The Theory of Constraints and Throughput Accounting Solutions

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 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.

Theory of Constraints, Version 1.0—page 1 of 7 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

5. Constraint Type Constraint Category a. Material External b. Policy Internal c. Market External d. Market External e. Market External f. Policy Internal g. Process Internal h. Process Internal i. Material External j. Policy Internal k. Process Internal l. Policy External* m. 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).

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,

Theory of Constraints, Version 1.0—page 2 of 7 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 $ 95.00 $ 65.00 Material Cost/Unit 40.00 25.00 Throughput Contribution/Unit $ 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

Profitability Analysis Bicycles Skateboards Total Production in units 160 -

Theory of Constraints, Version 1.0—page 3 of 7 Throughput/unit $ 55 $ 40 $ Total throughput $ 8,800 $ - 8,800

Less Operating Expenses 6,000 Net Profit/Loss $ 2,800

Errata Note: The solution provided in Part 2 below assumes an export price per bike of $75.00 (not $50.00). 13. 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 Bicycles Skateboards Demand in Units 110 50 Selling Price/Unit $ 95.00 $ 65.00 Material Cost/Unit 40.00 25.00 Throughput Contribution/Unit $ 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 $ 3.67 $ 2.00

Decision: Make all possible bicycles, then make skateboards with any remaining resources Total minutes available from Kelly 2,400minutes

Theory of Constraints, Version 1.0—page 4 of 7 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 Bicycles Skateboards Total Production in units 110 37 Throughput/unit $ 55 $ 40 $ Total throughput $ 6,050 $ 1,480 7,530

Part 2 Bicycles Bicycles (local) (Export) Skateboards Demand in Units 110 unlimited 50 Selling Price/Unit $ 95.00 $ 75.00 $ 65.00 Material Cost/Unit 40.00 40.00 25.00 Throughput Contribution/Unit $ 55.00 $ 35.00 $ 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

Bicycles Bicycles Profitability Analysis (local) (Export) Skateboards Total Production in units 110 50 Throughput/unit $ 55 $ 35 $ 40 $ Total throughput $ 6,050 $ 1,750 $ - 7,800

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).

TheoryYou of should Constraints, also ask yourselfVersion why 1.0—page Profit in Problem 5 of 7 #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.] 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 80.00 60.00 Throughput Contribution/Unit $ 90.00 $ 120.00 $ 40.00

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

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 3,500 - 750 4,250 89% Machine B 2,625 2,250 - 4,875 102% Machine C 875 1,625 1,500 4,000 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 4,800minutes Less # of minutes for 6 inch TVS (1250 units x 1.8 minutes) -2,250minutes Minutes available for 5 inch TVS 2,550minutes Divided by minutes of Machine B needed per 5 inch TV 1.5minutes Equals the number of 5 inch TVs possible to make 1,700 units

* Machine C appears to be the constraining operation for 3 inch TVs Total minutes available from Machine C 4,800minutes Less # of minutes for 6 inch TVS (1250 units x 1.3 minutes) -1,625minutes Less # of minutes for 5 inch TVS (1700 units x 0.5 minutes) -850minutes Remaining Machine C resources 2,325minutes Divided by minutes of Machine C needed per 3 inch TV 3minutes Equals the number of 3 inch TVs possible to make 775units Market demand in 3 inch TVs 500units

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

Theory of Constraints, Version 1.0—page 6 of 7 6 inch TVs, and 500 3 inch TVs (based on limited market demand)

Profitability Analysis 5 inch TV 6 inch TV 3 inch TV Total Production in units 1,700 1,250 500 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

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 3,400 - 750 4,150 4,572 (422) minutes Min/Mach B 2,550 2,250 - 4,800 4,856 (56) minutes Min/Mach C 850 1,625 1,500 3,975 4,402 (427) minutes Minutes Allowed* = Actual Production x Standard minutes per TV unit

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

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 Theoryavailability of Constraints, of raw materials Version (see 1.0—page the diagram 7 inof Part 7 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.