LIUC11 - 3b - Resource Scheduling [modalità compatibilità]my.liuc.it/MatSup/2010/N90312/LIUC11 -...

Project ManagementResource Scheduling

Mauro Mancini ©

Resource SchedulingEng. Giorgio Locatelli

Resource scheduling

Mauro Mancini © 2

Resource Scheduling

Project Management: “The planning, monitoring and controlof all aspects of theproject and the motivation of all those involved in it to achieve the projectobjectives on time and to the specified cost, quality and performance”. (ProjectManagement Institute - PMI)”

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Resource Scheduling

• Project scheduling with infinite capacity• Resources allocated profile evaluation• Comparison between resources requirements / availability• Resource leveling• Resource constrained project scheduling problem (RCPSP): fixed times or

resources

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Project disaggregation in more activities

Precedence relationships among activities

Trade - offLength activities/ resources allocation

Resource Scheduling

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Project’s resources reallocation

CPM Project length assessment

Resources requirements / availability evaluation

Plan execution

Reporting

5

CPM vs. Resource Scheduling

CPM Resource Scheduling

Consider infinite capacity Consider limits on resources availability

Precedence relationshipsarestable

Embodying all the kinds of relationships,consider that they may be dynamic andtemporary

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arestabletemporary

Critical chain is a functionof time and naturalprecedence

Critical chain is a function of time, all the kindsof relationships, resources need and availability,access priority of the activities to the resources

Activities floats dependonly on project duration

Activities floats depend on resources need andavailability

Steps to apply a Resource Management methodology

1. Infinite capacity programming

2. Aggregate resource need evaluation

3. Cumulative resources need evaluation

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4. Finite capacity programming (Resource Constrained Project

Scheduling Problem)

5. Levelling resources need profile (Resource Leveling)

Schedulation Types

Overload Fixed time

Resources

LevellingResources

Time

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Fixed resources

Time

LimitationResources

Time

Time

Resource Levelling

Resource leveling aims to minimize the period-by-period variations in resource loading by shifting tasks within their slack allowances.

The purpose is to create a smoother distribution of resource usage.Advantages:• much less hands-on management is required if the use of a

given resource is nearly constant over its period of use. The PM

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given resource is nearly constant over its period of use. The PM ― can arrange to have the resource available when needed ― can have the supplier furnish constant amounts ― can arrange for a backup supplier if advisable

• resource usage is leveled, the PM may be able to use a “just-in-time” inventory policy without much worry that the quantity delivered will be wrong

Resource Levelling advantages

• when resources are leveled, the associated costs also

tend to be leveled

• it is a procedure that can be used for almost all

projects, whether or not resources are constrained

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Resource Constrained Project Scheduling problem (RCPSP)

� Optimization techniques

Limits:

• heavy computation

•“static” definition of the problem

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•“static” definition of the problem

•difficulty to determine “optimality” criteria, considering

several possible objectives in contrast.


� Heuristic approaches

Limits:

•they can pursue only one objective for every scheduling

•they obtain different performance according to the network

characteristics to which they are applied

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they obtain different performance according to the network

characteristics to which they are applied

•they are based on priority rules (to solve conflict between

activities that require common resources) fixed a priori,

without the possibility to adapt them to the project

characteristics.


Heuristic approaches

Evaluation of conflicts among activities to the access to shared resources

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One time and at local level

RCPSP

In each step:

•Determination of the activities’ list with precedence constraints verified (in competition with shared resources)

•Activities’ group selection with the resource availability having:ominimum delay of project’ completion

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ominimum delay of project’ completionopriority rules

•Parallel approach, forward, early start (front loading)

RCPSP

Heuristic Approach

•In series approach (static)oOrdinate list of starting activitiesoIt tends to advance by paths, in order of criticality

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•In parallel approach (dynamic)oOrdinate list of activities updated at each stepoIt tends to advance by temporal intervals

RCPSP

•In parallel approach•Rolling wave approach•Different priority rules (problem’s dependent)•Splitting / interrupting•Multi-resources vision•“What if” analysis

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•“What if” analysis

RCPSP

�HOW TO INCREASE RESOURCES

� Working Overtime

� Working Shifts

� Increase Productivity

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� Job and Knock

� Learning Curve

� Sub-Contractors

� Scope of Work

RCPSP

� HOW TO REDUCE RESOURCES

� Move unemployed resources to other activities

� Move unemployed resources to R&D jobs

� Hire out resources internally or externally

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� Hire out resources internally or externally

