373
2400
2000
1300
655
1600
690 2
The best product mix is 43A, 70B, and 80C

40. Product Mix Decisions
Step 3: Compute profitability for the selected product mix. The new profitability figures are shown below based on the new production quantities of 43A, 70B, and 80C.
Profits
Revenue
Materials
Overhead
Labor
Profit

41. Product Mix Decisions
Step 3: Compute profitability for the selected product mix. The new profitability figures are shown below based on the new production quantities of 43A, 70B, and 80C.
Profits
Revenue
Materials
Overhead
Labor
Profit
$16220
–$2739
–$8000
–$1920
$3561
Manufacturing the product mix of 43 A, 70 B, and 80 C will yield a profit of $3561.

42. Solved Problem 1
Bill’s Car Wash offers two types of washes: Standard and Deluxe. The process flow for both types of customers is shown in the following chart. Both wash types are first processed through steps A1 and A2. The Standard wash then goes through steps A3 and A4 while the Deluxe is processed through steps A5, A6, and A7. Both offerings finish at the drying station (A8). The numbers in parentheses indicate the minutes it takes for that activity to process a customer. A3
(12)
Standard A4
(15) A8
(10)
Standard or Deluxe A1
(5) A2
(6) A5
(5)
Deluxe A6
(20) A7
(12)

43. Solved Problem 1
a. Which step is the bottleneck for the Standard car wash process? For the Deluxe car wash process? b. What is the capacity (measured as customers served per hour) of Bill’s Car Wash to process Standard and Deluxe customers? Assume that no customers are waiting at step A1, A2, or A8. c. If 60 percent of the customers are Standard and 40 percent are Deluxe, what is the average capacity of the car wash in customers per hour? d. Where would you expect Standard wash customers to experience waiting lines, assuming that new customers are always entering the shop and that no Deluxe customers are in the shop? Where would the Deluxe customers have to wait, assuming no Standard customers?

44. Solved Problem 1
SOLUTION a. Step A4 is the bottleneck for the Standard car wash process, and Step A6 is the bottleneck for the Deluxe car wash process, because these steps take the longest time in the flow.
b. The capacity for Standard washes is 4 customers per hour because the bottleneck step A4 can process 1 customer every 15 minutes (60/15). The capacity for Deluxe car washes is 3 customers per hour (60/20). These capacities are derived by translating the “minutes per customer” of each bottleneck activity to “customers per hour.”
c. The average capacity of the car wash is (0.60  4) + (0.40  3) = 3.6 customers per hour.

45. Solved Problem 1
d. Standard wash customers would wait before steps A1, A2, A3, and A4 because the activities that immediately precede them have a higher rate of output (i.e., smaller processing times). Deluxe wash customers would experience a wait in front of steps A1, A2, and A6 for the same reasons. A1 is included for both types of washes because the arrival rate of customers could always exceed the capacity of A1.