Industrial Project Management

RESOURCE SCHEDULING

Project scheduling without resource constraints:

• Analysis of the usage rate throughout time
• Comparison between resources required/available
• Long term – anticipate and remove possible overloads
• Short term – Resource Constrained Project Scheduling Problem (RCPSP) with resource or time constraints, based on priority rules

CPM is an algorithm that allows also to calculate project duration. If project duration is not feasible, we have to revise resource allocation and parallel/sequence configuration of the network. Once we have satisfied the project duration, we look at the resource allocation project: we have to develop a comparison between resource requirements and capacity/availability of resource. We have to check if resource requirement is consistent with resource availability. Also in this case there are some iterative processes.

RESOURCE COSTRAINED PROJECT SCHEDULING PROBLEM (RCPSP)

This is a complex problem and the main techniques

1. Optimization techniques: they try to find a global optimal solution for the scheduling. They have many limits, such as they require heavy computation, it is a static definition of the problem and there may be several possible objectives in contrast (difficult to determine the optimality criteria).
2. Heuristic approaches: they do not try to find a global optimal solution, but at least a local one, which can be an acceptable solution. The main limits are that they can pursue only one objective for every scheduling, they obtain different performance according to the network characteristics, they are based on priority rules (to solve conflict between activities that require common resources) fixed a priori.

• Minimise the project delay
• Minimise the interruptions of the single resource use
• Maximise resource saturation

• Determine the set of activities satisfying the precedence constraints
• Apply priority rules to the activities until resources are available.

• Activities ranked by initial priority (e.g. TF)
• Resource allocation based on path, from more critical to less

The series approach:

The series approach is static which means that we give a priority at the beginning and we keep this priority fixed for all the scheduling process. It is a static approach, it ordinate list of starting activities; it tends to advance by paths, in order of criticality.

Parallel approach (dynamic):

• Updated rank of activities at every step
• Resource allocation step by step

The parallel approach (better than the series, since it allows to schedule the resource step by step) is dynamic since the priority changes during the scheduling process. The activity has a priority level decided by the path it belongs to. It is a dynamic approach, it ordinate list of activities updated at each step; it tends to advance by temporal intervals.

• Rolling wave approach
• Different priority rules (give different results)
• Activity splitting / interrupting
• What if analysis

PRIORITY RULES:

1. TimeMIN TF (Minimum Total Float)

The conflict to access to shared resources by different

activities is solved giving priority to the activity with minimum float.

• MIN TF (Minimum Total Float) corresponding to MIN LST (late start time) MIN LFT ("Minimum Late Finish Time")
• SIO ("Shortest Imminent Operation")
• ...

2) Resource

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: D = max [0, EFT - LST ]ij j j 94

We are trying to give the priority to those activities which don't have any overlapping or which have a low value of overlapping.

• GRU ("Greatest Resource Utilization", by rate or by total quantity): This rule gives the priority, in each program step, to the combination of activities that obtaining the maximal possible saturation for the available resources.
• MJP ("Most Job Possible"): This rule gives the priority to the combination of...

activities that allows to program the maximum possible number of activities considering only the feasibility and not the saturation level.

• MixedGRD ("Greatest Resource Demand")

It uses the priority criterion of unit's resource requirements (considering all the demanded resources) associated to each activity, giving precedence to the activities characterised by a greater requirements, since they can potentially create bottlenecks. The priority grade is computed as:

Priority = d * ∑ri ij

considering the duration and the requirements.

dj = duration of activity j

rij = requirement per time unit of resource i by activity j

m = different types of resources

Series and parallel approach:

Exercise

1. Determine a project schedule and the corresponding profile of resource usage
2. Using a min total float rule, level the project respecting its duration (point 1), assuming the availability of 7 resource-units/day for resource A (and infinite for B) (i.e. double constrained).

Apply both approaches: Series and parallel

3. Such as point two with resource constraint. Schedule the project assuming the availability of 6 resource-units/day for both resources A and B.

1. Project scheduling without constraints

95Gantt chart: This is the early time scheduling ("I" is just after "G"). This is the starting situation with 2 overload.

