August is running a bakery, selling bread for $1.50 per loaf. She has a hundred pounds of flour, fifty pounds of yeast, and a dozen eggs. What’s the problem? Not enough eggs. Assume for purposes of this illustration that the recipe for bread is 1 pound flour, 2 cups of water, 3 eggs, and an ounce

Question

August is running a bakery, selling bread for $1.50 per loaf. She has a hundred pounds of flour, fifty pounds of yeast, and a dozen eggs. What’s the problem? Not enough eggs. Assume for purposes of this illustration that the recipe for bread is 1 pound flour, 2 cups of water, 3 eggs, and an ounce of yeast (don’t try to bake bread from these ingredients). How do we analytically determine where the constraint is?

Accepted Answer

One way is to list all the raw materials, then divide each material by the amount of that material in a unit of production, to determine how many units that resource can support. The material that provides the least units is the constraint. Figure 17–2 is an analysis of bakery resources.
In this example, the constraint is on the number of eggs. So the answer is to buy more eggs. Not more flour, not more yeast. So this analysis has met the first and second objectives of the theory of constraints, that is, to identify the constraining resource and avoid acquiring nonconstraining resources. That raises the question, how many eggs can we buy before we encounter the next constraint?
Examining Figure 17–2, we find that the next lowest number of loaves, 100, is for flour. We already have enough eggs to bake 4 loaves of bread, but we need enough eggs to bake an additional 96 loaves (100 4). Since it takes 3 eggs to bake a loaf, we need 288 eggs (3 96), or 24 dozen (288/12 eggs/dozen). The analysis can continue to find out how much flour and eggs are needed to consume all the yeast.
The incremental cost of eggs is $21.60 ($0.90/dozen × 24 dozen). However, the incremental revenue from this investment is $144 (96 loaves × $1.50). Clearly, it is advantageous to buy more eggs and expand production. This satisfies the third objective of constraint theory, which is to determine the marginal revenue and cost of acquiring more of the constraining resource.
The theory of constraints can also be applied to factory equipment, component parts, trucks, people, and so forth.
Consider the example of Pitcarn Pumps, which has three pump product lines: (1) agricultural, which sells pumps for irrigation; (2) municipal, which sells pumps for sewage lines; and (3) commercial, which sells pumps for HVAC equipment. Within Pitcarn’s plant, there are four operations: foundry, to make pump housings; machining, to grind and fabricate parts; assembly; and testing. Each of these four operations has a maximum capacity of 600 hours per week. Data on manufacturing costs and capacity are given in Figure 17–3.
Another foundry will cost $500,000 but will double foundry capacity. Milling machines can be added to the factory floor for $40,000, and each milling machine will increase capacity by 120 hours per week. Another assembly line can be constructed for $200,000, but it will double capacity. Another testing facility can be added for $30,000, which will increase test capacity by 120 hours per week.
In its current configuration, what variable (operation) provides the constraint on plant capacity? Note that the gross margin for agricultural pumps is 33% ($300/$900); for municipal pumps it is 50% ($2,000/$4,000); and for commercial pumps it is 33% ($200/$600). Since municipal pumps provide the greatest contribution margin, we should begin the analysis there. We see the limiting constraint is machining hours, which limits production to 30 pumps per week. By adding enough capacity to machine another 30 pumps per week, we reach the next level constraint, which is on foundry capacity. Since each municipal pump requires 20 machining hours, the total number of machining hours necessary is 600 hours (20 hours 30 pumps). If each milling machine can provide 120 hours, the number of machines needed is 5 (600/120).
The incremental annualized revenue is $6,240,000 ($4,000 per pump 30 pumps 52 weeks) compared to an incremental annualized cost of $3,720,000 (variable costs of $2,000 30 units/ week 52 weeks plus $600,000 for 5 milling machines costing $120,000 each; assume milling machines have a one year life for this example). Where the incremental revenue exceeds the incremental cost for resources, resources should be acquired to eliminate the constraint.

As long as Pitcarn can sell all the municipal pumps they can make, they should continue to add capacity in this high margin product line, provided incremental revenue exceeds incremental cost. However, if market demand shifts to other product lines, the constraint analysis will have to be performed anew.
Note: In this problem, we are concerned with purchase of capital equipment, not expendable resources. So although comparing incremental cost to incremental revenue is useful for a cash flow analysis, this approach should not be used to forecast sales and profits.

Question 17.6: August is running a bakery, selling bread for $1.50 per loaf...

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