Exercises: Project planning

Explain in your own words what a Gantt chart is and what it is used for in a technological project. Name at least two things that can be determined by looking at it.

To build a scale model of a bridge, a team has the following jumbled tasks: (a) test the strength of the model, (b) research information about bridges, (c) draw the chosen design, (d) buy the materials, (e) assemble the parts. Put them in a logical order and indicate which ones could not start until another is completed.

The figure shows the Gantt chart for a six-week project, but the bar for the 'Documentation' task is incomplete: it lasts two weeks and can only start when assembly is completed, as shown in the figure.

State in which week the 'Documentation' bar should end and explain how you deduced it. Which two tasks are being carried out at the same time during week 5?

In a Gantt chart, what does the horizontal axis represent and what is listed on the vertical axis? Also explain what it means when two bars overlap in time.

Explain what a milestone is in project planning and give two examples of milestones in a project to build a scale model for the school science fair.

A project has the following bars in its Gantt chart: A (weeks 1–2), B (week 3), C (weeks 3–4) and D (week 5). State in which weeks there are two tasks underway at the same time and in which weeks there is only one, and explain what that means for team organisation.

Explain in your own words what the critical path of a project is and why a delay in a task on the critical path delays the whole project, whereas for other tasks it does not.

Before drawing a Gantt chart, three pieces of information must be gathered about each task. Name them (what needs to be done, how long it will take and which other tasks it depends on) and explain what problem planning without knowing one of them causes.

A project has the following tasks: A (design, 3 weeks), B (buy materials, 1 week, depends on A), C (assemble, 2 weeks, depends on A and B), D (test, 1 week, depends on C) and E (write the project report, 2 weeks, can be done from the start). Calculate the minimum duration of the project and explain which task does not delay the end even if extended by one week.

Explain the difference between planning an entire project from the start (waterfall method) and working with Agile methodologies in short cycles. Give an example of a project in your environment where each approach fits best and justify your choice.

In a project planned with a Gantt chart, the task 'printing parts' (week 3) is delayed by one week, and assembly planned for week 4 depends on it. Explain what happens to the end of the project and propose two measures the team could take to make up for lost time.

In week 3 of a project, three tasks coincide: B (needs 2 people), C (1 person) and D (1 person), but the team only has 3 people. (a) Represent the staffing workload for that week (tasks vs capacity). (b) State by how many people the available capacity is exceeded. (c) Knowing that task C has one week of float (slack), propose a planning adjustment that does not exceed capacity and verify that the project is not extended (resource levelling).

A team reviews its project halfway through and compares the planned progress with what was actually executed, as shown in the figure.

(a) State which task was delayed compared to what was planned and by how many weeks. (b) Reason in which week the project will finish according to actual progress, knowing that it was planned to finish in week 5. (c) Propose two measures that could have prevented or absorbed this delay.

In Agile methodologies, work is done in 'sprints'. Explain what a sprint is, what must exist at the end of each one (a working product increment) and what is done in the review meeting that closes it.

Two tasks in your project are planned for the same week, but both need the only 3D printer in the workshop. Explain what type of planning problem this is (a resource conflict) and describe two ways to resolve it when constructing the Gantt chart.

Convert this list of tasks into a planning schedule table showing the start week and end week for each: A (prepare the ground, 1 week), B (lay foundations, 2 weeks, after A), C (build walls, 2 weeks, after B) and D (electrical installation, 1 week, after A). State the total duration of the project and which task has room to be delayed without consequences.

Your technology team plans the construction of a photovoltaic solar bench for the high school yard with the following tasks:

• A: Feasibility study and electrical sizing (2 weeks).

• B: CAD design of the structure and circuits (2 weeks, requires A).

• C: Administrative approval and component purchasing (1 week, requires B).

• D: Machining and mechanical and electrical assembly (3 weeks, requires C).

• E: Load, performance, and safety testing (1 week, requires D).

• F: Drafting of the technical report and final documentation (3 weeks, can start as soon as B is completed).

The management team requires inaugurating the bench within an unextendable deadline of 7 weeks.

1. a) Calculate the initial total duration of the project by determining its critical path and find the total float of task F.
2. b) Design a justified schedule compression proposal to meet the 7-week deadline, indicating which tasks you would overlap or crash, and analyzing the technical quality or safety risks that the team takes on with these changes.

A team builds a scale model of a cable-stayed bridge with a 1,5 m span. To organize the work, they decide not to use a Gantt chart and to apply a pure Agile methodology with one-week sprints. In the second sprint, they decide to modify the tilt of the main towers to improve aesthetics and lateral stiffness; however, the wooden decks had already been laser cut in the first sprint and the plaster footings had already fully cured.

