Resources Allocation

The default software problem

Network characteristics

Activities

Resources characteristics

Project characteristics

1. Network characteristics

• Finish-start

• Minimal time-lag of zero (second activity starts right after the first one)

2. Activity characteristics

• Fixed activity durations, possible to change fixed work (the duration will change accordingly to the number of resources allocated)

• No task splitting between activities (activity preemption)

• No specific constraints on activities (ready times - a task cannot begin before a certain date, deadlines)

3. Resources characteristics

• Fixed renewable resource availability - machines or people (after finishing the task they are available at the same amount for the next one, unlike non-renewable resources - money, material)

• Fixed resource requirements - stays the same for the entire duration of that task

4. Project characteristics

• Dominant force (target) is time

Scheduling definition with resource allocation

Schedule all project activities within the precedence (priority) relations and the limited resource constraints such that the total lead-time of the project is minimized

IF remove resource constraints → the critical path method

With resources → critical chain method

Critical chain vs critical path

CC - sequence of activities that determines how long your project takes, considering resources

Chain - not only precedence relations, but also resources

Scheduling target

Without resources:

Pert/CPM: Assign start and finishing times to the activities, considering precedence (order) → minimize time

With renewable resources:

RCP Resource Constrained Project Scheduling: Assign start and finishing times to the activities, considering precedence (order) and resource constraints → minimize time

RLP - Resource Leveling Problem: Activities have to be scheduled in order to level the resources, considering the techonological precedence constraints → minimize rsource jumps (leveling)

RCP-DC - Resource Constrained Project Scheduling with Discounted Cash Flows: Assign start and finishing times to activities, considering precedence (order) and resource constraints → maximize net present value

RCP-WC Resource Constrained Project Scheduling with Work Continuity: Assign start and finishing times to activities, considering precedence (order) and resource constraints → minimize resource idle time (maximize work continuity) - use resources in the most efficient way

RCP-DC

RCP + discounted cash flows (DC)

• take a very long time

• cash flows are huge

Maximize NPV:

• Positive cash flows as soon as possible

• Negative cash flows as late as possible

In case of the huge lump sum payment in the end - finish the project as soon as possible (time is also an objective)

RLP - Resource Leveling Problem

Schedule the project activities in order to level the renewable resources, considering the technological precedence constraints (with or without resource availability constraints)

Fixed work

Work (work content) = Duration * Demand

Can adjust the length of the critical path by changing the duration based on the resource demand. But also involves more risk

Resource arc

The connection in the critical chain between not sequential activities to solve the resource conflict