� Pre-manufacture components before they are needed

� Maintenance of equipment during slack periods

� Train workforce during slack periods to gain new skills which will make them more productive and flexible in

the future

� Send the under utilized workforce on leave

Series – Parallel Approach

P1 P2 P3

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Critical PathSeries approachParallel approach

Priority rules

MIN TF (Minimum Total Float)

The conflict to access to shared resources by different activities is solved giving priority to the activity with minimum float

It’s possible demonstrate that, using a parallel approach, the

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It’s possible demonstrate that, using a parallel approach, the MIN TF is equivalent to the MIN LST rule that grades activities according to the increasing values from the starting time at the latest

Priority rules

The precedence is given to the activity characterized by the minimum value for the dij parameter. It corresponds to the project duration increment that occurs when the j activity follows the i activity with:

RSM (“Resource Scheduling Method”)

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dij = max [0; EFTi-LSTj]

Where:EFTi = Earliest finish time for the i activityLSTj = Latest start time for the j activity

Priority rules

RSM (“Resource Scheduling Method”)

The comparison is made among all the pairs belonging to the sets ofactivities in conflict for the access to shared resources. This rulegives results similar to the MIN LFT rule.

EFTiLST

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dij

EFTiLSTi

MIN LFT (“Minimum Late Finish Time”)

This rule sequences the activities giving precedence to activitiescharacterized by minimum late finish Time.

Priority rules

GRD (“Greatest Resource Demand”)It use the priority criterion of unit’s resource requirements (considering allthe demanded resources) associated to each activity , giving precedence tothe activities characterized by a greater requirements (they can potentiallycreate bottlenecks). The priority grade associated to eachactivity iscomputed in this way:

m

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Where:dj = j activity durationrij = i type resource requirements for each unit of time by thej activitym = number of the different types of resources

Priority = di • Σ rij

m

i =1

Priority rules

GRU (“Greatest Resource Utilization”)

This rule gives the priority, in each program step, to the combination ofactivities that obtaining the maximal possible saturationfor the availableresources. The rule implementation requires the resolution of a linearprogramming problem of integer number (0,1).

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SIO (“Shortest Imminent Operation”)

The priority is given to the activities with shortest duration. This rulecomes from job-shop scheduling problem.

Priority rules

This rule gives the priority to the combination of activities

that allows to program the maximum possible number of

activities in each programming step.

It differs to the GRU rule because the determination of the

maximum possible number of activities considers only the

MJP (“Most Job Possible”)

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maximum possible number of activities considers only the

feasibility, that is the availability of resources, and not their

saturation level.

Series – Parallel Approach Exercise

Considering a project composed by the following activities

A 32 0

B 04 2

E 41 0

L 03 5

Att. RaDur. Rb

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C 62 0

F 24 0

D 05 2

H 48 4

G 31 0

I 53 0

M 25 0

N 22 0


1. To compute the EST, EFT, LST, LFT and the resource allocatedtemporal profile

2. Using the “min total float” with fixed time levelling andresource availability of 7 units/day for the A resource (andinfinite availability for the B resource) to schedule the activitieswith:

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with:Series approachParallel approach

3. Like at point 2, but levelling with fixed resources respecting theavailability for the A and B resources (6 units/day)


From the provided data is possible to obtain:

2

6

1

7

A 32 0

6

8

3

11

B 04 2

21

7

12

7

12

E 41 0

14

13

12

15

L 03 5

11873 1716

EFT

LST

EST

LFT

A 32 0

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1 2

C 62 0

13 15

9 12

F 24 0

4 8

D 05 2

10

3

3

10

H 48 4

1

7

1

7

G 31 0

4

8

2

10

I 53 0

15

11

11

15

M 25 0

16 17

N 22 0


Attività EST EFT LST LFT TF Ra Rb

A 1 2 6 7 5 3 -

B 3 6 8 11 5 - 2

C 1 2 1 2 - 6 -

D 3 7 4 8 1 - 2

E 7 7 12 12 5 4 -

F 8 11 9 12 1 2 -

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F 8 11 9 12 1 2 -

G 1 1 7 7 6 3 -

H 3 10 3 10 - 4 4

I 2 4 8 10 6 5 -

L 12 14 13 15 1 - 5

M 11 15 11 15 - 2 -

N 16 17 16 17 - 2 -


A

B

C

D

E

F

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F

G

H

I

L

M

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


8

9

10

11

12

13

14

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1

2

3

4

5

6

7

8

Resource - A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


8

9

10

11

12

13

14

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1

2

3

4

5

6

7

8

Resource - B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Series Approach – Fixed Times

