Zenren ElectroProducts is considering making changes in the way it procures the Z-1524 microprocessor chip. In addition to the status quo, which is in-house production at its current California plant, Zenren is considering either purchasing from an offshore manufacturer or making the chip in its new Arizona plant. There are three attributes for this decision: cost per batch of 10,000 chips, operational ease (a constructed scale from 1 to 4), and quality as measured by the number of defective chips per batch of 10,000. Zenren has assessed its preferences for these three attributes and found that these attributes are mutually preferential independent.

A multi-criteria value analysis is being done to evaluate these alternatives. The single dimensional value function for cost per batch ranges from $500 to $1,000. The value function has a midvalue equal to $750.

The value function for operational ease is assessed using marginal analysis. Zenren gets 0 value if operational ease equals 1. The marginal value going from a score of 1 to a score of 2 is the same as the marginal value going from 2 to 3. The marginal value going from a score of 3 to 4 is four times as great as the marginal value going from 1 to 2.

For the number of defects per batch, Zenrens ideal is to have 0 parts per batch. The company gets no value if the number of defects is greater than 80. Zenren is indifferent between decreasing from 80 to 25 defects and decreasing from 25 to 0 defects per batch. Zenren is also indifferent between decreasing from 25 to 15 defects and from 15 to 0 defects per batch. Zenrens midvalue between 25 and 80 defects per batch is 35 defects.

The trade-off weights are assessed using swing weighting. If all of the attributes are set at their worst level, Zenren prefers improving the cost per batch from $1,000 to $500 three times as much as improving operational ease. Decreasing the number of defects per batch from 80 to 0 defects is twice as valuable as improving the cost per batch from $1,000 to $500.

a) Assess the single-attribute value functions for each of the three attributes. Write down the value functions for the cost per batch and the number of defects per batch. Write down the values when operational ease equals 1, 2, 3, and 4.

b) Determine the trade-off weights for the three attributes.