Operations and Supply Chain Management The Core

198 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
CHAPTER 6A
BREAK-EVEN ANALYSIS
The choice of which specific equipment to use in a process often can be based on an
analysis of cost trade-offs. There is often a trade-off between more and less specialized
equipment. Less specialized equipment is referred to as “general purpose,” meaning it can
be used easily in many different ways if it is set up in the proper manner. More specialized
equipment, referred to as “special purpose,” is often available as an alternative to a
general-purpose machine. For example, if we need to drill holes in a piece of metal, the
general-purpose option may be to use a simple hand drill. An alternative special-purpose
drill is a drill press. Given the proper setup, the drill press can drill holes much quicker
than the hand drill can. The trade-offs involve the cost of the equipment (the manual drill is
inexpensive, and the drill press expensive), the setup time (the manual drill is quick, while
the drill press takes some time), and the time per unit (the manual drill is slow, and the drill
press quick).
A standard approach to choosing among alternative processes or equipment is break-even
analysis. A break-even chart visually presents alternative profits and losses due to the number
of units produced or sold. The choice obviously depends on anticipated demand. The method
is most suitable when processes and equipment entail a large initial investment and fixed cost,
and when variable costs are reasonably proportional to the number of units produced.
Example 6A.1: Break-Even Analysis
Suppose a manufacturer has identified the following options for obtaining a machined part: It can
buy the part at $200 per unit (including materials); it can make the part on a numerically controlled
semiautomatic lathe at $75 per unit (including materials); or it can make the part on a machining
center at $15 per unit (including materials). There is negligible fixed cost if the item is purchased; a
semiautomatic lathe costs $80,000; and a machining center costs $200,000.
The total cost for each option is
Purchase cost = $200 × Demand
Produce-using-lathe cost = $80,000 + $75 × ​ Demand​
Produce-using-machining-center cost = $200,000 + $15 × Demand
SOLUTION
Whether we approach the solution to this problem as cost minimization or profit maximization really
makes no difference as long as the revenue function is the same for all alternatives. Exhibit 6A.1
shows the break-even point for each process. If demand is expected to be more than 2,000 units
(point A), the machine center is the best choice because this would result in the lowest total cost. If
demand is between 640 (point B) and 2,000 units, the semiautomatic lathe is the cheapest. If demand
is less than 640 (between 0 and point B), the most economical course is to buy the product.
The break-even point A calculation is
$80,000 + $75 × Demand = $200,000 + $15 × Demand ​
Demand (point A) = 120,000 / 60 = 2,000 units ​