The article Multi-objective Scheduling Problems: Determination of Pruned Pareto Sets (H. Taboada and D. Coit, IIE Transactions, 2008:552564), presents examples in a discussion of optimization

The article €œMulti-objective Scheduling Problems: Determination of Pruned Pareto Sets€ (H. Taboada and D. Coit, IIE Transactions, 2008:552€“564), presents examples in a discussion of optimization methods for industrial scheduling and production planning. In one example, seven different jobs were performed on each of five machines. The cost of each job on each machine is presented in the following table. Assume that it is of interest to determine whether costs differ between machines, but that it is not of interest whether costs differ between jobs.

a. Identify the blocking factor and the treatment factor.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Can you conclude that there are differences in costs between some pairs of machines? Explain.

d. Which pairs of machines, if any, can you conclude, at the 5% level, to have differing mean costs?

Job Machine 2 3 4 20 A 16 24 18 22 26 22 B 22 18 30 20 28 18 26 12 12 15 18 22 12 16 18 28 16 26 34 18 18 14 14 11 16 18 10 12