Project ManagementResources Scheduling

Prof. Mauro Mancini

e-mail: Mauro.Mancini@polimi.it

tel.: +39-02-23994057

POLITECNICO DI MILANO

Department of Management, Economics and Industrial Engineering

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Resource Scheduling

Project Management: “The planning, monitoring and control of all

aspects of the project and the motivation of all those involved in it to

achieve the project objectives on time and to the specified cost, quality

and performance”. (Project Management 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 - off

Length activities/ resources allocation

Project’s resources

reallocation

CPM Project length

assessment

Resources requirements /

availability evaluation

Plan execution

Reporting

4

Resource Scheduling

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Precedence constraints among activities

“Natural” Constraints Constant

Resources Constraints Dynamic

•Natural

•Environmental (ex. resources availability constraints)

•Preferential

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CPM vs. Resource Scheduling

CPM Resource Scheduling

Consider infinite capacity Consider limits on resources availability

Precedence relationships

are stable

Embodying all the kinds of relationships,

consider that they may be dynamic and

temporary

Critical chain is a function

of time and natural

precedence

Critical chain is a function of time, all the kinds

of relationships, resources need and availability,

access priority of the activities to the resources

Activities floats depend

only on project duration

Activities floats depend on resources need and

availability

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Steps to apply a Resource Management

methodology

1. Infinite capacity programming

2. Aggregate resource need evaluation

3. Cumulative resources need evaluation

4. Finite capacity programming (Resource Constrained

Project Scheduling Problem)

5. Levelling resources need profile (Resource Leveling)

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Schedulation Types

Overload Fixed time

Fixed resources

Resources

LevellingResources

Time

LimitationResources

Time

Time

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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 ― 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

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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

•difficulty to determine “optimality” criteria, considering

several possible objectives in contrast.

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Resource Constrained Project Scheduling

problem (RCPSP)

� 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

•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.

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Resource Constrained Project Scheduling

problem (RCPSP)

Heuristic approaches

Evaluation of conflicts among activities to the access to

shared resources

One time and at local level

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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

opriority rules

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

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RCPSP

Heuristic Approach

•In series approach (static)

oOrdinate list of starting activities

oIt tends to advance by paths, in order of criticality

•In parallel approach (dynamic)

oOrdinate list of activities updated at each step

oIt tends to advance by temporal intervals

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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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RCPSP

�HOW TO INCREASE RESOURCES

� Working Overtime

� Working Shifts

� Increase Productivity

� Job and Knock

� Learning Curve

� Sub-Contractors

� Scope of Work

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RCPSP

� HOW TO REDUCE RESOURCES

� Move unemployed resources to other activities

� Move unemployed resources to R&D jobs

� 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

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Series – Parallel Approach

Critical Path

Series approach

Parallel approach

P1 P2 P3

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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 MIN TF is equivalent to the MIN LST rule

that grades activities according to the increasing values

from the starting time at the latest

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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”)

dij = max [0; EFTi-LSTj]

Where:

EFTi = Earliest finish time for the i activity

LSTj = Latest start time for the j activity

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Priority rules

RSM (“Resource Scheduling Method”)

The comparison is made among all the pairs belonging to

the sets of activities in conflict for the access to shared

resources. This rule gives results similar to the MIN LFT rule.

dij

EFTiLSTi

MIN LFT (“Minimum Late Finish Time”)

This rule sequences the activities giving precedence to

activities characterized by minimum late finish Time.

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Priority rules

GRD (“Greatest Resource Demand”)

It use the priority criterion of unit’s resource requirements

(considering all the demanded resources) associated to each

activity , giving precedence to the activities characterized by a

greater requirements (they can potentially create bottlenecks).

The priority grade associated to each activity is computed in this

way:

Where:

dj = j activity duration

rij = i type resource requirements for each unit of time by the j

activity

m = number of the different types of resources

Priority = di • Σ rij

m

i =1

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Priority rules

GRU (“Greatest Resource Utilization”)

This rule gives the priority, in each program step, to the

combination of activities that obtaining the maximal possible

saturation for the available resources. The rule implementation

requires the resolution of a linear programming problem of

integer number (0,1).

SIO (“Shortest Imminent Operation”)

The priority is given to the activities with shortest duration. This

rule comes from job-shop scheduling problem.

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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

feasibility, that is the availability of resources, and not

their saturation level.

