THE THEORY OF CONSTRAINTS AND THROUGHPUT …



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.

c. 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 Not enough workers to complete a process

One machine is slower than all others

Policy Overtime freeze

Purchasing restriction

Logistic Specified batch sizes

Particular processing sequence

Material Mining regulations

Freeze in Florida

Market Obsolete product

Downtrend in the economy

h. 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 non-existent. 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.

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: | $ | |

| | |400 | |

| | |x 50 units | $ 20,000|

| |Materials |$100 | |

| | |x 50 units | |

| | | |(5,000) |

| |Throughput | | $ 15,000 |

| | | | |

| |Salaries, insurance, taxes | $ |

| | |750 |

| |Supplies | | |

| | | |200 |

| |Miscellaneous | |

| | |2,200 |

| |Operating Expense | $ 3,150 |

| | | | |

| |Throughput | | $ 15,000|

| |Operating Expense | |

| | |(3,150) |

| |Income | | $ 11,850 |

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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).

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. | | | |Bicycles |Skateboards | | |

| |Demand in Units | |unlimited |unlimited | | |

| |Selling Price/Unit | | $ | $ 65.00 | | |

| | | |95.00 | | | |

| |Material Cost/Unit | | | 25.00| | |

| | | |40.00 | | | |

| |Throughput Contribution/Unit | $ | $ 40.00 | | |

| | |55.00 | | | |

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| |Resource minutes required per unit | | | | |

| | |Bicycles |Skateboards | | | | |

| |Gordy |10 |10 | | | | |

| |Kelly |15 |20 | | | | |

| |David |8 |15 | | | | |

| |Beckie |10 |20 | | | | |

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| |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 | | | |63% | | |

| | |750 |750 |1,500 | | | |

| |Kelly | | | |109% | | |

| | |1,125 |1,500 |2,625 | | | |

| |David | | | |72% | | |

| | |600 |1,125 |1,725 | | | |

| |Beckie | | | |94% | | |

| | |750 |1,500 |2,250 | | | |

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| |* 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 | | | |

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| |Decision: Make all possible Bicycles, then make Skateboards with any remaining resources |

| |Total minutes available from Kelly | |2,400 |minutes | |

| |Divided by minutes of Kelly needed per Bicycle |15 |minutes | |

| |Equals the number of Bicycles to make | |160 |units | |

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| |Bogeeta should make 160 Bicycles and no Skateboards | | | |

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| |Profitability Analysis |Bicycles |Skateboards |Total | | |

| |Production in units | | | | | |

| | |160 |- | | | |

| |Throughput/unit | $ | $ | | | |

| | |55 |40 | | | |

| |Total throughput | $ | $ | $ 8,800 | | |

| | |8,800 |- | | | |

| |Less Operating Expenses | | | 6,000 | | |

| |Net Profit/Loss | | | $ 2,800 | | |

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| |Part 1 | | |Bicycles |Skateboards | | | |

| |Demand in Units | | | | | | |

| | | |110 |50 | | | |

| |Selling Price/Unit | | $ | $ 65.00 | | | |

| | | |95.00 | | | | |

| |Material Cost/Unit | | | 25.00| | | |

| | | |40.00 | | | | |

| |Throughput Contribution/Unit | $ | $ 40.00 | | | |

| | |55.00 | | | | |

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| |Resource minutes required per unit | | | | | |

| | |Bicycles |Skateboards | | | | | |

| | |(110 units) |(50 units) | | | | | |

| |Gordy |10 |10 | | | | | |

| |Kelly |15 |20 | | | | | |

| |David |8 |15 | | | | | |

| |Beckie |10 |20 | | | | | |

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| |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 | | | |67% | | | |

| | |1,100 |500 |1,600 | | | | |

| |Kelly | | | |110% | | | |

| | |1,650 |1,000 |2,650 | | | | |

| |David | | | |68% | | | |

| | |880 |750 |1,630 | | | | |

| |Beckie | | | |88% | | | |

| | |1,100 |1,000 |2,100 | | | | |

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| |* Kelly continues to be the constraining operation | | | | |

