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					 Resource Allocation & Leveling
Resource Leveling: Reschedule the noncritical
  tasks to smooth resource requirements
Resource Allocation: Minimize project
  duration to meet resource availability constraints
Resource Allocation & Leveling
Three types of resources:
  1) Renewable resources: “renew” themselves
      at the beginning of each time period (e.g.,
      workers)
  2) Non-Renewable resources: can be used at
      any rate but constraint on total number
      available
  3) Doubly constrained resources: both
      renewable and non-renewable
Resource Leveling
                                  Tas k C
                                   9 wk s


                Tas k A
                 3 wk s           Tas k D
                                   5 wk s

    START                                            Tas k G
                                                      5 wk s            END



                Tas k B           Tas k E
                 2 wk s            3 wk s




                                  Tas k F
                                   2 wk s



        Tas k      Work ers   Duration (tj)   Early Start      Late Start
         A           7              3              0               0
         B           3              2              0               3
         C           2              9              3               4
         D           10             5              3               3
          E          4              3              2               5
          F          5              2              2              11
         G           6              5              8               8
Resource Leveling: Early Start Schedule
Resource Leveling: Late Start Schedule
Resource Leveling: Microsoft Project
         De c 1 7, '0 0                                                  De c 2 4, '0 0                               De c 3 1, '0 0                               Ja n 7, '01
     T          W         T           F           S   S   M          T           W        T    F    S   S   M    T            W        T    F    S   S   M    T          W       T    F    S
25




20




15




10




 5




                10        10         10                   10        10          10        10   10           10   10          16        16   16           16   16        21       21   21
     Work ers                  Overa ll ocated:            Al l oca te d:
Renewable Resource Allocation Example
(Single Resource Type)

              3 workers        6 workers


              Task A            Task C
               4 wks             1 wk




   START                                   Task E
                                            4 wks         END

              Task B          Task D
              3 wks            5 wks       7 workers



              5 workers      8 workers



    Maximum number of workers available = R = 9 workers
      Resource Allocation Example: Early Start Schedule

                               Tas k A:                Tas k C:
                               3 work ers             6 work ers


              Start
                                                                                                               End

                          Tas k B:
                         5 work ers                                                          Tas k E:
                                                                                            7 work ers
                                                            Tas k D:
                                                           8 work ers




              Week       1       2          3    4    5        6        7    8    9    10        11      12
   No. of Work e rs/wk   8      8           8    11   14       8        8     8   7     7        7        7
 Cumulative Work ers     8      16          24   35   49       57       65   73   80   87        94      101
"Waste d" work er-wk s   1      1           1     -    -        -        -    -    -    -         -       -

                  Maximum number of workers available = R = 9 workers
       Resource Allocation Example: Late Start Schedule


                                                 Tas k A:
                                                 3 work ers
              Start
                                                                        Tas k C:
                                                                                                                End
                                                                       6 work ers
                          Tas k B:
                                                                                              Tas k E:
                         5 work ers
                                                                                             7 work ers
                                                      Tas k D:
                                                     8 work ers



              Week       1       2    3    4    5        6        7     8           9   10        11      12
   No. of Work e rs/wk   5      5     5    11   11       11       11    14      7        7        7        7
 Cumulative Work ers     5      10    15   26   37       48       59    73      80      87        94      101
"Waste d" work er-wk s   -       -     -    -    -        -        -     -      2        2        2        2


                   Maximum number of workers available = R = 9 workers
    Resource Allocation Heuristics
n    Some heuristics for assigning priorities to available tasks j, where       Rk denotes the
                                                                                 j
     number of units of resource k used by task j

n    1) FCFS:    Choose first available task
n    2) GRU: (Greatest) resource utilization =   • Rk
                                                    j

n
                                                   k
     3) GRD: (Greatest) resource utilization x task duration =  • Rk  j    tj
                                                                 k
n    4) ROT: (Greatest) resource utilization/task duration =   • Rk / tj
                                                                   j
n    5) MTS: (Greatest) number of total successors               k

n    6) SPT: Shortest processing time = min {tj}
n    7) MINSLK: Minimum (total) slack
n    8) LFS: Minimum (total) slack per successor
n    9) ACTIMj: (Greatest) time from start of task j to end of project = CP - LSj
n    10) ACTRESj: (max) (ACTIMj)
n    11) GENRESj: w ACTIMj + (1-w) ACTRESj where 0 ≤ w ≤ 1
Resource Allocation Problem #2


                Tas k A1          Tas k A2
                 6 days            4 days




 Start          Tas k B1          Tas k B2
                 3 days                        End
                                   5 days




               Tas k C1           Tas k C2
                2 days             5 days



              Gold Crew          Purple Crew
    How to schedule tasks to minimize project makespan?

