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Atwater, B. and M. L. Gagne. 1997. The theory of constraints versus contribution margin analysis for product mix decisions. Journal of Cost Management (January/February): 6-15.

Summary by Michael C. Massi
Master of Accountancy Program
University of South Florida, Summer 2002

Contribution Marging Main | Theory of Constraints Main

In recent times, cost accounting has taken much criticism due to its inability to provide appropriate guidance to management concerning strategic product mix decisions. One voice of criticism has come from Eliyahu Goldratt who has described cost accounting as "a powerful solution that changed the behavior and performance of industrial companies but has had the rug pulled from under it due to industry impacting overall technology which made cost accounting assumptions no longer valid and solutions obsolete." Due to cost accounting’s inadequacies, Goldratt developed the theory of constraints (TOC), which differs from traditional cost accounting because it does not trace operating expenses to specific products. As described by critics, cost accounting uses absorption cost which is irrelevant for decision making because it is "too late, too aggregated, and too distorted." An alternative to absorption cost is the contribution margin approach, which resembles the TOC, but is different in one aspect: assigning costs to specific products. This article describes the TOC and the contribution margin approaches through an example and concludes that the TOC is the best.

The TOC focuses on continuous improvement by managing constraints within a system. The TOC is a five-step process which is as follows (p. 7): 1) Identify the system’s constraints. 2) Exploit the system’s constraints. 3) Subordinate everything else to the above decision. 4) Elevate the system’s constraints. 5) If a constraint has been broken in the previous steps, go back to step 1. A constraint, found in every system, is defined as anything that limits the performance of a system relative to its goal. Also, the TOC is developed based on the primary goal of most business which is to make money and since businesses do not yield infinite sums of money there must be a constraint limiting their performance. Constraints can be classified into five categories (p. 7):

Type Defined
1. Market constraints Inadequate market demand to fully utilize a company’s capacity to make a product.
2. Resource constraints A resource in the company has insufficient capacity to fully satisfy market demand.
3. Policy constraints Management enforces a rule that limits the company’s ability to react to opportunities.
4. Material constraints An outside source of material becomes restricted.
5. Logistic constraints Specific business methods used require batching of processes or specified procedures that restrict operations.

Also, most systems have few primary constraints (constraints that truly limit a system’s performance) and that management usually deals with interactive constraints (constraints that affect the system indirectly through their interaction with the primary constraint). Interactive constraints may constrain a system for a short period of time if they are not managed correctly and usually develop for a variety reasons. Two of the most common causes are: 1) Poor scheduling of a non-constraint resource. 2) Policies that restrict the capacity of resources.

Furthermore, the third step of TOC provides the solution for improving the scheduling of non-constraint resources by subordinating them to the processing demands and capabilities of a constraint resource. If there is improper scheduling, the non-constraint resource restricts the system’s throughput and becomes an interactive constraint. Also, constraints should be fully exploited to optimize the system’s overall performance. The article states that there are many ways to exploit a constraint but two common methods are as follows:

1) Operate the constraint 24 hours a day and to stagger workers’ breaks so that there is no loss of throughput.

2) Process those items that contribute the most throughput per use of the constraining resource’s time.

Goldratt defines throughput as revenue generated by the system through the production of sold product. In technical terms, throughput is a product’s selling price minus the cost of raw materials used to make the product and the difference is the money generated. In addition, throughput places emphasis on sold product and not on products processed and placed in inventory. This ensures that time on a constraint resource is not wasted on overproduction only to be efficient or to achieve an economic lot size. Also, the TOC defines inventory and operating expense differently from traditional cost accounting. Inventory is defined as all money the system invests in items it intends to sell. The value of product inventory is at its raw material cost for internal reporting purposes thus resembling just-in-time manufacturing. Operating expense is defined as all the money the system invests to convert inventory into throughput (all costs other than raw materials). Under the TOC, direct labor is treated as period expense and there is no attempt to allocate direct labor or overhead costs to products. Thus, if throughput of a business does not meet period expense, the business will terminate operations and any increase in throughput for a certain period greater than any increase in operating expenses generates greater profit for a company.

To illustrate the application of the TOC in an example, Atwater and Gagne describe a company with a single constraint and two products, Product P (selling price = $50; market demand = 100/week) and Product Q (selling price = $60; market demand =50/week). First, the TOC identifies the system constraints by checking resource constraints by multiplying the time used by each product at each resource by the weekly demand and summing across. The result is required capacity and if it is less than available capacity, the system does not have a resource constraint and identification continues. In the example, a system constraint is found in Machine 2 (Exhibit 1).

