Welcome to Creating Schedules!
Ever tried to plan a busy Saturday so you could fit in a movie, a football match, and a birthday dinner? If so, you’ve already practiced scheduling! In the Cambridge Thinking Skills syllabus, scheduling is all about taking a list of tasks and organizing them into a timeline that works without breaking any rules.
This skill is part of the Searching, scheduling and optimising section. While other chapters focus on finding the best way (optimising) or just any way (searching), this chapter focuses on the mechanics of building the plan itself. Don’t worry if it feels like a big puzzle at first—we will break it down into simple steps!
What is a Schedule?
In your exam, a schedule isn't just a list. It is a logical arrangement of events. To create one, you usually need three things:
1. Tasks: The specific things that need to happen.
2. Durations: How long each task takes (e.g., \(45\) minutes or \(2\) hours).
3. Constraints: The rules you must follow (e.g., "The paint must dry for \(1\) hour before you can add a second coat").
Step-by-Step: How to Build a Schedule
When you face a Paper 1 problem involving a schedule, follow these steps to avoid getting overwhelmed:
1. Identify the "Fixed Points"
Start with the things that cannot move. These are your anchors. For example, if a train departs at exactly \(09:15\), or a shop opens at \(08:00\), mark those down first. These are your "non-negotiables."
2. Respect the Dependencies
A "dependency" is when one task relies on another. You cannot put the roof on a house before you build the walls!
Example: If Task B requires Task A to be finished first, and Task A ends at \(11:00\), Task B cannot start before \(11:00\).
3. Calculate the "Gaps"
Check how much time you have between fixed points. If you have a meeting at \(10:00\) and another at \(11:00\), you have a gap of exactly \(60\) minutes. If you have a task that takes \(75\) minutes, it cannot fit in that gap.
4. Work Backwards (The "Pro" Trick)
Sometimes the question tells you when you need to finish. In this case, subtract the durations from the finish time to find the latest possible start time.
Example: If you must arrive at \(18:00\) and the journey takes \(40\) minutes, you must leave by \(17:20\).
Calculation: \(18:00 - 40\) minutes \( = 17:20\).
Quick Takeaway: Always start with the "fixed" information and then fill in the flexible tasks around them.
Handling Constraints (The "Rules")
The exam will often give you tricky rules to make the scheduling harder. Watch out for these common types:
Resource Constraints: Only one person can do a job at a time. If Alice is painting, she cannot also be cooking dinner at the same moment.
Sequence Constraints: Task X must happen immediately after Task Y, or perhaps there must be a break of at least \(15\) minutes between them.
Time Windows: Some tasks can only happen during certain hours (e.g., "Deliveries must be made between \(09:00\) and \(12:00\)").
Did you know? Scheduling isn't just for exams! Airlines use these exact logical patterns to make sure pilots, planes, and passengers all end up at the right gate at the right time.
Common Mistakes to Avoid
Ignoring "Changeover" Time: In some problems, there is a hidden time cost. If a machine finishes one job at \(14:00\) but needs \(10\) minutes of cleaning before the next job, the next task cannot start until \(14:10\).
Mixing Units: Be very careful with hours and minutes. Remember that \(1.5\) hours is \(90\) minutes, NOT \(150\) minutes! Always convert everything into the same unit (usually minutes) before doing your math.
Miscalculating "Inclusive" Time: If a task starts at the beginning of hour \(1\) and lasts \(3\) hours, it finishes at the end of hour \(3\).
Calculation: \(1 + 3 = 4\), so it is ready at the start of hour \(4\).
Communicating Your Reasoning
For the 2028 Syllabus, examiners place a high value on how you show your work. Don't just write down a final time like \(15:45\).
Label your values! Instead of just writing \(30 + 15 = 45\), write:
Travel time (\(30\) mins) + Prep time (\(15\) mins) = Total time needed (\(45\) mins).
This helps you get marks even if you make a small calculation error!
Key Summary Table
Term: Fixed Point
Meaning: An event with a set time that cannot change.
Term: Duration
Meaning: The length of time a task takes to complete.
Term: Constraint
Meaning: A rule or limit (like a shop's closing time).
Term: Dependency
Meaning: When one task must be finished before another can start.
Note: For more information on finding the very best schedule possible, see the chapter on Find optimal solutions. If you are just trying to see if a schedule is possible at all, see Search for solutions in simple situations.
Final Encouragement
Don't worry if these problems seem like a lot of data at first. Use a scrap of paper to draw a simple timeline. Once you see the "gaps" in the day, the answer usually reveals itself. You've got this!