| |Based on her minutes per unit, throughput per constraint minute is: | | | |

| | | |Bicycles |Skateboards | | | | |

| | | | $ | $ | | | | |

| | | |3.67 |2.00 | | | | |

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| |Decision: Make all possible bicycles, then make skateboards with any remaining resources | |

| |Total minutes available from Kelly | | |2,400 |minutes | |

| |Less # of minutes for bicycles (110 units x 15 minutes) | |-1,650 |minutes | |

| |Minutes available for skateboards | | |750 |minutes | |

| |Divided by minutes of Kelly needed per skateboard | |20 |minutes | |

| |Equals the number of skateboards possible to make | |37.5 |units | |

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| |Decision: Bogeeta should make 110 Bicycles and 37 Skateboards | | | |

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| |Profitability Analysis |Bicycles |Skateboards |Total | | | |

| |Production in units | | | | | | |

| | |110 |37 | | | | |

| |Throughput/unit | $ | $ | | | | |

| | |55 |40 | | | | |

| |Total throughput | $ | $ | $ 7,530 | | | |

| | |6,050 |1,480 | | | | |

| |Less Operating Expenses | | | 6,000 | | | |

| |Net Profit/Loss | | | $ 1,530 | | | |

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| |Part 2 | | |Bicycles |Bicycles | | | |

| | | | |(local) |(Export) |Skateboards | | |

| |Demand in Units | |110 |unlimited |50 | | |

| |Selling Price/Unit | | $ | $ 75.00 | $ 65.00 | | |

| | | |95.00 | | | | |

| |Material Cost/Unit | | | 40.00| 25.00| | |

| | | |40.00 | | | | |

| |Throughput Contribution/Unit | $ | $ 35.00 | $ 40.00 | | |

| | |55.00 | | | | |

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| |* 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 | | $ | $ | $ 2.00| | | |

| | | |3.67 |2.33 | | | | |

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| |Decision: Make all possible bicycles for local sale, then make bicycles for export with any remaining resources |

| |Total minutes available from Kelly | | |2,400 |minutes | |

| |Less # of minutes for local bicycles (110 units x 15 minutes) |-1,650 |minutes | |

| |Minutes available for export bicycles | | |750 |minutes | |

| |Divided by minutes of Kelly needed per bicycle | |15 |minutes | |

| |Equals the number of export bicycles possible to make | |50 |units | |

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| |Decision: Bogeeta should make 110 bicycles for local sale, 50 bicycles for export, and no skateboards |

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| | | |Bicycles |Bicycles | | | | |

| |Profitability Analysis |(local) |(Export) |Skateboards |Total | | |

| |Production in units | |50 | | | | |

| | |110 | | | | | |

| |Throughput/unit | $ | $ | $ | | | |

| | |55 |35 |40 | | | |

| |Total throughput | $ | $ | $ | $ 7,800 | | |

| | |6,050 |1,750 |- | | | |

| |Less Operating Expenses | | | | 6,000 | | |

| |Net Profit/Loss | | | | $ 1,800 | | |

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|14. |Part 1 | | |5 inch TV |6 inch 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| | 60.00| | |

| | | | |80.00 | | | |

| |Throughput Contribution/Unit | $ 90.00| $ 120.00| $ 40.00 | | |

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| |Resource minutes required per unit | | | | | |

| | |5 inch TV |6 inch TV |3 inch TV | | | | |

| |Machine A |2 |0 |1.5 | | | | |

| |Machine B |1.5 |1.8 |0 | | | | |

| |Machine C |0.5 |1.3 |3 | | | | |

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| |Total resource minutes based on demand (minutes/unit x demand) | | | |

