Critical paths and scheduling · Rutas críticas y programación
| English | Español |
|---|---|
| float/fləʊt/ | float |
Must every activity wait for every other?
- A school event has activities that can run in parallel. Adding every duration overestimates the minimum completion time.
- This lesson studies float 浮动时间: The time an activity can be delayed without delaying completion under the network model.
Choose the mathematical structure
- For an activity network, calculate earliest event times forward and latest event times backward. Total float for activity i to j is L_j-E_i-duration. A critical activity has zero total float; more than one critical path may exist.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines float? · ¿Qué descripción define correctamente la holgura?
The time an activity can be delayed without delaying completion under the network model. · El tiempo que una actividad puede retrasarse sin retrasar la finalización bajo el modelo de red.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
Activities A=3 and B=5 start together. C=4 follows A, and D=2 follows both B and C. The earliest completion of C is 7; D must wait until max(5,7)=7 and finishes at 9. Path A-C-D is critical; B has float 2.
Critical paths and scheduling · Rutas críticas y programación
For an activity network, calculate earliest event times forward and latest event times backward · Para una red de actividades, calcule los tiempos de evento más tempranos hacia adelante y los tiempos de evento más tardíos hacia atrás
Compare the model with the worked case and explain one change. · Compara el modelo con el caso resuelto y explica un cambio.
For A=3,C=4 after A,D=2 after C, find total path duration. · Para A=3, C=4 después de A, D=2 después de C, encuentre la duración total del camino.
The path A-C-D takes 3+4+2=9 time units. · El camino A-C-D toma 3+4+2=9 unidades de tiempo.
Test a tempting shortcut
- Do not add durations of independent parallel activities. A zero-float activity belongs to a critical path, but there may be several such paths. Resource limits can require a schedule longer than the network's theoretical minimum.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The minimum project duration is always the sum of every activity duration. This claim is false. Explain which definition or assumption it violates.
B=5 must finish before D starts at time 7. Find B's float. · B=5 debe terminar antes de que D comience en el tiempo 7. Encuentre la holgura de B.
B normally finishes at 5 but can finish at 7: total float=7-5=2. · B normalmente termina en 5 pero puede terminar en 7: holgura total=7-5=2.
The minimum project duration is always the sum of every activity duration. · La duración mínima del proyecto no es siempre la suma de todas las duraciones de las actividades.
Do not add durations of independent parallel activities. A zero-float activity belongs to a critical path, but there may be several such paths. Resource limits can require a schedule longer than the network's theoretical minimum. · No sume las duraciones de actividades paralelas independientes. Una actividad con holgura cero pertenece a una ruta crítica, pero pueden existir varias rutas de este tipo. Las limitaciones de recursos pueden requerir un cronograma más largo que el mínimo teórico de la red.
Interpret a new situation
- Draw precedence relationships before assigning times. Distinguish activity duration from event time. Explain what a delay does to the completion date, and record any resource assumptions.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
A project starts at time 0 and finishes at 9. Find its minimum duration. · Un proyecto comienza en el tiempo 0 y termina en 9. Encuentre su duración mínima.
Project duration=end time-start time=9-0=9. · Duración del proyecto = hora final - hora inicial = 9 - 0 = 9.
Match each part of a complete solution to its purpose. · Emparejar cada parte de una solución completa con su propósito.
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · Una suposición justifica el modelo; una comprobación verifica el resultado; la interpretación lo conecta con la pregunta.
Use this in your course
- edexcel IAL mathematics; official unit D1. Other-unit enrichment is identified in the scope review; it is not an extra cash-in requirement.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The time an activity can be delayed without delaying completion under the network model. Choose the relationship, show the method, check its assumptions and interpret the result.