2. The activities are scheduled considering the min total float

Activity C H M N D F L A B E G I

TF 0 0 0 0 1 1 1 5 5 5 6 6

The activities are scheduled considering the network diagram

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Available ACG � C

Available AGDH � H

Available AGD � D


2. The activities are scheduled considering the min total float

Activity C H M N D F L A B E G I

TF 0 0 0 0 1 1 1 5 5 5 6 6


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Available ACG � C

Available AGDH � H

Available AGD � D

Scheduling order

1° 2° 3° 4° 5° 6° 7° 8° 9° 10° 11° 12°C H D F A B E L G I M N


Programming phase (fixed times)

The C activity has been programmed (days 1-2 with 6 days delayresp. A)The H activity has been programmed (days 3-10 with 4 days delay resp. A)The D activity has been programmed (days 3-7 with 0 days delayresp. A)

Thepredeterminedorderis closelyfollowed

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Thepredeterminedorderis closelyfollowed


A

B

C

D

E

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F

G

H

I

L

M

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


7

8

9

10

11

12

13

14

I

Resource A (series)

I M

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1

2

3

4

5

6

7

C

H

A G

F

F

M N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

I

E

M

In order to respect the project deadline is necessary to havean overload (I)

Parallel Approach – Fixed Times

Algorithm’s step:

1. Creation the list of programmable activities2. Re-compute the relative TF and EST3. Tidy up the list activities4. Collocatedoneata time following thepoint3 order

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4. Collocatedoneata time following thepoint3 order5. Come back to point 1


Step 1 DATEAVAILABLEACTIVITIES TOTAL FLOAT

RESURCE AREQUIREMENTS

C 0 6

1° d. A 5 3

G 6 3

AVAILABLEUPDATED RESURCE A

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Step 2

H 0 4

3° d. D 1 -

A 3 3

G 4 3

AVAILABLEACTIVITIES

UPDATEDTOTAL FLOAT

RESURCE AREQUIREMENTSDATE

H, D, A start. G has been postponed because of lack of resources


Step 3 DATEAVAILABLEACTIVITIES

UPDATEDTOTAL FLOAT


G 2 3

5° d. B 3 --


UPDATEDTOTAL FLOAT


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The available resource is not enough, but is necessary starting the I activity the 6°day, in fact in order to respect the resource constraint, should be postpone I to the 11° day, with 3 days project’ delay

6° d. I 2 5





F 0 29° d.

E 3 4

UPDATEDTOTAL FLOAT

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Step 6

M 0 211° d.

E 1 4

AVAILABLEACTIVITIES

UPDATEDTOTAL FLOAT


H, D, A start. G has been postponed because of lack of resources





L 10 -12/13° d.

UPDATEDTOTAL FLOAT

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Step 8

N 0 216° d.

AVAILABLEACTIVITIES

UPDATEDTOTAL FLOAT



A

B

C

D

E

F

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FG

H

I

L

M

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


8

9

10

11

12

13

14Resource A (Parallel)

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1

2

3

4

5

6

7

8

CH

A G

F

F

M N1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

I E

M

Series and Parallel Approach – Fixed Resources

3.In case of fixed resources programming the project’ deadlineconstraint is not considered, but it is no longer possible havingoverload.

The series and parallel approach stay unchanged.Thesamescheduleremainsor theseriesapproach.

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Thesamescheduleremainsor theseriesapproach.


1

2

3

4

5

6

7

8

9

C

H

A G

F

F

M N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

E I

18 19 20 21 22

Resource - A

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

1

2

3

4

5

6

7

8

9

H

D B

B

L

Resource - B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Series Approach – Fixed Resources

A

BC

D

E L

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E

F

G

H I

L

M N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Series Approach – Fixed Resources

A

BC

D

EFG

L

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G

H I

M N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1718 19 20 21 22

Parallel Approach – Fixed Resources

123456789

C

H

A GF

M N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

I

18 19 20 21 22

Resource A

F

E

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1

2

3

4

5

6

7

8

9

H

D B

B

L

Resource - B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Suggestions

To obtain the best results it is convenient to adopt the followingexpedient:

• to use preferably parallel approach• to attempt different priority rules• to executeresourcelevelingalonga limited temporal period

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• to executeresourcelevelingalonga limited temporal period(according to a rolling wave approach)• to use options available on the software (splitting, interrupting,reprofiling, etc.)• to verify the possibility to maintain a “multi-resource” visionof the utilization resources profile coming from scheduling• to led what-if analysis, hypothesizing possible corrective actions

