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Cost Accounting

Constraint Analysis: Use Of Limited Resources



Constraint Analysis - Use Of Limited ResourcesAll of us have experienced time as a limiting or constraining resource. With two exams the day after tomorrow and a paper due next week, our problem is how to allocate limited study time. The solution depends on our objectives, our current status (grades, knowledge, skill levels, and so forth), and available time. Given this information, we devise a work plan to best meet our objectives. Managers must also decide how to best use limited resources to accomplish organizational goals. A supermarket may lose sales because limited shelf space prevents stocking all available brands of soft drinks. A manufacturer may lose sales because limited machine hours or labor hours prevent filling all orders. Managers of for-profit organizations will likely find the problems of capacity constraints less troublesome than the problems of excess capacity; nonetheless, these problems are real.

Ultimately, the problem often boils down to a product-mix decision, in which we must decide the mix of products or services we are going to offer our customers with the limited resources available to us. This post emphasize this issue with constraints analyses. Follow on…



If the limited resource is not a core business activity, it may be appropriate to outsource additional units of the limited resource externally. For example: many organizations have a small legal staff to handle routine activities; if the internal staff becomes fully committed, the organization seeks outside legal counsel.

The long-run solution to the problem of limited resources to perform core activities may be to expand capacity. However, this is usually not feasible in the short run. Economic models suggest that another solution is to reduce demand by increasing the price. Again, this may not be desirable. A hotel, for example, may want to maintain competitive prices. A manufacturer might want to maintain a long-run price to retain customer goodwill to avoid attracting competitors or to prevent accusations of price gouging.


Single Constraint

The allocation of limited resources should be made only after a careful consideration of many qualitative factors. The following rule provides a useful starting point in making short-run decisions of how to best use limited resources:

To achieve short-run profit maximization, a for-profit organization should allocate limited resources in a manner that maximizes the contribution per unit of the limited resource.


The application of this rule is illustrated in the following example:

Case Example

Luxury Auto Care Company offers three different service packages (A, B, and C) to its customers. These packages vary from a complete detailing of the automobile (wash, wax, carpet shampoo, etc.) to a simple hand wash. A limitation of 120 labor hours per week prevents Luxury from meeting the demand for its services. Information for the three service packages is as follows:

                                             A         B        C

Unit selling price                $100    $80    $50
Unit variable costs               (60)     (35)    (25)
Unit contribution margin   $ 40     $45      $25
Hours per unit                       4          3          1

Package A has the highest selling price and Package B has the highest unit contribution margin. Package Cis shown here to have the highest contribution per hour.

                                             A      B       C
Unit contribution margin   $40    $45    $25
Hours per unit                    :  4     :  3     :  1
Contribution per hour        $10     $15   $25

Following the rule of maximizing the contribution per unit of a constraining factor, Luxury should use its limited labor hours to sell Package C. As shown in the following analysis, any other plan would result in lower profits:

                                      A               B                       C
                                      Highest     Highest              Highest       
                                      Selling       Contribution     Contribution
                                      Price          Per Unit            Per
                                      Per Unit                              Constraining Factor
Hours available                120              120               120
Hours per unit                  :   4              :  3                  : 1
Weekly production-
in units                               30                40               120
Unit contribution margin  x$40            x $45         x $25
Total weekly-
contribution margin          $1,200        $1,800        $3,000

Despite this analysis, management may decide on a product mix that includes some units of A or B or both to satisfy the requests of some “good” customers or to offer a full product line. However, such decisions sacrifice short-run profits


Multiple Constraints

Continuing our illustration, assume the weekly demand for C is only 90 units although the company is capable of producing 120 units of C each week. In this case, the limited labor resource should first be used to satisfy the demand for Package C, with any remaining capacity going to produce Package B, which has the next highest contribution per unit of constraining factor. This allocation provides a total weekly contribution of $2,700 as follows:

Available hours                                   120
Required for C (90 units x 1 hour)      (90)
Hours available for B                            30
Labor hours per unit                           :  3
Production of B in units                       10
Unit contribution margin of B         x $45
Contribution from B                        $ 450
Contribution from C
($25 per unit x 90 units)                 2,250
Total weekly contribution margin $2,700

When an organization has alternative uses for several limited resources, the optimal use of those resources cannot be determined using the rule for short-run profit maximization. In these situations, techniques such as “linear programming” can be used to assist in determining the optimal mix of products or services.


