A university is conducting a study to evaluate the relative efficiency of four c

Question

A university is conducting a study to evaluate the relative efficiency of four colleges using the students Credit hours and Research publications as evaluation criteria. The input resources considered in this study includes the number of faculty, the number of support staff, and the budget. The data is given in the table below.

a) Formulate a linear mathematical model to determine the relative efficiency of colleges using the data provided. The model formulation must include the problem data and not just a generic model. It is sufficient to include a model for college 1 and there is no need to repeat the same model for each college.

b) Implement your formulation in part (a) in Excel and use Solver to find the relative efficiency for each college and identify those that are inefficient. Provide a summary table of all college efficiency values.

College Faculty Support Staff Budget (millions) Credit Hours (thousands) Research Publications 1 150 70 5 15 225 2 60 20 3 5.4 70 3 800 140 20 56 1300 4 30 15 1 2.1 40

Explanation / Answer

Ans:

College Faculty Support Staff Budget (millions) Credit Hours (thousands) Research Publications SUM AVG 1 150.0 70.0 70.0 5.0 225.0 520.0 104.00 2 60.0 20.0 20.0 3.0 70.0 173.0 34.60 3 800.0 140.0 140.0 20.0 1300.0 2400.0 480.00 4 30.0 15.0 15.0 1.0 40.0 101.0 20.20     SUM 1040 245 1635 3194.0 2.      REQUISITE CALCULATIONS FOR ANOV n = 20 SS TOT = 1954728.2 by =VARP(Range) * n AVG = 159.7 SS YR = 2640090.8 by =VARP(YR SUMS) * 9/3 SS VAR = 108079.63 by =VARP(VARIETY SUMS) * 3/9 3.     ANOV AS A CRD (treating years as samples) SOURCE df df code SS MS F F.05,.01 Total 19 v * y -1 1954728.2 Variety 2 v - 1 108079.63 54039.81 0.50 3.4,5.61 Error 17 v * (y - 1) 1846648.6 108626.39     CV = 206.38% 4.     ANOV AS AN RCB (treating years as reps) SOURCE df df code SS MS F F.05,.01 Total 19 v * r -1 1954728.2 Variety 2 v - 1 108079.63 54039.81 -0.61 3.63,6.23 Rep (yr.) 8 r - 1 2640090.8 330011.34 -3.74 2.59,3.89 Error 9 (v-1)*(r-1) -793442.18 -88160.24     CV = #NUM! 5.     RELATIVE EFFICIENCY OF THE TWO DESIGNS; VARIOUS APPROACHES     5-1   CV values can be directly compared CRD RCB 206.38% vs. #NUM! (a great improvement)     5-2   Error Variances can be compared to calculate percent reduction in error variance [MSe (CRD) - MSe (RCB)] / [MSe (CRD)]    = 181.16% (MS error was greatly reduced)     5-3   Significance of Replication variance      If F values for reps (blocks) is significant, we have observed a significant reduction of     error variance due to blocking; Here, F for 'reps' (= years) did prove highly significant.     5-4    Relative Efficiency Formula Relative Efficiency   =   [100*MSe(CRD) / MSe(RCB)] * CF       Where the CF = (e1+1)(e2+3)/(e1+3)(e2+1)      And e1 = df of the MSe in a RCB = 9      And e2 = df of the MSe in a CRD = 17      The CF is thus calculated here to be = 0.966315789

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.