The Theory of Constraints and Throughput Accounting, Version 1.0
Solutions to Assigned Homework
1. Solutions to self-test questions.
c. The drum-buffer-rope system is used to manage production schedules around a constraint. The drum
communicates the speed of the constraint so that all processes can coordinate their efforts to coincide
with the production constraint. The rope keeps all processes in front of the constraint from getting too
far ahead. And finally, the buffer in front of the constraint should include just enough WIP inventory
to handle any typical halts that potentially could hinder the production of the constraint.
d. The five steps in the TOC process are:
1. Identify the system’s constraint(s).
2. Decide how to exploit the constraint(s).
3. Subordinate everything else to the above decision.
4. Elevate the constraint(s).
5. If the constraint has been broken, go back to step 1.
e. Process
Policy
Logistic
Material
Market
h.
Not enough workers to complete a process
One machine is slower than all others
Overtime freeze
Purchasing restriction
Specified batch sizes
Particular processing sequence
Mining regulations
Freeze in Florida
Obsolete product
Downtrend in the economy
Throughput accounting is used to support a very specific managerial view of an operation—the
implementation of TOC in an organization. The focal point of throughput accounting is on the
incremental value of more effective employment of a constraint. The focus is very short-term.
Throughput accounting does not necessarily provide data useful for long-term strategic planning
objectives.
o. Benefit: Avoids local optimization. The system will not succeed if one or more individual processes
are continually being rewarded for optimizing individual production. However, throughput accounting
helps avoid such sub-optimization by encouraging cooperation to accomplish the organization’s profit
goals.
Benefit: Improves communication between departments. The focus of everyone must be on the
large-scale needs of the organization. This is not possible if communication is hindered or nonexistent. Throughput accounting uses the Drum-Buffer-Rope process as a communication vehicle
throughout the organization.
Potential conflict: Excessive budget cuts. When implementing throughput accounting, management
must be careful not to reduce the flexibility of non-bottlenecks through excessive budget cuts. This
can also harm morale, thus decreasing productivity.
Potential conflict: Lack of focus on non-bottlenecks. All processes must be continually improving
if the organization as a whole is to succeed. Accountants implementing a throughput system need to
include performance measures specific to non-bottlenecks that encourage continuous improvement.
Potential conflict: Short-run behavior affecting strategy. One risk of using a very short-term view
of operations (such as throughput accounting or contribution margin analysis) is that the organization
may be incrementally make decisions with strategic consequences without consciously evaluating the
long-term effects of those day-to-day operating decisions.
Theory of Constraints, Version 1.0—page 1 of 8
p. Traditionally, the focus has been on keeping workers busy. However, under TOC, the focus is on
identifying what the customer wants, then managing operations to ensure customer needs are
satisfied—regardless of the effect on variances.
2.
Revenues:
Materials
$
400
x 50 units $
$100
x 50 units
Throughput
Salaries, insurance, taxes
Supplies
Miscellaneous
Income
(5,000)
$
15,000
$
750
200
2,200
$
3,150
Operating Expense
Throughput
Operating Expense
20,000
$
15,000
(3,150)
$
11,850
5.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
Constraint Type
Constraint Category
Material
External
Policy
Internal
Market
External
Market
External
Market
External
Policy
Internal
Process
Internal
Process
Internal
Material
External
Policy
Internal
Process
Internal
Policy
External*
Policy
Internal
*Note this exception as policy constraints are typically internal to the organization.
7.
Throughput accounting systems are a dramatic departure from classic standard cost systems. One
example of this departure is the contrast between how throughput accounting and standard cost
systems handle measures of efficiency. Standard cost systems are typically focused on maximizing the
efficiency (i.e., output) of each work cell or operation within the organization. Producing less than the
work cell capacity results in unfavorable efficiency variances. In contrast, throughput accounting is
focused on maximizing the efficiency of the total system. Since the capacity of the total system is
limited by the bottleneck operation, then efficiency variances are only appropriate when applied to the
bottleneck operation(s).