MJP (“Most Job Possible”)

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Series – Parallel Approach Exercise

Considering a project composed by the following activities

A 32 0

B 04 2

C 62 0

E 41 0

L 03 5

F 24 0

D 05 2

H 48 4

G 31 0

I 53 0

M 25 0

N 22 0

Att. RaDur. Rb

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Series – Parallel Approach Exercise

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

allocated temporal profile

2. Using the “min total float” with fixed time levelling and

resource availability of 7 units/day for the A resource

(and infinite availability for the B resource) to schedule

the activities with:

Series approach

Parallel approach

3. Like at point 2, but levelling with fixed resources

respecting the availability for the A and B resources (6

units/day)

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Series – Parallel Approach Exercise

From the provided data is possible to obtain:

2

6

1

7

A 32 0

6

8

3

11

B 04 2

2

1

1

2

C 62 0

7

12

7

12

E 41 0

14

13

12

15

L 03 5

11

9

8

12

F 24 0

7

4

3

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

17

16

16

17

N 22 0

EFT

LST

EST

LFT

A 32 0

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Series – Parallel Approach Exercise

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 -

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 -

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Series – Parallel Approach Exercise

A

B

C

D

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

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Series – Parallel Approach Exercise

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Resource - A

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

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Series – Parallel Approach Exercise

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Resource - B

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

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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

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

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Series Approach – Fixed Times

Programming phase (fixed times)

The C activity has been programmed (days 1-2 with 6 days delay resp. 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 delay resp. A)

The predetermined order is closely followed

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Series Approach – Fixed Times

A

B

C

D

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

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Series Approach – Fixed Times

1

2

3

4

5

6

7

8

9

10

11

12

13

14

C

H

A G

F

I

F

M N

Resource A (series)

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 have an overload (I)

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Parallel Approach – Fixed Times

Algorithm’s step:

1. Creation the list of programmable activities

2. Re-compute the relative TF and EST

3. Tidy up the list activities

4. Collocated one at a time following the point 3 order

5. Come back to point 1

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Parallel Approach – Fixed Times

Step 1 DATEAVAILABLE

ACTIVITIES TOTAL FLOATRESURCE A

REQUIREMENTS

C 0 6

1° d. A 5 3

G 6 3

Step 2

H 0 4

3° d. D 1 -

A 3 3

G 4 3

AVAILABLE

ACTIVITIES

UPDATED

TOTAL FLOATRESURCE A

REQUIREMENTSDATE

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

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Parallel Approach – Fixed Times

Step 3 DATEAVAILABLE

ACTIVITIES

UPDATED

TOTAL FLOATRESURCE A

REQUIREMENTS

G 2 3

5° d. B 3 --

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

Step 4 DATEAVAILABLE

ACTIVITIES

UPDATED

TOTAL FLOATRESURCE A

REQUIREMENTS

6° d. I 2 5

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Parallel Approach – Fixed Times

Step 6

M 0 211° d.

E 1 4

AVAILABLE

ACTIVITIES

UPDATED

TOTAL FLOATRESURCE A

REQUIREMENTSDATE

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

Step 5 DATEAVAILABLE

ACTIVITIES

RESURCE A

REQUIREMENTS

F 0 29° d.

E 3 4

UPDATED

TOTAL FLOAT

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Parallel Approach – Fixed Times

Step 8

N 0 216° d.

AVAILABLE

ACTIVITIES

UPDATED

TOTAL FLOATRESURCE A

REQUIREMENTSDATE

Step 7 DATEAVAILABLE

ACTIVITIES

RESURCE A

REQUIREMENTS

L 10 -12/13° d.

UPDATED

TOTAL FLOAT

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Parallel Approach – Fixed Times

A

B

C

D

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

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Parallel Approach – Fixed Times

1

2

3

4

5

6

7

8

9

10

11

12

13

14

C

H

A G

F

F

M N

Resource A (Parallel)

1 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17

I E

M

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Series and Parallel Approach – Fixed

Resources

3.

In case of fixed resources programming the project’

deadline constraint is not considered, but it is no longer

possible having overload.

The series and parallel approach stay unchanged.

The same schedule remains or the series approach .

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Parallel Approach – Fixed Times

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

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

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Series Approach – Fixed Resources

A

BC

D

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

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Series Approach – Fixed Resources

A

BC

D

EF

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

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Parallel Approach – Fixed Resources

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

1

2

3

4

5

6

7

8

9

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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Suggestions

To obtain the best results it is convenient to adopt the

following expedient:

• to use preferably parallel approach

• to attempt different priority rules

• to execute resource leveling along a 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”

vision of the utilization resources profile coming

from scheduling

• to led what-if analysis, hypothesizing possible corrective

actions