Practice Problems
                                                   Practice Problems
             Problem 1:
             The following represent activities in a major construction project. Draw the 
             network to represent this project. 
                                                   Activity                   Immediate Predecessor
                                                         A                                          —
                                                         B                                          —
                                                         C                                           A
                                                         D                                           B
                                                         E                                           B
                                                         F                                        C, E
                                                        G                                            D
                                                         H                                        F, G
                PowerPoint presentation to accompany Heizer/Render –                      3-2                      © 2004 by Prentice Hall, Inc.,  Upper Saddle River, N.J. 07458
                Principles of Operations Management, 5e, and Operations 
                Management, 7e
                                                  Practice Problems
                                                   Practice Problems
             Problem 2:
             Given the following Time Chart and Network Diagram, find the Critical Path.
                 Activity             a          m           b           t         Variance                                 Activity C
                                                                                                                               t = 6
                      A               2           3          4           3              1/9
                      B               1           2          3           2              1/9                 Activity A                                           Activity E
                      C               4           5         12           6             16/9                    t = 3                                                 t = 2
                      D               1           3          5           3              4/9                                                    Activity D
                      E               1           2          3           2              1/9                                                       t = 3
                                                                                                                               Activity B
                                                                                                                                  t = 2
                PowerPoint presentation to accompany Heizer/Render –                      3-3                      © 2004 by Prentice Hall, Inc.,  Upper Saddle River, N.J. 07458
                Principles of Operations Management, 5e, and Operations 
                Management, 7e
                                                  Practice Problems
                                                   Practice Problems
             Problem 2:
             Given the following Time Chart and Network Diagram, find the Critical Path.
                 Activity             a          m           b           t         Variance                                 Activity C
                                                                                                                               t = 6
                      A               2           3          4           3              1/9
                      B               1           2          3           2              1/9                 Activity A                                           Activity E
                      C               4           5         12           6             16/9                    t = 3                                                 t = 2
                      D               1           3          5           3              4/9                                                    Activity D
                      E               1           2          3           2              1/9                                                       t = 3
                                                                                                                               Activity B
                                                                                                                                  t = 2
                                                                                                                       Critical Path
                PowerPoint presentation to accompany Heizer/Render –                      3-4                      © 2004 by Prentice Hall, Inc.,  Upper Saddle River, N.J. 07458
                Principles of Operations Management, 5e, and Operations 
                Management, 7e
                                                  Practice Problems
                                                   Practice Problems
             Problem 3:
             What is the variance in completion time for the 
             critical path found in Problem 2? 
                 Activity             a          m           b           t         Variance                                 Activity C
                                                                                                                               t = 6
                      A               2           3          4           3              1/9
                      B               1           2          3           2              1/9                 Activity A                                           Activity E
                      C               4           5         12           6             16/9                    t = 3                                                 t = 2
                      D               1           3          5           3              4/9                                                    Activity D
                      E               1           2          3           2              1/9                                                       t = 3
                                                                                                                               Activity B
                                                                                                                                  t = 2
                                                                                                                       Critical Path
                PowerPoint presentation to accompany Heizer/Render –                      3-5                      © 2004 by Prentice Hall, Inc.,  Upper Saddle River, N.J. 07458
                Principles of Operations Management, 5e, and Operations 
                Management, 7e
                                         Total variance =  variances of activities on critical path
                                                  Practice Problems
                                                   Practice Problems
             Problem 3:
                                         Total variance = 1/9 + 16/9 + 4/9 + 1/9 = 23/9 = 2.56
                                                                  23                 23               4.796
             What is the variance in completion time for the 
                                         And  =              =             =                = 1.6 and     2.56 = 1.6
                                                                    9                 3                    3
             critical path found in Problem 2? 
                 Activity             a          m           b           t         Variance                                 Activity C
                                                                                                                               t = 6
                      A               2           3          4           3              1/9
                      B               1           2          3           2              1/9                 Activity A                                           Activity E
                      C               4           5         12           6             16/9                    t = 3                                                 t = 2
                      D               1           3          5           3              4/9                                                    Activity D
                      E               1           2          3           2              1/9                                                       t = 3
                                                                                                                               Activity B
                                                                                                                                  t = 2
                                                                                                                       Critical Path
                PowerPoint presentation to accompany Heizer/Render –                      3-6                      © 2004 by Prentice Hall, Inc.,  Upper Saddle River, N.J. 07458
                Principles of Operations Management, 5e, and Operations 
                Management, 7e