Theory of Constraints, Version 1.0—page 2 of 8
One could appropriately compute an efficiency variance on non-bottleneck operations if the capacity
used in the efficiency variance computation is based on the actual capacity of the bottleneck operation,
not the capacity of the non-bottleneck operation. Other potential non-bottleneck performance
measures could involve:
1) Identifying how often the bottleneck operation had to wait for the non-bottleneck (measured in
time),
2) Calculating the product defects in products or services being produced at the non-bottleneck (its
excess capacity should allow a greater focus on high-quality output),
3) Minimizing or eliminating all inventory currently in place to support the non-bottleneck,
Workers at non-bottleneck operations could also be measured on their ability to perform other
functions during downtime that are not directly related to their production operation. These functions
could include cross training on other machines or operations and developing improvements in costs or
quality at their own operation.
12.
Demand in Units
Selling Price/Unit
Material Cost/Unit
Throughput Contribution/Unit
Bicycles Skateboards
unlimited
unlimited
$
95.00 $
65.00
40.00
25.00
$
55.00 $
40.00
Resource minutes required per unit
Bicycles Skateboards
Gordy
10
10
Kelly
15
20
David
8
15
Beckie
10
20
Resource minutes for an assumed demand (minutes/unit x demand)
Assume a demand of 75 units each for Bicycles and Skateboards
Total
%Capacity
Resources (Capacity is
Bicycles Skateboards
Needed
2,400 min.)
Gordy
750
750
1,500
63%
Kelly
1,125
1,500
2,625
109%
David
600
1,125
1,725
72%
Beckie
750
1,500
2,250
94%
* Based on this analysis, Kelly appears to be the constraining operation.
Based on her minutes per unit, throughput per constraint minute is:
Bicycles Skateboards
$
3.67 $
2.00
Decision: Make all possible Bicycles, then make Skateboards with any remaining resources
Total minutes available from Kelly
2,400minutes
Divided by minutes of Kelly needed per Bicycle
15minutes
Equals the number of Bicycles to make
160units
Bogeeta should make 160 Bicycles and no Skateboards
Theory of Constraints, Version 1.0—page 3 of 8
Profitability Analysis
Production in units
Throughput/unit
Bicycles Skateboards
160
$
55 $
40
Total throughput
$
8,800 $
Less Operating Expenses
$
8,800
6,000
$
2,800
Net Profit/Loss
13.
-
Total
Errata Note: The solution provided in Part 2 below assumes an export price per bike of $75.00 (not $50.00).
It is recommended that the instructor adjust Problem 13 to reflect an export price of $75.00 since the solution
to Part 2 based on an export price of $50.00 is no different from the solution to Part 1.
Teaching Note: The previous solution to Problem #12 indicates that Kelly is the bottleneck. Given that her
throughput per constraint minute is $3.67 for bicycles and $2.00 for skateboards, the previous solution (based
on unlimited demand for bicycles) indicates that all of the Kelly's resources should be dedicated to producing
the maximum number of bicycles. The resulting calculation suggests that 160 bikes and no skateboards will
be produced. Optimal profit in the unlimited demand scenario is $2,800 (the solution to Problem #12 can be
reviewed for specific calculations).
Part 1
Demand in Units
Selling Price/Unit
Material Cost/Unit
Throughput Contribution/Unit
Bicycles
Skateboards
110
50
$
95.00 $
65.00
40.00
25.00
$
55.00 $
40.00
Resource minutes required per unit
Bicycles
Skateboards
(110 units)
(50 units)
Gordy
10
10
Kelly
15
20
David
8
15
Beckie
10
20
Total resource minutes based on demand (minutes/unit x demand)
Total
%Capacity
Bicycles
Skateboards Resources
(Capacity is
(110 units)
(50 units)
Needed
2,400 min.)
