# Constraints of Differential Analysis

### Constraints on Decision-Making Analysis

As companies make decisions, they must consider the effects of volume trade-offs, constraints, and bottlenecks.

Companies are often unable to produce certain goods or services because they lack the capacity to produce everything they would like to produce. They then have to make a volume trade-off decision, which is a decision a company makes when it has to sacrifice one production effort to go forward with another production effort, with the goal of maximizing profits overall. A constraint is a factor that limits a company from producing as much of a product as it wants and meeting full demand. For example, a company may not have enough resources or enough workforce labor capacity to produce as many product items as it would want.

There can be limits in distribution channels because of how long it takes and how expensive it is to ship certain products. This is especially likely if the product being made is perishable.

Also, there can be a bottleneck, or a slowdown or stoppage in one stage of a process that lessens the output of the entire system. For example, a company may have a limited number of machines in a factory that produce a key component for making widgets. In that case, it doesn't matter how much the company increases the workforce, factory space, and collection of raw materials. Until and unless the company can increase the number of machines it has that produce that one key widget component, it will be limited in terms of how many overall widgets it produces.

Sometimes companies can work around bottlenecks or capacity limitations. Maybe a company can outsource production of the key widget component. In other words, it can hire another vendor to make that component. The company could buy more machines, or it could buy that component from a third-party vendor.

However, in some situations the bottleneck might be beyond the company's control. For instance, there could be a limit to how much of the needed raw materials the company can access. Or there could be limits to how many planes, trains, ships, and cars the company can find or contract with that ship goods into certain hard-to-reach regions. When companies use differential analysis, they consider what the bottlenecks and limits are involving various decision choices and what constraints they can change or not change.

Looking at a specific case study can make these concepts easier to understand. Assume that Leathertime Sports makes baseball gloves and baseballs. The company wants to find the ideal production mix in terms of the bottleneck it has with a stitching machine.

### Differential Analysis and a Production Bottleneck

VARIABLES Baseballs Baseball Gloves
Selling Price per Unit $5$25
Variable Cost per Unit $2$10
Contribution Margin per Unit $3$15
Monthly Demand in Units 10,000 5,000
Stitching Machine Time Needed to Make One Unit, in Minutes 2 15
Total Stitching Time Required to Meet Monthly Demand 20,000 75,000
Contribution Margin per Unit of Constrained Resource, in Minutes $1.50 per minute$1.00 per minute
Monthly Stitching Machine Time Available = 50,000 minutes

Managers considered this data while trying to pinpoint its most profitable production mix.

The constrained resource is the stitching machine. The baseball is more profitable per minute of stitching machine use. For these reasons, the company should make the maximum number of baseballs it can per month—10,000 baseballs, using up 20,000 machine minutes.

Then Leathertime Sports should use the remaining stitching machine minutes that are available each month to make baseball gloves. There are 50,000 stitching machine minutes available each month, minus 20,000 minutes spent making baseballs, which leaves 30,000 minutes left to make baseball gloves.

Thus, the company can produce a total of 10,000 baseballs each month (earning $30,000) and 2,000 baseball gloves (earning$30,000) for a combined contribution margin of \$60,000 each month.

### Using Differential Analysis for Constrained Resources

Differential analysis helps managers make decisions when resources are constrained.

Differential analysis is a powerful tool that companies can use when they are dealing with situations where constraints need to be managed. If there are multiple constraints in a process, then a company will want to focus on improving the weakest step that it controls, assuming the goal is to increase capacity and production.

A company that has enough factory space and access to raw materials and production tools for producing its products may still have constraints. These include the length of laborer shifts and the number of hours laborers work per week. The company can take action to ease these constraints. The company could start asking people to work overtime. This would raise labor costs. In most cases, it would also increase the hourly per-unit labor cost. This is because many factory employees would be entitled to time-and-a-half pay for overtime hours worked each week. However, if the increase in capacity would lead to enough additional revenues from increasing the number of units produced, then the company can justify the overtime expense as likely to lead to increased profits.

Some businesses are seasonal. These include construction and vacation businesses, in which weather often dictates demand. In retail stores, the holiday shopping season often brings increased demand for product offerings. Businesses in these areas may have production resources, raw materials, and other goods that are enough to meet the times of year where there are peak demands. Then they adjust their labor needs as appropriate based on what capacity they need to operate at to meet demand at any given time.

Seasonal businesses that use differential analysis must evaluate the constrained resource in relation to the temporary increase in demand. Doing this will help managers determine when it is worthwhile to support increased costs and thereby increase the amount of the constrained resources available. Only by comparing the contribution margin per unit of the constrained resources to the overall increased revenue and profit can a company determine if it is beneficial to produce more of the constrained resources.