Managerial Decision Making and Problem Solving

1. Managerial Decision Making and Problem Solving Computer Lab Notes 1

2. Basic Excel functions and operators • Arithmetic Operations • Addition of cells A1and B1: • Subtracting cell B1 from A1: • Multiplication of cell A1 by B1: • Division of cell A1 by B1: • Cell A1xraised to the power in cell B1: = A1 + B1 = A1 - B1 = A1 * B1 = A1 / B1 = A1^ B1

3. Basic Excel functions and operators • Relative and absolute addresses • All row and column references are considered relative unless preceded by a “$” sign • When copied, ‘relative addresses’ change relative to the original cell position.Example: Cell E5 =A1+B$3+$C4+$D$6 = C5+D$3+$C8+$D$6 Cell G9

4. Basic Excel functions and operators • Arithmetic functions • Sum =SUM(A1:A3) • Returns the sum A1+A2+A3 • Average =Average(A1:A3) • Returns the arithmetic average of cells A1, A2, A3 • SUMPRODUCT =SUMPRODUCT(A1:A3,B1:B3) • Returns the sum of products A1·B1+A2·B2+A3·B3 • ABS =ABS(A3) • Returns the absolute value of the entry in cell A3.

5. Basic Excel functions and operators • Arithmetic functions – continued • SQRT =SQRT(A3) • Returns ÖA3 • MAX =MAX(A1:A9) • Returns the Maximum of the entries in cells A1 through A9. • MIN =MIN(A1:A9) • Returns the Minimum of the entries in cells A1 through A9.

6. Basic Excel functions and operators • Statistical functions • RAND() =RAND() • Generate a random number between 0 and 1 from a uniform distribution. • Probabilities and variable values under the normal distribution • NORMDISTNORMINV=NORMDIST(25,20,3,TRUE) =NORMINV(.55,20,3) Returns P(X<25) when m = 20 Returns x0,, such that P(X<x0)=.55 and s = 3 when m = 20 and s = 3 • NORMSDISTNORMSMINV=NORMSDIST(1.78) =NORMSINV(.55)Returns P(Z<1.78) Returns z0, such that P(Z<z0)=.55

7. Basic Excel functions and operators • Statistical functions • Probabilities and variable values under the t- distribution • TDISTTINV=TDIST(1.5,12,1) =TINV(.05,15) Returns P(t>1.5) when n=12 Returns t0,, such that P(t<-t0)=.025 and P(t>t0)=.025 when n=15.Note:=TDIST(1.5,12,2) returns P(t<-1.5) + P(t>1.5) when n=12.

8. Basic Excel functions and operators • Statistical functions – Other probability distributions • Poisson =POISSON(7,5,TRUE) • Returns P(X<7) for Poisson with l = 5.Note: false returns the probability density P(X = 7) • EXPONDIST =EXPONDIST(40,1/20,TRUE) • Returns P(X<40) for the exponential distribution with 1/m=20Note: false returns the probability density f(40)=20exp(-20(40))

9. Basic Excel functions and operators • Conditional functions: • IF =IF(A4>4,B1+B2, B1 – B2) • Returns B1+B2 if A4>4, and B1 – B2 if A4£4. • SUMIF =SUMIF(F1:F12, “>60”,G1:G12) • Returns G1+G2+…+G12 only if F1+F2+…+F12>60

10. Basic Excel functions and operators • VLOOKUP =VLOOKUP(6.6,A1:E6,4) • If the values in column A of a given table [A1:E6] are sorted (in an ascending order), VLOOKUP finds the largest value in column A that is less than or equal to 6.6, identifies the row it belongs to, and returns the value in the fourth column that correspond to this row.Note: If the values in column A are not sorted, =VLOOKUP(6.6,A1:E6,4,FALSE) finds the value 6.6 in column A, identifies the row it belongs to, and returns the value in the fourth column that corresponds to this row.

11. Using Excel Solver to Find an Optimal Solution and Analyze Results

12. Using Excel Solver to Find an Optimal Solution and Analyze Results

13. Using Excel Solver to Find an Optimal Solution and Analyze Results

14. Using Excel Solver to Find an Optimal Solution and Analyze Results

15. Using Excel Solver to Find an Optimal Solution and Analyze Results

16. Using Excel Solver – Optimal Solution

17. Using Excel Solver –Answer Report

18. Using Excel Solver –Sensitivity Report

19. Solver – Infeasible Model

20. Solver – Unbounded solution

21. Solver – An Alternate Optimal Solution • Solver does not alert the user to the existence of alternate optimal solutions. • Many times alternate optimal solutions exist when the allowable increase or allowable decrease is equal to zero. • In these cases, we can find alternate optimal solutions using Solver by the following procedure:

22. Solver – An Alternate Optimal Solution • Observe that for some variable Xj the Allowable increase = 0, or Allowable decrease = 0. • Add a constraint of the form: Objective function = Current optimal value. • If Allowable increase = 0, change the objective to Maximize Xj • If Allowable decrease = 0, change the objective to Minimize Xj