Gordy
1,100
500
1,600
67%
Kelly
1,650
1,000
2,650
110%
David
880
750
1,630
68%
Beckie
1,100
1,000
2,100
88%
* Kelly continues to be the constraining operation
Based on her minutes per unit, throughput per constraint minute is:
Bicycles
Skateboards
Theory of Constraints, Version 1.0—page 4 of 8
$
3.67 $
2.00
Decision: Make all possible bicycles, then make skateboards with any remaining resources
Total minutes available from Kelly
2,400minutes
Less # of minutes for bicycles (110 units x 15 minutes)
-1,650minutes
Minutes available for skateboards
750minutes
Divided by minutes of Kelly needed per skateboard
20minutes
Equals the number of skateboards possible to make
37.5units
Decision: Bogeeta should make 110 Bicycles and 37 Skateboards
Profitability Analysis
Production in units
Throughput/unit
Total throughput
Less Operating Expenses
Net Profit/Loss
Bicycles
Skateboards
110
37
$
55 $
40
$
6,050 $
1,480
Total
$
$
Part 2
Demand in Units
Selling Price/Unit
Material Cost/Unit
Throughput Contribution/Unit
7,530
6,000
1,530
Bicycles
Bicycles
(local)
(Export)
110
unlimited
$
95.00 $
75.00
40.00
40.00
$
55.00 $
35.00
Skateboards
50
$
65.00
25.00
$
40.00
* The calculations for Part 1 are relevant. Kelly is still the constraining resource
Based on her minutes per unit, throughput per constraint minute is:
Bicycles
Bicycles
(local)
(Export)
Skateboards
Throughput
$
3.67 $
2.33 $
2.00
Decision: Make all possible bicycles for local sale, then make bicycles for export with any remaining resources
Total minutes available from Kelly
2,400minutes
Less # of minutes for local bicycles (110 units x 15 minutes)
-1,650minutes
Minutes available for export bicycles
750minutes
Divided by minutes of Kelly needed per bicycle
15minutes
Equals the number of export bicycles possible to make
50units
Decision: Bogeeta should make 110 bicycles for local sale, 50 bicycles for export, and no skateboards
Profitability Analysis
Production in units
Throughput/unit
Total throughput
Less Operating Expenses
Net Profit/Loss
Bicycles
Bicycles
(local)
(Export)
Skateboards
110
50
$
55 $
35 $
40
$
6,050 $
1,750 $
-
Theory of Constraints, Version 1.0—page 5 of 8
Total
$
$
7,800
6,000
1,800
Note that in Part 1 Profit is $1,530 and in Part 2 Profit is $1,800. What causes the Profit to rise? [Answer: The
opportunity to more profitably use Kelly's constraint minutes to produce bicycles for export ($2.33 per minute)
versus skateboards ($2.00 per minute).
You should also ask yourself why Profit in Problem #12 was so much higher than in Problem #13 ($2,800
versus $1,530 or $1,800)? [Answer: the limited market demand in Problem #13 is creating a market constraint
requiring
Kelly to use her slack minutes to produce
14. Part
1
5 inch less
TV profitable
6 inchproducts.]
TV
3 inch TV
Weekly Demand in Units
1,750
1,250
500
Selling Price/Unit
$
190.00 $
200.00 $
100.00
Material Cost/Unit
100.00
80.00
60.00
Throughput Contribution/Unit
$
90.00 $
120.00 $
40.00
Resource minutes required per unit
5 inch TV
6 inch TV
Machine A
2
0
Machine B
1.5
1.8
Machine C
0.5
1.3
3 inch TV
1.5
0
3
Total resource minutes based on demand (minutes/unit x demand)
Total
Resources
5 inch TV
6 inch TV
3 inch TV
Needed
Machine A
3,500
750
4,250
Machine B
2,625
2,250
4,875
Machine C
875
1,625
1,500
4,000
%Capacity
(Capacity is
4,800 min.)
89%
102%
83%
* Machine B appears to be the constraining operation
Throughput per constraint (Machine B) minute is:
5 inch TV
6 inch TV
3 inch TV
$
60.00 $
66.67
'N/A (division by 0)
Decision:6 inch TVs should have bottleneck priority over 5 inch TVs.
3 inch TVs can be made without using bottleneck resources.
