Gantt charts are one of many tools of project management.

Among other classical methods you'll hear about Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT). More contemporary variations include agile project management, lean project management, and benefits realization management.

Consider the following recipe

Mushroom-Braised Short Ribs

Ingredients: short ribs, coarse salt, black pepper, garlic powder, olive oil, onion, celery, carrot, garlic, dry white wine, white wine vinegar, beef broth, sprig of thyme, bay leaf, dried mushrooms

Instructions (time estimates in minutes)

  1. Day before season ribs with salt, pepper, garlic powder and refrigerate for 24 hours.
  2. Chop
    • a: onions (3),
    • b: celery (3),
    • c: carrot (3),
    • d: peel and smash garlic (3).
  3. Measure out
    • a: 1/4 cup olive oil, (1)
    • b: 1/3 cup vinegar,
    • c: 9 cups broth, (1)
    • d: 2 cups wine (1)
    • e: 1 cup mushrooms (1)
  4. Preheat oven to 325 (15)
  5. Heat olive oil in a roasting pan (7).
  6. Add ribs and brown on all sides, about 1 minute per side (10). Set aside.
  7. Discard all but 2 tablespoons of fat from pan. Add onions, celery, carrot, and garlic. Cook about 8 minutes. (10)
  8. Add wine, vinegar, broth, thyme, bay leaf. (1)
  9. Stir in mushrooms. (1)
  10. Bring to a boil. (5)
  11. Return ribs to pan. Cover with foil, braise in oven at 325 for 1 hour.
  12. Remove foil and cook for 3 more hours.

You want to eat at 7, when should you start cooking? How much can you speed up the process by getting some help?

Let's begin by assuming we will do the job single handedly. Let's then talk about how the various subtasks relate to one another.

Some tasks cannot be started before another task is finished. An obvious example is that step 11 cannot start until step 10 is complete.

If we are working alone then tasks 2a, 2b, 2c, and 2d have to be in a sequence because you cannot do more than one of them at a time. The order doesn't matter but they have to be one at a time.

Steps 7, 8, and 9 have a sequence given by the recipe so 8 has to wait on 7 and 9 has to wait on 8.

Let's list them all

12 -> 11
11 -> 10, 4
10 -> 9
9 -> 8, 3e
8 -> 7, 3b, 3c, 3d
7 -> 6, 2a, 2b, 2c, 2d
6 -> 5, 1
5 -> 3a