  Priority scheme: schedule tasks using total slack (i.e., tasks with
  smaller total slack have higher priority)




                        Task A1               Task B1        Task C1
Gold Crew
            1   2   3      4      5   6   7      8       9   10    11   12    13   14   15   16   17    18   19   20


                                               Task A2                       Task B2                   Task C2
 Purple
            1   2   3      4      5   6   7      8       9   10    11   12    13   14   15   16   17    18   19   20
  Crew
     Resource Allocation Example (cont’d)

     But, can we do better? Is there a better priority scheme?




Gold Crew
            1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20



 Purple
            1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20
  Crew
Microsoft Project Solution (Resource Leveling Option)




                                      Solution by: Microsoft Project 2000
Critical Chain Project Management
• Identify the critical chain: set of tasks that determine the overall
           duration of the project
• Use deterministic CPM model with buffers to deal with uncertainty
• Remove padding from activity estimates (otherwise, slack will be
        wasted). Estimate task durations at median.
• Place project buffer after last task to protect customer’s completion
          schedule
• Exploit constraining resource(s)
• Avoid wasting slack times by encouraging early task completions
• Have project team focus 100% effort on critical tasks
• Work to your plan and avoid tampering
• Carefully monitor and communicate buffer status
Critical Chain Buffers


Project Buffer                       : placed after last task in project to protect schedule




Feeding Buffers                           : placed between a noncritical task and a critical task

when the noncritical task is an immediate predecessor of the critical task


Resource Buffers                             : placed just before a critical task that uses a new


resource type
Critical Chain Illustrated

                                   Feeding Buffers

              Tas k C1        Tas k B1           Tas k A1
               2 days          3 days             6 days



 Start                                                          End



                   Tas k C2        Tas k B2          Tas k A2
                    5 days          5 days            4 days


Resource Buffers
Non-Renewable Resources
                                       12 units


                                      Task B
                                      5 wks
                 6 units                                          8 units


                    Task A                                 Task D
   ST ART                                                                            END
                     6 wks                                  2 wks

                                       Task C
                                        3 wks


                                        10 units


                                  No. of Nonrene wable
                                    Resource s Units
            Tas k      Duration          Needed          Early Start        Late Start
             A             6               6                 0                 0
             B             5               12                6                 6
             C             3               10                6                 8
             D             2               8                 11                11
                       Non-Renewable Resources: Graphical Solution


                                                                                                           Cumulative Res ources
                                                                                                                Supplied


                       40

                       36
Cumulative Resources




                       32                   Cumulative Res ources
                                                Required
                       28

                       24

                       20

                       16

                       12

                       8

                       4


                            1   2   3   4       5     6    7        8   9   10   11   12   13   14   15   16   17   18    19   20
                                                                        Weeks
Resource Allocation Problem #3
Issue: When is it better to “team” two or more
       workers versus letting them work separately?

• Have 2 workers, Bob and Barb, and 4 tasks: A, B, C, D
• Bob and Barb can work as a team, or they can work separately
• When should workers be assigned to tasks? Which configuration
        do you prefer?
How to Assign Project Teams?

                         A                       C

        Start                                                  End
                         B                       D



                              Configuration #1
  Bob and Barb work jointly on all four tasks; assume that they can complete each
        task in one-half the time needed if either did the tasks individually


                              Configuration #2
   Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is
                          assigned to tasks B and D
Bob and Barb: Configuration #1

  TASK A                TASK B                TASK C              TASK D
 Dur ation   Pr ob     Dur ation     Pr ob   Dur ation   Pr ob   Dur ation   Pr ob
      6      0.33          9         0.667       12       0.6        10      0.25
      5      0.33          6         0.333        7       0.4         6      0.75
      4      0.33
 Expected
 dur ation   5.0                      8.0                10.0                7.0