Exhibit 1
Capacity Requirements for Each Work Center
Machine Center 1   Machine Center 2
Product Time Weekly Demand Capacity Needed Product Time Weekly Demand Needed
P 10 100 1,000

P 15 100 1,500
Q 5 50 250 Q 25 50 1,250


Machine Center 3   Machine Center 4
Product Time Weekly Demand Capacity Needed Product Time Weekly Demand Capacity Needed
P 10 100 1,000 P 20 100 2,000
Q 3 50 150 Q 2 50 100



Secondly, exploiting the constraint by operating continuously with no down time and by processing the product mix that generates the most return for the constraint time used. This is accomplished (illustrated in Exhibit 2) by calculating throughput value of each product and then calculating throughput per constraint use for each product (divide throughput per product by amount of processing time required per product per constraining resource). Then a production priority is assigned to each product so the highest throughput per constraint use receives the highest priority. Next, calculating the production quantities by subtracting time required to process the highest priority product from the available capacity at that constraint. If capacity is still available, repeat for the product next in priority (Exhibit 3). Thus, the TOC determines that the optimal product mix is 100Ps and 36Qs that generates a total throughput of $4,692.

Exhibit 2
Contribution/Constraint Utilization Using Throughput Value
1 2 3 4 5 6 7
Product Selling Price Raw Material Throughput Value [2-3] Time on Constraint T/CU [4-5] Production Priority
P $50 $20 $30 15 min. $2.00/min. 1
Q $60 $13 $47 25 min. $1.88/min 2

Exhibit 3
Optimal Product Mix Using Throughput Value
1 2 3 4 5 6 7*
Product Capacity Available Weekly Demand Processing Time/Unit Capacity Required [3X4] Percentage of Market Demand Possible [2/5] Optimal Quantity Produced
P 2,400 min. 100 units 15 min. 1,500 min. 160% 100 units
Q 900 min. 50 units 25 min. 1,250 min. 72% 36 units

Atwater and Gagne also describe the contribution margin approach, which is currently taught in cost accounting textbooks. The contribution margin of a product is its selling price minus its variable production cost which includes direct materials, direct labor, and variable overhead. The only difference between the TOC approach and the contribution margin approach is the treatment of direct labor and variable overhead. As discussed in the article, with today’s manufacturing environment, variable costs represent a small percentage of total costs with the shift to automation that increases a firm’s fixed production costs. Thus, the TOC does not account for variable costs in its decision making approach while the contribution margin approach does.

Continuing with the same example for the TOC, the article describes the process from the contribution margin approach. First, one must determine the contribution margin (CM) for each product (selling price minus direct labor, variable costs, and raw material costs) illustrated in Exhibit 4. Next, product priority is calculated by dividing CM by the time on the constraint (Exhibit 4). Thus, results in 76Ps and 50Qs, which is the reverse of the TOC analysis (Exhibit 5).

Exhibit 4
Contribution/Constraint Utilization Using Contribution Margin
1 2 3 4 5 6 7
Product Selling Price Variable Mfg. Costs Contribution Margin [2-3] Time on Constraint CM/CU [4-5] Production Priority
P $50 $32.10 $17.90 15 min. $1.19/min. 2
Q $60 $20.70 $39.30 25 min. $1.57/min 1

Exhibit 5
Optimal Product Mix Using Contribution Margin
  2 3 4 5 6 7*
Product Capacity Available Weekly Demand Processing Time/Unit Capacity Required [3X4] Percentage of Market Demand Possible [2/5] Optimal Quantity Produced
P 1.150 min. 100 units 25 min. 1,500 min. 76.7% 76 units
Q 2,400 min 50 units 25 min. 1,250 min. 192.0% 50 units

The authors state that the only way to see which approach is better is to see which provides the greatest profit. Thus, the TOC generates a profit of $1,692 and the contribution margin approach generates only $1,630. The difference is within the contribution margin’s approach of allocating direct labor and variable costs to specific products. The article then uses a sensitivity analysis to identify the cause of using direct labor and variable overhead to give a certain product more priority than another on the constraint. The first step is to find the indifference point for both approaches, then the analysis showed that the contribution margin approach would have to yield a cost increase of 124 percent just to equal the TOC at that point. This is not too likely due to the fact that direct labor and variable overhead cost would need to dramatically increase taking in consideration today’s manufacturing environment, this is not a realistic solution. Thus, the contribution margin approach signals managers in the wrong direction.

