Refer to the Asian Journal of Industrial Engineering (Vol. 4, 2012) evaluation of a computerized mathematical model used in single machine batch scheduling, Exercise 10.27. Recall that the performance of the model was graded using a variable called Value of Object Function (VOF).

Data on VOF, run time (in seconds), and number of batches scheduled for six software runs are reproduced in the table (p. 874). Consider a straight-line regression model for y = VOF as a function of either run time or number of batches.

a. Conduct a nonparametric test to determine if the slope of the line relating y = VOF and x = number of batches is positive. Use α = .05.

b. Conduct a nonparametric test to determine if the slope of the line relating y = VOF and x = run time is negative. Use α = .05.

Data from Exercise 10.27

In a manufacturing process that involves a single machine, decisions must be made on whether to deliver the product to the customer immediately upon completion of the job or to hold the finished product in a batch with other jobs to be delivered at a later time. A computerized mathematical model for solving the batch scheduling problem was proposed in the Asian Journal of Industrial Engineering (Vol. 4, 2012). The performance of the model was graded using a variable called Value of Object Function (VOF). Simulation yielded the following data on VOF and run time (in seconds) for six software runs, each run with a different number of held batches.

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SWRUN Number Run Time Software Run of Batches VOF (seconds) 1 3 86.68 27 4 232.87 14 5 372.36 12 4 6. 496.51 18 5 7 838.82 42 6. 8. 1183.00 33 2. 3.