                                   Configuration #1
              Bob and Barb work jointly on all four tasks.
                    What is the expected project makespan?
     Bob and Barb: Configuration #2
                 Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is
                                        assigned to tasks B and D
                                                                                      m ax
                                                                Bob       Barb      (A+C,
Re alization #         A          B          C         D       A+C        B+D        B+D)     Pr ob
        1              6          9         12        10         18        19         19      0.03
        2              6          9         12         6         18        15         18      0.10
        3              6          9          7        10         13        19         19      0.02
        4              6          9          7         6         13        15         15      0.07
        5              6          6         12        10         18        16         18      0.02
        6              6          6         12         6         18        12         18      0.05
        7              6          6          7        10         13        16         16      0.01
        8              6          6          7         6         13        12         13      0.03
        9              5          9         12        10         17        19         19      0.03
       10              5          9         12         6         17        15         17      0.10
       11              5          9          7        10         12        19         19      0.02
       12              5          9          7         6         12        15         15      0.07
       13              5          6         12        10         17        16         17      0.02
       14              5          6         12         6         17        12         17      0.05
       15              5          6          7        10         12        16         16      0.01
       16              5          6          7         6         12        12         12      0.03
       17              4          9         12        10         16        19         19      0.03
       18              4          9         12         6         16        15         16      0.10
       19              4          9          7        10         11        19         19      0.02
       20              4          9          7         6         11        15         15      0.07
       21              4          6         12        10         16        16         16      0.02
       22              4          6         12         6         16        12         16      0.05
       23              4          6          7        10         11        16         16      0.01
       24              4          6          7         6         11        12         12      0.03
Bob and Barb: Configuration #2

  Bob and Barb work independently. Bob is assigned to tasks A and C; Barb is
                         assigned to tasks B and D



                      m ax (A+C,              Cum ulative
                         B+D)        Pr ob       Pr ob
                          12         0.07         0.07
                          13         0.03         0.10
                          15         0.20         0.30
                          16         0.20         0.50
                          17         0.17         0.67
                          18         0.17         0.83
                          19         0.17         1.00




          Expected Project Makespan: 16.42
Parallel Tasks with Random Durations


                              Task A

        START
                                                        END


                              Task B




  • Assume that both Tasks A and B have possible durations:
            8 days with probability = 0.5
            10 days with probability = 0.5
  • What is expected duration of project? (Is it 9 days?)
Project Monitoring and Control
          n   “It is of the highest importance in
              the art of detection to be able to
              recognize, out of a number of acts,
              which are incidental and which are
              vital. Otherwise your energy and
              attention must be dissipated instead
              of being concentrated.”

                         Sherlock Holmes
Status Reporting?

One day my Boss asked me to submit a status
report to him concerning a project I was working
on. I asked him if tomorrow would be soon enough.
He said, "If I wanted it tomorrow, I would have
waited until tomorrow to ask for it!"

             New business manager, Hallmark Greeting Cards
    Control System Issues
n   What are appropriate performance metrics?
n   What data should be used to estimate the value of each
    performance metric?
n   How should data be collected? From which sources? At
    what frequency?
n   How should data be analyzed to detect current and future
    deviations?
n   How should results of the analysis be reported? To whom?
    How often?
Controlling Project Risks
 Key issues to control risk during projecct:
 (1) what is optimal review frequency, and
 (2) what are appropriate review acceptance levels
        at each stage?


    “Both over-managed and under-managed
    development processes result in lengthy design
    lead time and high development costs.”
                  Ahmadi & Wang. “Managing Development Risk in
                  Product Design Processes”, 1999
Project Control & System Variation

 Common cause variation: “in-control” or normal
     variation
 Special cause variation: variation caused by forces
        that are outside of the system

  According to Deming:
  • Treating common cause variation as if it were special cause variation
           is called “tampering”
  • Tampering always degrades the performance of a system
Control System Example #1
 n   Project plan: We estimate that a task
         will take 4 weeks and require
            n   1600 worker-hours

     At the end of Week 1, 420 worker-hours
                  have been used



       Is the task “out of control”?
Control System Example (cont’d)
 Week 2: Task expenses = 460 worker-hours
                                                                Cumulative
          Planned Cost                                          Actual Cost
     Week   (BCWS)                             Actual Cost       (ACWP)
      1        400                                 420              420
      2        400                                 460              880
                                     470
                                     460
                                     450
            Cost (in worker-hours)




                                     440
                                     430
                                     420
                                     410
                                     400
                                     390
                                     380
                                     370
                                           1    2           3    4
                                                    We ek




   Is the task “out of control”?
Control System Example (cont’d)
   Week 3: Task expenses = 500 worker-hrs
             Planned cost            Actual cost    Cumulative cost
  We ek     (worker-hours)         (worker-hours)   (worker-hours)
   1             400                    420              420
   2             400                    460              880
   3             400                    500              1380

