Question

An industrial engineer is conducting an experiment using a Monte Carlo simulation model of an inventory system. The independent variables in her model are the order quantity (A), the reorder point (B), the setup cost (C), the backorder cost (D), and the carrying cost rate (E). The response vari- able is average annual cost. To conserve computer time, she decides to investigate these factors using a 2011 design with 1 = ABD and I = BCE. The results she obtains are de = 95, de = 134, b = 158, abd = 190, cd = 92, ac = 187, bce = 155, and abcde = 185.

Suppose that the fraction abc = 189, ce = 96, bcd = 154, acde = 135, abe = 193, bde = 152, ad = 137, and (1) = 98 was run. How was this fraction obtained? Add this data to the original fraction and estimate the effects.

Answer 1

The fraction was obtained using a fractional factorial design. Effects are estimated by analyzing the sum of squares for each effect after combining the new data with the original fraction.

Step-by-step explanation:

The correct answer is that the fraction was obtained using a fractional factorial design considering the industrial engineer's constraints to conserve computer time. To estimate the effects, add the new fraction to the original fraction and analyze the sum of squares for each effect. Due to the complexity of the question and the specifics needed in constructing factorial designs and analytical computations, a step-by-step guide would usually involve utilizing specialized statistical software or manual calculations following the principles of experimental design and analysis of variance (ANOVA).

The fraction abcde = 185 was obtained by multiplying the fractions abc = 189 and de = 98. This means that abcde = abc * de. To estimate the effects, we can calculate the differences between the results obtained and the baseline fraction abcde = 185:

de - abcde = 98 - 185 = -87

abcde - abc *[de - abcde] = 185 - (189 * -87) = 185 + 16263 = 16448

Therefore, the effects can be estimated as:

de - abcde = -87

abcde - abc *[de - abcde] = 16448