Example 2

Activity Duration Precendence ResourceA 2 g a[300%]B 4 g A b[200%]C 2 g a[600%]D 5 g C b[200%]E 1 g B a[400%]F 4 g D a[200%]G 1 g a[300%]

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G 1 g a[300%]

H 8 g Ca[400%];b[400%

]I 3 g G a[500%]L 3 g E;F b[500%]M 5 g H;I a[200%]N 2 g L;M a[200%]

Find the critical path, and the resources utilisation diagram (hypothesis of

infinite resources available). Assume to start on september 1

The Gantt and precedence diagramID Nome attività Durata Inizio Fine PredecessoriNomi risorse

1 A 2 g lun 01/09/08 mar 02/09/08 a[300%]

2 B 4 g mer 03/09/08 sab 06/09/08 1 b[200%]

3 C 2 g lun 01/09/08 mar 02/09/08 a[600%]

4 D 5 g mer 03/09/08 dom 07/09/08 3 b[200%]

5 E 1 g dom 07/09/08 dom 07/09/08 2 a[400%]

6 F 4 g lun 08/09/08 gio 11/09/08 4 a[200%]

7 G 1 g lun 01/09/08 lun 01/09/08 a[300%]

8 H 8 g mer 03/09/08 mer 10/09/08 3 a[400%];b[400%]

9 I 3 g mar 02/09/08 gio 04/09/08 7 a[500%]

10 L 3 g ven 12/09/08 dom 14/09/08 5;6 b[500%]

11 M 5 g gio 11/09/08 lun 15/09/08 8;9 a[200%]

0%

0%

0%

0%

0%

0%

0%

0%

0%

0%

0%

L M M G V S D L M M G V S D L M M G V S D01 set 08 08 set 08 15 set 08

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11 M 5 g gio 11/09/08 lun 15/09/08 8;9 a[200%]

12 N 2 g mar 16/09/08 mer 17/09/08 10;11 a[200%]

0%

0%

Resource a: utilisation diagram

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Resource b: utilisation diagram

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Resource constraints

Assume now that only 7 resources “a” are available.

What’s happen?

Solve the problem with a series approach

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Solve the problem with a series approach

Resource constraints:

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Schedule: step 1

Acivity duration EST EFT LST LFT TF Ra RbA 2 1 2 6 7 5 3B 4 3 6 8 11 5 2C 2 1 2 1 2 0 6D 5 3 7 4 8 1 2E 1 7 7 12 12 5 4F 4 8 11 9 12 1 2

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F 4 8 11 9 12 1 2G 1 1 1 7 7 6 3H 8 3 10 3 10 0 4 4I 3 2 4 8 10 6 5L 3 12 14 13 15 1 5M 5 11 15 11 15 0 2N 2 16 17 16 17 0 2

Schedule: step 2

Schedule with the serial approach1 2 3 4 5 6 7 8 9 10 11 12C H D F A B E L G I M N

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With same project duration 7 resources are not

enough (even with a parallel approach)

A possible solution: to add 4 more days

ID Nome attività Durata Inizio Fine PredecessoriNomi risorse

1 A 2 g mer 03/09/08 gio 04/09/08 a[300%]

2 B 4 g v en 05/09/08 lun 08/09/08 1 b[200%]

3 C 2 g lun 01/09/08 mar 02/09/08 a[600%]

4 D 5 g mer 03/09/08 dom 07/09/08 3 b[200%]

5 E 1 g lun 15/09/08 lun 15/09/08 2 a[400%]

6 F 4 g lun 08/09/08 gio 11/09/08 4 a[200%]

0%

0%

0%

0%

0%

0%

L M M G V S D L M M G V S D L M M G V S D L M01 set 08 08 set 08 15 set 08 22 set 08

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6 F 4 g lun 08/09/08 gio 11/09/08 4 a[200%]

7 G 1 g mer 03/09/08 mer 03/09/08 a[300%]

8 H 9 g mer 03/09/08 gio 11/09/08 3 a[400%];b[400%]

9 I 3 g v en 12/09/08 dom 14/09/08 7 a[500%]

10 L 3 g mar 16/09/08 gio 18/09/08 5;6 b[500%]

11 M 5 g lun 15/09/08 v en 19/09/08 8;9 a[200%]

12 N 2 g sab 20/09/08 dom 21/09/08 10;11 a[200%]

0%

0%

0%

0%

0%

0%

0%

It was the 17/09

A possible solution: to add 4 more days

Mauro Mancini © 60

LIUC11 - 3b - Resource Scheduling [modalità compatibilità]my.liuc.it/MatSup/2010/N90312/LIUC11 -...

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