                         600

                         500
          Worker-hours




                         400

                         300

                         200

                         100

                           0
                               1    2           3        4
                                        We ek



     Is the task “out of control”?
Earned Value Analysis
• Integrates cost, schedule, and work performed
• Based on three metrics that are used as the basic
      building blocks:


BCWS: Budgeted cost of work scheduled
ACWP: Actual cost of work performed
BCWP: Budgeted cost of work performed
Schedule Variance (SV)

Schedule Variance (SV) = difference between value of
      work completed and value of scheduled work


Schedule Variance (SV) = Earned Value - Planned Value
                        = BCWP - BCWS
Cost Variance (CV)

Cost Variance (CV) = difference between value of
                    work completed and actual
                    expenditures


Cost Variance (CV) = Earned Value - Actual Cost
                   = BCWP - ACWP
Earned Values Metrics Illustrated
                                                        Planned Value
                                Present time               (BCWS)
                                                                                    BAC
  Worker-Hours




                      Actual Cost
                       (ACWP)
                                                                 Cost Variance
                                                                     (CV)
                 Earned Value
                   (BCWP)
                                                             Schedule Variance
                                                                   (SV)




                    Week 1      Week 2     Week 3   Week 4      Week 5     Week 6
Relative Measure: Schedule Index

        Schedule Index     (SI ) =   BCWP
                                     BCWS



   If SI = 1,   then task is on schedule
   If SI > 1,   then task is ahead of schedule
   If SI < 1,   then task is behind schedule
Relative Measure: Cost Index

                Cost Index (CI) =   BCWP
                                    ACWP


   If CI = 1,      then work completed equals
                    payments (actual expenditures)
   If CI > 1,      then work completed is ahead
                    of payments
   If CI < 1,      then work completed is behind
                    payments (cost overrun)
Example #2
                                     W E E K
              1    2        3        4        5        6      7        8       9          10

                  Tas k A (36 work e r-hrs)

              6    6        6        8        10


                                  Tas k B (36 work er-h rs)


                                     12       12       12

                                                              Tas k C (56 worke r-h rs)

                                                       10     10      12       12         12

  Weekly
 Scheduled
 Worker-Hrs
 Cumulative   6    6        6        20       22      22      10      12       12         12
 Scheduled
 Worker-Hrs
  (BCWS)      6   12       18        38       60      82      92     104      116         128
Example #2 (cont’d)
        Progress report at the end of week #5:


       Cumulative Percent of Work Completed:

          Week    1     2         3           4     5
         Task A 15%    30%       40%      60%      80%
         Task B                           25%      65%
         Task C             Not started yet




         Worker-Hours Charged to Project:

          Week    1     2         3           4     5
         Task A   5     6         8           10   10
         Task B                               15   10
         Task C             Not started yet
Example #2 (cont’d)
                          Progress report at the end of week #5:


                                           W E E K
                    1       2      3       4       5     6    7    8     9     10
  Cumulative
   Sche duled
  Work er-Hrs
    (BCWS)          6       12    18      38      60     82   92   104   116   128
 Actual Work er-
    Hrs Use d
    (ACWP)          5       11    19      44      64
 Earned Value
   (BCWP)          5.4     10.8   14.4   30.6    52.2
   Sche dule
 Variance (SV)     -0.6    -1.2   -3.6   -7.4    -7.8
 Cost Varian ce
     (CV)          0.4     -0.2   -4.6   -13.4   -11.8
Example #2 (cont’d)
                         140
                                                                                        BAC


                         120
                                                                            BCWS



                         100
    Performance Metric




                          80
                                               Cost
                                             Variance
                                                                        Sch edule
                          60
                                                                        Variance

                                       ACWP
                          40

                                                        BCWP

                          20



                           0
                               1   2     3        4     5           6       7       8     9   10
                                                            We ek
Using a Fixed 20/80 Rule
                   Cumulative Percent of Work Completed:

                          Week     1          2         3        4          5
                         Task A 20%          20%       20%       20%       20%
                         Task B                                  20%       20%
                         Task C                   Not started yet