Also, the article discusses that there is no value in tracking and allocating variable costs to individual products when variable costs make up such a small percentage of the total costs within a manufacturing cost structure. Given the current environment, the authors state that tracking variable costs are difficult as well as not economically feasible. Thus, this creates the illusion that the contribution margin product mix will cost less to produce but there is no real savings. The apparent savings fail to recognize that employees at a non-constraint work center do not need to work at 100 percent capacity to meet product demand because they are paid even if no output is produced. Also, if employees do work at 100 percent, then excess products are produced which results in a host of problems including (p. 14): 1) Increased production lead-time. 2) Priority problems on the floor. 3) Increased operating expenses. 4) Increased risk from obsolescence of inventory. 5) Delays in the introduction of engineering changes. In addition, the authors state that a risk with tracking direct labor is the effect of terminating employees and that effect on morale and the value of a worker. Morale would drop if employees were expected to achieve continuous improvement when their reward is a loss of job. Also, the contribution margin approach only values workers if they produce and does not allow them to learn different jobs or cross-train. This could result in employee neglect and less production and less improvement.

In conclusion, the TOC approach looks for the product mix that maximizes total sales dollars for a period while the contribution margin approach creates the illusion that producing the lowest-cost item will decrease expenses in a period and produce more earnings.


Related Summaries:

Goldratt, E. M. 1990. What is this thing called Theory of Constraints. New York: North River Press. (Summary). (In Chapter 4 Goldratt says that the word "cost" is a dangerous and confusing multi-meaning word and that the word "product cost" is "an artificial, mathematical phantom" p. 49).

Goldratt, E. M. 1990. The Haystack Syndrome: Sifting Information Out of the Data Ocean. New York: North River Press. (Summary). (In Chapter 7 Goldratt tells us that the business world today has changed and cost accounting has been slow to react. They have not reexamined the fundamentals, the financial statement logic, to create new solutions. Instead, they have formulated ineffective answers like “cost drivers” and “activity-based costing.” We can no longer allocate based on direct labor. So allocating expenses at the unit level, batch level, group level, and company level is meaningless. These cannot be aggregated at their respective levels nor at the top. So why do it?).

Goldratt, E. M. 1992. From Cost world to throughput world. Advances In Management Accounting (1): 35-53. (Summary).

Goldratt, E. M. and J. Cox. 1986. The Goal: A Process of Ongoing Improvement. New York: North River Press. (Summary).

Hall, R., N. P. Galambos, and M. Karlsson. 1997. Constraint-based profitability analysis: Stepping beyond the Theory of Constraints. Journal of Cost Management (July/August): 6-10. (Summary).

Louderback, J. And J. W. Patterson. 1996. Theory of constraints versus traditional management accounting. Accounting Education 1(2): 189-196. (Summary).

Luther, R. and B. O’Donovan. 1998. Cost-volume-profit analysis and the theory of constraints. Journal of Cost Management (September/October): 16-21. (Summary).

Martin, J. R. Not dated. Comparing Dupont's ROI with Goldratt's ROI. Management And Accounting Web.

Martin, J. R. Not dated. Drum-Buffer-Rope System. Management And Accounting Web.

Martin, J. R. Not dated. Global measurements of the theory of constraints. Management And Accounting Web.

Martin, J. R. Not dated. Goldratt's dice game or match bowl experiment. Management And Accounting Web.

Martin, J. R. Not dated. TOC problems and introduction to linear programming.  Management And Accounting Web.

Rezaee, Z. and R. C. Elmore. 1997. Synchronous manufacturing: Putting the goal to work. Journal of Cost Management (March/April): 6-15. (Summary).

Ruhl, J. M. 1996. An introduction to the theory of constraints. Journal of Cost Management (Summer): 43-48. (Summary).

Ruhl, J. M. 1997. The Theory of Constraints within a cost management framework. Journal of Cost Management (November/December): 16-24. (TOC Illustration).

Westra, D., M. L. Srikanth and M. Kane. 1996. Measuring operational performance in a throughput world. Management Accounting (April): 41-47. (Summary).

Yahya-Zadeh, M. 1999. Integrating long-run strategic decisions into the theory of constraints. Journal of Cost Management (January/February): 11-19. (Summary).