1. a) Justify why the agile principle of "responding to change over following a plan" failed in this physical context compared to what would happen in a software project.
2. b) Design a hybrid management proposal (predictive and agile) for this project: specify which phases must be managed strictly sequentially using a Gantt chart with a critical path and in which deliverables or tasks it is advantageous to apply short iterations.

A team designs an IoT-connected weather station. The coordinator scheduled all activities strictly sequentially to "avoid confusion":

• A: Programming and testing of sensor firmware (3 weeks).

• B: 3D design of the waterproof housing (2 weeks).

• C: 3D printing and machining of the enclosure (1 week).

• D: Calibration and climatic testing of the sensors (2 weeks).

• E: Final assembly of electronics into the housing (1 week).

The total sum is 9 weeks, but the delivery deadline for the tech fair is 6 weeks. The team consists of a programming specialist, a mechanical design specialist, and they have the 3D printing equipment available full-time.

1. a) Determine the mandatory logical technical dependencies between tasks and justify which ones can be run in parallel based on available resources.
2. b) Prepare the timetable (earliest start, earliest finish) for the new optimized schedule, identify the critical path, and determine whether meeting the 6-week deadline is feasible.

The schedule for a sorting robotic arm consists of four tasks: A (Kinematic design, 2 weeks), B (Machining and chassis assembly, 4 weeks, after A), C (Motor control programming, 2 weeks, after A), and D (Hardware-software integration and calibration, 1 week, after B and C are completed).

1. a) Determine the total project duration, the critical path, and the total float of task C.
2. b) During execution, task B suffers a 1-week delay due to a lack of drill bits for the lathe. Justify numerically what happens to the float of task C and how it impacts the final delivery date of the project.
3. c) Now assume that, starting from the initial situation, task C suffers an unexpected delay of 3 weeks. Reason whether the project's critical path would change and what the new overall duration would be.

To coordinate the high school's Science and Technology Week, the technical department has a maximum deadline of 9 weeks and the following activity forecast:

• A: Institutional approval and booking of spaces (2 weeks).

• B: Contact and confirmation of external speakers (3 weeks, requires A).

• C: Design and dissemination of posters and website (2 weeks, requires A).

• D: Technical design and procurement of materials for interactive workshops (4 weeks, requires A).

• E: Opening and management of attendee registrations (2 weeks, requires B and C).

• F: Booth assembly and equipment setup (1 week, requires D and E).

• G: Event execution and closing (1 week, requires F).

1. a) Prepare the planning table with early and late start and finish times, calculate the total float of each task, and identify the critical path of the event.
2. b) If task D is delayed by 2 weeks due to supply issues with the robotics kits, predict mathematically using float calculations whether this delay will force the postponement of the opening (task G).

During the construction of a vehicle chassis for a school competition, the team accumulates a 2-week delay in the welding and assembly task of the steel tubular frame. The class representative proposes adding 4 more students to that same task to make up for lost time.

1. a) Refute this proposal quantitatively and technically based on Brooks' law: analyze the impact on the number of possible communication channels if the team grows from 2 to 6 members using the formula C = n(n - 1) / 2, as well as the learning curve and the physical space limitations at the welding workstation.
2. b) Design a viable technical alternative for task redistribution that allows those 4 new members to help the project by reducing the overall deadline without directly intervening in the chassis welding.

A team of students is developing a web application to manage tool loans in the high school workshops. It was initially planned under a traditional waterfall model with an expected duration of 12 weeks. In week 6, with the design finalized and backend programming halfway through, the Technology department changes the requirements: it demands adding authentication via the school's RFID cards and an incident reporting module for broken tools.

1. a) Justify why the waterfall model technically collides with this situation and predict the impact on rework costs and on the original Gantt chart.
2. b) Design a transition plan to an agile methodology (Scrum) for the remaining 6 weeks: define the duration of the sprints, how you would restructure the backlog in light of the new requirements, and define precisely what the Minimum Viable Product (MVP) would be that would allow launching the system on the scheduled date without collapsing the project.

Two students, Alex and Bea, must submit a mechatronic prototype and its technical report within a strict deadline of 4 weeks. They have only one 3D printer in the Technology classroom. The tasks are:

• T1: 3D modeling of the mechanism parts (2 weeks, exclusively assigned to Alex).

• T2: 3D printing of all parts (1 week, continuous use of the 3D printer, requires T1 completed).

• T3: Physical assembly and electrical wiring (1 week, requires the joint and intensive presence of Alex and Bea, and cannot start until T2 is finished).

• T4: Writing the technical report and drawings (2 weeks, exclusively assigned to Bea, requires having completed the T1 modeling).

1. a) Represent the weekly schedule by resources (Alex, Bea, and 3D Printer). Show what resource overallocation conflict occurs in week 4 that makes on-time delivery unfeasible.
2. b) Identify the resource acting as a bottleneck and propose a well-founded modification in task sequencing or division that resolves the conflict and allows the project to be completed within the planned 4 weeks without overallocating anyone.