Total minutes available from Machine B
Less # of minutes for 6 inch TVS (1250 units x 1.8 minutes)
Minutes available for 5 inch TVS
Divided by minutes of Machine B needed per 5 inch TV
Equals the number of 5 inch TVs possible to make
4,800minutes
-2,250minutes
2,550minutes
1.5minutes
1,700units
* Machine C appears to be the constraining operation for 3 inch TVs
Total minutes available from Machine C
Less # of minutes for 6 inch TVS (1250 units x 1.3 minutes)
Less # of minutes for 5 inch TVS (1700 units x 0.5 minutes)
Remaining Machine C resources
Divided by minutes of Machine C needed per 3 inch TV
Equals the number of 3 inch TVs possible to make
Market demand in 3 inch TVs
4,800minutes
-1,625minutes
-850minutes
2,325minutes
3minutes
775units
500units
Theory of Constraints, Version 1.0—page 6 of 8
Decision: The Rochester plant should make 1700 5 inch TVs, 1250
6 inch TVs, and 500 3 inch TVs (based on limited market demand)
Profitability Analysis
Production in units
Throughput/unit
Total throughput
Less Operating Expenses
Net Profit/Loss
Part 2
Actual Prod.
5 inch TV
1,700
units
5 inch TV
6 inch TV
3 inch TV
1,700
1,250
500
$
90 $
120 $
40
$
153,000 $
150,000 $
20,000
Total
$ 323,000
267,000
$ 56,000
6 inch TV
3 inch TV
1,250
500
units
units
Actual
Minutes
Minutes
Minutes
Total Min.
Operating
Allowed*
Allowed*
Allowed*
Allowed
Minutes
Min/Mach A
3,400
750
4,150
4,572
Min/Mach B
2,550
2,250
4,800
4,856
Min/Mach C
850
1,625
1,500
3,975
4,402
Minutes Allowed* = Actual Production x Standard minutes per TV unit
Min/Mach A
Min/Mach B
Min/Mach C
Volume
Capacity
(in minutes)
4,800
4,800
4,800
Actual
Operating
Minutes
4,572
4,856
4,402
Efficiency
Variance
(Unfavorable)
(422) minutes
(56) minutes
(427) minutes
Excess
Capacity
(minutes)
228
(56)
398
With respect to the efficiency variances, it appears that all three machines are performing inefficiently. In
particular, Machines A and C are generating very large unfavorable variances. However, Rochester
management must be cautious to not "over interpret" these two variances. Remember that Machine B is the
designated bottleneck operation. The process view of a TOC system recommends that the main function of
all nonbottleneck operations is to support the efficient and effective output of the bottleneck operation (Step 3
of the five-step TOC process). In the short run, the output capacity and costs of all operations are fixed.
Hence, Machines A and C have 4,800 minutes during any two-week production period to support the
bottleneck operation at Machine B. The fact that Machine A (Machine B) used 422 (427) more minutes than
was minimally required to construct the all the TV units produced during the last two weeks is not a cause for
concern. The logic for this lack of concern is that both of these machines still had excess capacity (228
minutes on Machine A and 398 minutes on Machine C) and that operating costs are fixed. These efficiency
variances have not cost Rochester any money! On the other hand, the last two weeks' work at the Machine B
operation also resulted in a small unfavorable efficiency variance. Further, since Machine B was scheduled to
work at capacity, this efficiency variance resulted in Machine B being used past its normal capacity.
Management at the Rochester plant apparently had to schedule about 56 minutes of overtime on Machine B to
complete the expected production output. Although this is a small variance, Rochester management may
want to carefully evaluate its cause. Likely the variance is the result of two potential problems. One problem
may be that Machine B is actually operating inefficiently. Management should then invest effort into
improving the Machine B operation. On the other hand, Machine B may have been idle while waiting for
availability of raw materials (see the diagram in Part 1 of the original problem). In this case, Rochester is at
risk of losing throughput. In this case, management should spend some effort on better managing suppliers
and the buffer inventories in front of Machine B.
Theory of Constraints, Version 1.0—page 7 of 8
Theory of Constraints, Version 1.0—page 8 of 8