Limitations of Decision Analysis Models

Analytical models, such as the relevant cost analysis model and applications presented in this post, are very useful in organizing information for purposes of determining the economics of a decision. However, it is important always to keep in mind that models do not make decisions-managers make decisions. The results of analytical models are an essential and necessary starting point in many decisions, but often there are other factors that weigh heavily on a decision that may cause the manager to go against the most economical alternative. There may be human resource, marketing, cultural, logistical, technological, or other factors that outweigh the analytics of a decision situation. It is in these situations where managers demonstrate leadership, problem-solving, and executive skill and potential, or the lack thereof.


Delta Airline Adopts Theory of Constraints for Technical Operations

Recently coming out of bankruptcy, Delta Airline’s management has focused on improving customer service, improving on-time performance, and making operations more efficient. Its Technical Operations (TechOps) division, which is responsible for the maintenance of Delta’s fleet of airplanes, as well as providing third-party maintenance for other airlines, has been at the forefront of the emphasis on improving efficiency. TechOps has shown a Willingness to embrace change, especially when it delivers greater efficiency. The work management tool that TechOps currently uses is “theory of constraints.”

The intent is to identify and deal with the primary constraint preventing it from achieving its goal in order to better manage the maintenance process. Delta sees the theory of constraints as an ongoing improvement process that conjures three questions: What to change? What to change to? And how to cause the change?

We’re rolling the theory of constraints out into several of our work areas,” said John Laughter, Delta TechOps’ vice president of maintenance operations. “We rolled it out in 2006 in our engine shop; it starts in the support shops and then it will make its way into the engine assembly area.”

We are already beginning to see the benefits,” he added, “as much as a 20 percent improvement on certain engine lines.”

[Source: David Jensen. “Delta TechOps Rejuvenated ,” Aviation Maintenance, April 15,2007, Vol. 26; Issue 4]


Theory of Constraints

The theory of constraints states that every process has a bottleneck (constraining resource) and that production cannot take place faster than it is processed through that bottleneck. The goal of the theory of constraints is to maximize throughput (defined as sales revenue minus direct materials costs) in a constrained environment. The theory has several implications for management:

  • Management should identify the bottleneck – This is often difficult when several different products are produced in a facility containing many different production activities. One approach is to walk around and observe where inventory is building up in front of workstations. The bottleneck will likely have the largest piles of work that have been waiting for the longest time.
  • Management should schedule production to maximize the efficient use of the bottleneck resource – Efficiently using the bottleneck resource might necessitate inspecting all units before they reach the bottleneck rather than after the units are completed. The bottleneck resource is too valuable to waste on units that may already be defective.
  • Management should schedule production to avoid a buildup of inventory – Reducing inventory lowers the cost of inventory investment and the cost of carrying inventory. It also assists in improving quality by making it easier to identify quality problems that might otherwise be hidden in large piles of inventory. Reducing inventory will require a change in the attitude of managers who like to see machines and people constantly working. To avoid a buildup of inventory in front of the bottleneck, it may be necessary for people and equipment to remain idle until the bottleneck resource calls for additional input.
  • Management should work to eliminate the bottleneck, perhaps by: increasing the capacity of the bottleneck resource, redesigning products so they can be produced with less use of the bottleneck resource, rescheduling production procedures to substitute nonbottleneck resources, or outsourcing work performed by bottleneck resources.


The theory of constraints has implications for management accounting performance reports. Keeping people and equipment working on production full-time is often a goal of management. To support this goal, management accounting performance reports have traditionally highlighted underutilization as an unfavorable variance. This has encouraged managers to have people and equipment producing inventory, even if the inventory is not needed or cannot be further processed because of bottlenecks. The theory of constraints suggests that it is better to have nonbottleneck resources idle than it is to have them fully utilized. To support the theory of constraints, performance reports should:

  • Measure the utilization of bottleneck resources
  • Measure factory throughput
  • Not encourage the full utilization of nonbottIeneck resources
  • Discourage the buildup of excess inventory


While the theory of constraints is similar to our general rule for how to best use limited resources, it emphasizes throughput (selling price minus direct materials) rather than contribution (selling price minus variable costs) in allocating the limited resource. The exclusion of direct labor and variable manufacturing overhead yields larger unit margins, and it may affect resource allocations based on throughput rankings. The result will likely be a reduction in profits from those that could be achieved using our general rule for how to allocate limited resources.

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