Series approach, time constraint

2. Activities ranked by min total float

Scheduling based on network precedence:

1. ready ACG → C
2. ready AGDH → H
3. ready AGD → D

Scheduling sequence:

Activity C (gg. 1-2 with 6 res. A)

Activity H (gg. 3-10 with 4 res. A)

Activity D (gg. 3-7 with 0 res. A)

Initial priority ranking must be respected throughout the overall project duration

Due to the TF constraint, two work overloads emerge

96Parallel approach, time constraint

At each step:

1. Define the set of ready activities
2. Update TF and EST
3. Rank the activities based on the rule adopted
4. Schedule activities step by step based on

point 3 if the resource is available
5. Back to point one
Step 1: Step 2
At day 1 we have 3 activities ready 
ACTIVITIES TOTAL FLOAT Usage of
DATE READY UPDATED Resource A
ACTIVITIES TOTAL Usage of
DATE READY FLOAT Resource A H 0 4
D 1 -
C 0 6 3°d
A 5 3 A 3 31°d 
G 6 3 G 4 3
Activities H, D, A are scheduled. G is delayed, due to
the lack of resources
Step 3 Step 4
ACTIVITIES TOTAL FLOAT Usage of ACTIVITIES TOTAL FLOAT Usage of
DATE DATE
READY UPDATED Resource A READY UPDATED Resource A
G 2 3 6°d I 2 5
B 3 -5°d
Resource available is not sufficient, so activity I can't start on day six.
In order to respect the resource constraint, activity I should be delayed to day eleven, causing a three days
delay of the project completion.
Step 5 Step 6
ACTIVITIES TOTAL FLOAT Usage of ACTIVITIES TOTAL FLOAT Usage of
DATE DATE
READY UPDATED Resource A READY UPDATED Resource A
F 0 2 M 0 2
E 3 4 E 1 49°d 11°d
Step 7 Step 8
ACTIVITIES TOTAL FLOAT Usage of ACTIVITIES TOTAL FLOAT Usage of
DATE DATE
READY UPDATED Resource A READY

UPDATED Resource A READY UPDATED Resource AL 1/0 - N 0 212/13°d 16°d 97

Resource constraint, series and parallel

3. In case of a resource constraint, work overloads must be avoided. Series and parallel approaches remain the same as above.

Series approach

Parallel approach

9845 PROJECT SCHEDULING ‼‼‼‼…Project control

About work performed we can monitor and measure the performances. About work remaining we can forecast and control (introduce some corrective actions).

If we consider the scheduling, after some months from the beginning of the project, there are some activities that are already completed, and we have the actual duration. Time now indicates the time in progress. (re)planned are those activities that me be replanned.

In terms of network we have:

• a set of completed activities with actual start and finish (AS and AF).
• In progress: we know the actual start (AS) but not the actual finish, we only know the expected finish (EF)
• Planned: we only know expected times

(ES and EF). 9916.3 PERT AND CIM

We want to analyse what happens if we want to maintain the uncertainty about the duration of an activity.

In this case we have to give the probability distribution.

PERT is not very used, but it’s important from a didactic point of view since it is analytical (gives a very precise structure of the problem). So, we can rely on simulation which is flexible (can be adjusted to any type of network) and is very used.

PERT (Program Evaluation and Review Technique)

Each activity duration is described by a Beta distribution (since it can be asymmetric). Asymmetry is important because in the practical execution of the project, the probability of an early completion is smaller than the probability of a late completion. The delay is always more likely than the advance completion. Also the extension of delay is greater than the extension of advance completion.

Actually, we never saw an activity completed in advance, so the beta curve should be represented in this

way:The estimate of distribution parameters is based on three values a, m, b, corresponding to the• optimistic, most likely and pessimistic duration respectively (e.g. 5% percentile; mode; 95% percentile)

The expected duration of the critical path must be longer than the expected• duration of any other path;

Knowing that the total expected value is the sum of the expected values: EV = ∑EVtot i

The sum of activity distributions tends to generate a normal distribution as the number of activities• increases (central limit theorem). This is very useful also in simulation

Activity dur