Production Flexibility[1] Richard de Neufville – October 2008
This example illustrates how flexibility to allocate production capacity between products can increase investment value – when there is variability both in the overall and relative levels of demand for the products.
Consider the design of a simple two-stage manufacturing process for two products, SUVs and sedans. Both share one of the stages, as in the Figure. The issue is: how should we think about the level of capacity to be allocated to the facilities?
A numerical example provides insight. Assume that the fixed cost of the site is $40 million, and that the variable costs per unit of capacity for the assembly of SUVs and sedans, and for the finishing process are $300, 200, and 800 respectively. Assume further that the gross margins for products 1 and 2 are $4000 and $3000. For simplicity, everything is in present dollars.
Situation 1: Design based on best forecast
Suppose that the forecast is for 30,000 units each of SUVs and sedans. The design capacities should thus be 30,000 for each assembly facility and 60,000 for product finishing. This leads to the following estimate of results, in millions:
Gross Revenues = 30(4) + 30(3) = 210
Fixed cost 40
Variable costs = 30(0.3) + 30(0.2) + 60(0.8) = 63
Total costs 103
Gross Profit 107 Million
Situation 2: Best forecast plus or minus symmetrically
Suppose that the designers recognize that forecasts are unreliable and that total volumes could be plus or minus about 15%, as in the table below. This variability lowers profitably.
Demand Scenarios: Balanced VariationPessimistic / Expected / Optimistic / Mean
Demand / SUV / 25000 / 30000 / 35000 / 30000
Sedans / 25000 / 30000 / 35000 / 30000
Total / 50000 / 60000 / 70000 / 60000
Probability / 0.25 / 0.50 / 0.25
Why does variability lower profitability? Because the system loses revenues when sales are down, but this is not counterbalanced when demand is up, because capacity constraints limit sales. Specifically, in this pessimistic scenario sales are 5,000 units lower in each category, for a revenue loss of 5(4 + 3) = 35. As the probability of this scenario is estimated at 25%, the overall results are:
Expected Gross Profit = 107 – (0.25) 35 = 98.75 Million
This situation illustrates the “Flaw of Averages”. Although average demand is the same as the “best forecast”, the expected profits are about 10% less!
Situation 3: Asymmetric variation across products
Suppose now that, as often happens, market research has confirmed that customers’ variability in demand varies across products. When the overall demand is low, customers not only buy less but also buy cheaper. For this example, this means that in the pessimistic case they buy more sedans, and in the optimistic case they buy more SUVs. This phenomenon makes things worse.
ScenariosPessimistic / Expected / Optimistic / Average
Demand / SUVs / 15000 / 30000 / 45000 / 30000
Sedans / 35000 / 30000 / 25000 / 30000
Total / 50000 / 60000 / 70000 / 60000
Probability / 0.25 / 0.50 / 0.25
Why does this negative correlation between types of sales accentuate the effects of a downturn?
· More obviously, it not only reduces sales in the pessimistic scenario, but also reduces the margins on these sales.
· Counter intuitively, this phenomenon can reduce sales in the optimistic scenario! This is because while the growth in demand for the more profitable products is limited, the demand for the cheaper products falls.
The overall production results are thus:
ProductionFacility / Capacity / Pessimistic / Expected / Optimistic / Average
SUV / 30000 / 15000 / 30000 / 30000 / 26250
Sedan / 30000 / 30000 / 30000 / 25000 / 28750
Joint / 60000 / 45000 / 60000 / 55000 / 55000
The corresponding overall expected results are thus as below, and are far worse than estimated by an analysis that does not take into account this negative correlation when it exists.
Expected Gross Profit = 88.25 Million
This further illustrates the “Flaw of Averages” and the desirability of taking actual distributions into account, both as to level and the possibility of correlations between elements.
Pessimistic / Expected / Optimistic / AverageInvestment / 103 / 103 / 103 / 103
Gross Margin / 150 / 210 / 195 / 191.25
Gross Profit / 47 / 107 / 92 / 88.25
Situation 4: Cutting Capacity
A possible instinctive response to the previous situation, which shows that average production would drop to 55,000 units overall, would be to cut capacity and size for the lower expected production. For example:
ProductionFacility / Capacity / Pessimistic / Expected / Optimistic / Average
SUV / 27000 / 15000 / 27000 / 27000 / 24000
Sedan / 27000 / 27000 / 27000 / 25000 / 26500
Joint / 54000 / 42000 / 54000 / 52000 / 50500
As can be seen, this approach does deal with the gap between available capacity and average use. This is because limiting overall capacity does nothing for dealing with the greater imbalances in the demands for SUVs and Sedans in the scenarios different from the expected.
Moreover, cutting back on the size of a profitable business has the net effect of reducing overall profits! This approach leads to the worst results so far:
Expected Gross Profit = 78.8 Million
Pessimistic / Expected / Optimistic / AverageInvestment / 96.7 / 96.7 / 96.7 / 96.7
Gross Margin / 141 / 189 / 183 / 175.50
Gross Profit / 44.3 / 92.3 / 86.3 / 78.8
Situation 5: Flexibility to Allocate Capacity
Flexibility to allocate capacity to different products as the mix changes increases overall value.
Perhaps paradoxically, when confronted by the possible losses associated with negative correlations in the product mix, it makes sense to increase the available capacity, to increase the initial expense.
By example, consider the case when the capacity for producing SUVs and sedans is each increased from 30,000 to 35,000, but the overall capacity is kept at 60,000. In other words, we create a situation in which at least one of the plants will be producing below capacity. This might appear strange, as the instinctive reflex might be to aim for the possibility of balanced capability so that all facilities could operate at full capacity. Yet the present proposal deliberately unbalances the facilities so that the combined SUV and sedan facilities, with a joint capacity of 70,000, could never operate at more than 60/70 ~ 86%, since they are limited by the capacity of the finishing facility.
This flexibility has a great benefit, however: it enables the system to respond to shifts in the relative demands for the products. When the optimistic scenario occurs, the oversized SUV facility can ramp up toward the higher demand for SUVs. Conversely, when the pessimistic scenario occurs, the oversized sedan facility enables the manufacturer to capture unit sales that might otherwise be lost, as seen below.
Facility / Capacity / Pessimistic / Expected / Optimistic / Average
SUV / 35000 / 15000 / 30000 / 35000 / 27500
Sedan / 35000 / 35000 / 30000 / 25000 / 30000
Joint / 60000 / 50000 / 60000 / 60000 / 57500
This flexibility increases the value of the system compared to the balanced design in Situation 3:
Expected Gross Profit = 94.5 Million > 88.25
Pessimistic / Expected / Optimistic / AverageInvestment / 105.5 / 105.5 / 105.50 / 105.5
Gross Margin / 165 / 210 / 215 / 200
Gross Profit / 59.5 / 104.5 / 109.5 / 94.5
The advantage of this flexible design, compared to the balanced design, appears clearly in the VARG chart:
We may also calculate the value of the flexibility and the benefit cost ratio of the investment in the extra capacity:
The flexibility increases the overall net expected value by (94.5 – 88.25) = 6.25.
The cost of the flexibility = cost of extra capacity = 5(0.3) + 5(0.2) = 2.5 million
So:
Benefit / Cost of Flexibility = (6.25 + 2.5) / 2.5 = 3.5
Production Flexibility Page 1 of 4
[1] Inspired by Jan van Mieghem’s Seagate example, and developed with the help of João Claro