| | | | | |Total |%Capacity | | |

| | | | | |Resources |(Capacity is | | |

| | |5 inch TV |6 inch TV |3 inch TV |Needed |4,800 min.) | | |

| |Machine A | | | | |89% | | |

| | |3,500 |- |750 |4,250 | | | |

| |Machine B | | | | |102% | | |

| | |2,625 |2,250 |- |4,875 | | | |

| |Machine C | | | | |83% | | |

| | |875 |1,625 |1,500 |4,000 | | | |

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| |* Machine B appears to be the constraining operation | | | | |

| |Throughput per constraint (Machine B) minute is: | | | | |

| | |5 inch TV |6 inch TV |3 inch TV | | | | |

| | | $ | $ | 'N/A (division by 0) | | | |

| | |60.00 |66.67 | | | | |

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| |Decision: |6 inch TVs should have bottleneck priority over 5 inch TVs. | | |

| | |3 inch TVs can be made without using bottleneck resources. | | |

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| |Total minutes available from Machine B | | |4,800 |minutes | |

| |Less # of minutes for 6 inch TVS (1250 units x 1.8 minutes) |-2,250 |minutes | |

| |Minutes available for 5 inch TVS | | |2,550 |minutes | |

| |Divided by minutes of Machine B needed per 5 inch TV | |1.5 |minutes | |

| |Equals the number of 5 inch TVs possible to make | | 1,700|units | |

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| |* Machine C appears to be the constraining operation for 3 inch TVs | | | |

| |Total minutes available from Machine C | | |4,800 |minutes | |

| |Less # of minutes for 6 inch TVS (1250 units x 1.3 minutes) |-1,625 |minutes | |

| |Less # of minutes for 5 inch TVS (1700 units x 0.5 minutes) |-850 |minutes | |

| |Remaining Machine C resources | | |2,325 |minutes | |

| |Divided by minutes of Machine C needed per 3 inch TV | |3 |minutes | |

| |Equals the number of 3 inch TVs possible to make | |775 |units | |

| |Market demand in 3 inch TVs | | |500 |units | |

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| |Decision: The Rochester plant should make 1700 5 inch TVs, 1250 | | | |

| |6 inch TVs, and 500 3 inch TVs (based on limited market demand) | | | |

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| |Profitability Analysis |5 inch TV |6 inch TV |3 inch TV |Total | | |

| |Production in units | | |500 | | | |

| | |1,700 |1,250 | | | | |

| |Throughput/unit | $ | $ | $ | | | |

| | |90 |120 |40 | | | |

| |Total throughput | $ 153,000 | $ 150,000 | $ 20,000| $ 323,000 | | |

| |Less Operating Expenses | | | | 267,000 | | |

| |Net Profit/Loss | | | | $ 56,000 | | |

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| |Part 2 |5 inch TV |6 inch TV |3 inch TV | | | | |

| |Actual Prod. | | | | | | | |

| | |1,700 |1,250 |500 | | | | |

| | | units | units | units | | | | |

| | | | | | |Actual |Efficiency | |

| | | Minutes | Minutes | Minutes |Total Min. | Operating |Variance | |

| | | Allowed* | Allowed* | Allowed* |Allowed |Minutes |(Unfavorable) | |

| |Min/Mach A | | | | | 4,572| |minutes |

| | |3,400 |- |750 |4,150 | |(422) | |

| |Min/Mach B | | | | | 4,856| |minutes |

| | |2,550 |2,250 |- |4,800 | |(56) | |

| |Min/Mach C | | | | | 4,402| |minutes |

| | |850 |1,625 |1,500 |3,975 | |(427) | |

| | |Minutes Allowed* = Actual Production x Standard minutes per TV unit | |

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| | |Volume |Actual |Excess | | | | |

| | |Capacity | Operating |Capacity | | | | |

| | |(in minutes) |Minutes |(minutes) | | | | |

| |Min/Mach A | | | | | | | |

| | |4,800 |4,572 |228 | | | | |

| |Min/Mach B | | | | | | | |

| | |4,800 |4,856 |(56) | | | | |

| |Min/Mach C | | | | | | | |

| | |4,800 |4,402 |398 | | | | |

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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).

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 less profitable products.]

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.

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