                                             W E E K
                   1         2         3           4         5         6         7   8     9     10
   Cumulative
   Sche duled
   Work er-Hrs
    (BCWS)         6        12         18         38        60       82         92   104   116   128
 Actual Work er-
    Hrs Use d
    (ACWP)         5        11         19         44        64
  Earned Value
    (BCWP)         7.2      7.2        7.2     14.4      14.4
    Sche dule
 Variance (SV)     1.2      -4.8   -10.8      -23.6      -45.6
 Cost Varian ce
      (CV)         2.2      -3.8   -11.8      -29.6      -49.6
Using a Fixed 20/80 Rule
                               140



                               120



                               100
    Cost (in Worke r-hour s)




                                80
                                                                                  BCWS
                                                 ACWP
                                60



                                40


                                                                       BCWP
                                20



                                 0
                                     1   2   3          4   5          6      7      8   9   10
                                                                Week
Updating Forecasts: Pessimistic Viewpoint

         Assumes that rate of cost overrun will continue
                      for life of project….




  Estimate at Completion (EAC) = ACWP BAC = 1 BAC .
                                 BCWP       CI

                      = (64/52.2) 128 = 1.23 x 128 = 156.94 worker-hrs
Updating Forecasts: Optimistic Viewpoint

             Assumes that cost overrun experienced to date
             will cease and no further cost overruns will be
               experienced for remainder of project life…




Estimate at Completion (EAC) = BAC - CV = 128 + 11.8 = 139.8 worker-hrs .
Multi-tasking with Multiple Projects

  How to prioritize your work when you have multiple
                   projects and goals?

   Consider two projects with and without multi-tasking

               Project A                     Project B



         A-1   B-1         A-2   B-2   A-3   B-3         A-4   B-4
Due-Date Assignment with Dynamic Multiple Projects


• Projects arrive dynamically (common situation for both
        manufacturing and service organizations)
• How to set completion (promise) date for new projects?
• Firms may have complete control over due-dates or only partial
        control (i.e., some due dates are set by external sources)
• How to allocate resources among competing projects and tasks (so
        that due dates can be realized)?
• What are appropriate metrics for evaluating various rules?
  What Does the Research Tell Us?
• Study by Dumond and Mabert* investigated four due date assignment
        rules and five scheduling heuristics
• Simulated 250 projects that randomly arrive over 2000 days
        • average interarrival time = 8 days
        • 6 - 49 tasks per project (average = 24); 1 - 3 resource types
        • average critical path = 31.4 days (range from 8 to 78 days)
• Performance criteria: 1) mean completion time
                             2) mean project lateness
                             3) standard deviation of lateness
                             4) total tardiness of all projects
• Partial and complete control on setting due dates
                  * Dumond, J. and V. Mabert. “Evaluating Project Scheduling and Due Date Assignment Procedures:
                  An Experimental Analysis” Management Science, Vol 34, No 1 (1988), pp 101-118.
Experimental Results


 • No one scheduling heuristic performs best across all due date
         setting combinations
 • Mean completion times for all scheduling and due date rules not
         significantly different
 • FCFS scheduling rules increase total tardiness
 • SPT-related rules do not work well in PM (SASP)
 • Best to use more detailed information to establish due dates
Project Management Maturity Models

• Methodologies to assess your organization’s current level of
        PM capabilities
• Based on extensive empirical research that defines “best
        practice” database as well as plan for improving PM process
• Process of improvement describes the PM process from
        “ineffective” to “optimized”
• Also known as “Capability Maturity Models”
PM Maturity Model Example*
1)   Ad-Hoc      The project management process is described as disorganized, and occasionally even
     chaotic. Systems and processes are not defined. Project success depends on individual effort.
     Chronic cost and schedule problems.
2)   Abbreviated: Some project management processes are established to track cost, schedule,
     and performance. Underlying disciplines, however, are not well understood or consistently
     followed. Project success is largely unpredictable and cost and schedule problems are the norm.
3)   Organized: Project management processes and systems are documented, standardized, and
     integrated into an end-to-end process for the company. Project success is more predictable. Cost
     and schedule performance is improved.
4) Managed: Detailed measures of the effectiveness of project management are collected and used
     by management. The process is understood and controlled. Project success is more uniform.
     Cost and schedule performance conforms to plan.
5) Adaptive:     Continuous improvement of the project management process is enabled by feedback
     from the process and from piloting innovative ideas and technologies. Project success is the
     norm. Cost and schedule performance is continuously improving.

* source: The Project Management Institute PM Network (July, 1997), Micro Frame Technologies, Inc. and
                   Project Management Technologies, Inc. (http://pm32.hypermart.net/)

				
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