Modeling a situation of task dependencies

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In summary, the conversation is about a project that requires building a model to simulate scenarios involving objects and different types of equipment. The goal is to use each piece of equipment sequentially on the objects to take them through different states before resetting and starting again. There are constraints and the goal is to see the impact of changing parameters and eventually use random variables. The conversation also mentions using tools like MS Project or mathematical methods such as linear programming or Markov chains.
  • #1
danago
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An interesting problem has come up in a project I'm working on and I'm looking to build a model to simulate what would happen in particular scenarios. I'll describe the situation in generic terms.

I have x objects {1,2,3,...,x}, a pieces of type-A equipment, b pieces of type-B equipment and c pieces of type-C equipment (each object is identical to all other objects; the same can be said of each piece of equipment). The objects all start in state S0, and the goal is to use each piece of equipment sequentially on the objects (it must be sequential) to take them from state S0 to state SA by using a type-A piece of equipment, then to state SB, and then finally to state SC. Then, once an object is in state SC, it must wait until a particular time (e.g. midnight), at which point a a counter increases by 1. The object then reverts to state S0 and the process starts again.

There are some constraints here. Each type of equipment takes a certain amount of time to complete its task - tA, tB, and tC respectively, and a piece of equipment can only operate on one object at any given point in time. After it has finished a task, the piece of equipment can then move on to any other object that is waiting and at the appropriate state (remembering that the equipment must act on each object in the order A, B and C).

I am trying to set up a simulation of this so we can see what the impact is of changing various parameters. Eventually I'd also like to treat the times taken for each task as random variables (probably normally distributed). I was going to write something in visual basic to effectively simulate this, however I first wanted to ask the advice of this forum. My initial thought is that this is a fairly well-defined problem with seemingly many applications - is there a name for this type of problem? Are there any articles that look at modelling this?

Thanks in advance - any thoughts are much appreciated! More than happy to clarify anything if needed.
 
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Sounds like an application of, e.g. MS Project or similar tools. Mathematically it can range from linear programming to Markov chains and every combination of it. I'd probably look out for the tools to play around with them. As I entered "MS Project" into Google to check whether it is still an available program I found several alternatives. The (economic) literature on this fills probably libraries.
 
  • #3
fresh_42 said:
Sounds like an application of, e.g. MS Project or similar tools. Mathematically it can range from linear programming to Markov chains and every combination of it. I'd probably look out for the tools to play around with them. As I entered "MS Project" into Google to check whether it is still an available program I found several alternatives. The (economic) literature on this fills probably libraries.

Thanks for the reply. I did think about MS Project, though it's maybe a little rigid for what I'm looking for (though I haven't used it much, so it may be a lot more flexible than I'm thinking - I'll check it out again).
 
  • #4
With fixed times, it should be possible to find an expression for the total processing time, maybe with a few cases to go through. Apart from starting up and finishing, one type of equipment will limit processing time, the other two equipment types will just determine the speed of the start and end - and I would expect this delay to be just the sum of the two processing times unless I miss some special case.
With random times, you'll need a simulation.
 

Related to Modeling a situation of task dependencies

1. What is task dependency modeling?

Task dependency modeling is a process of identifying and mapping the relationships between different tasks within a project or system. It helps to understand how tasks are connected and how they depend on each other to achieve a specific goal.

2. Why is task dependency modeling important?

Task dependency modeling is important because it allows for better planning and management of tasks in a project. It helps to identify potential risks and dependencies that may affect the completion of a project. It also helps to optimize the sequence of tasks and ensure that they are completed in a logical and efficient manner.

3. What are the different types of task dependencies?

The different types of task dependencies include finish-to-start, start-to-start, finish-to-finish, and start-to-finish. Finish-to-start is the most common type, where one task must be completed before the next one can start. Start-to-start means that two tasks can start at the same time. Finish-to-finish means that two tasks must be completed at the same time. Start-to-finish means that one task cannot finish until another one starts.

4. How do you model task dependencies?

To model task dependencies, you first need to identify all the tasks involved in a project and their dependencies. Then, you can use tools such as Gantt charts or PERT charts to visually represent the dependencies. You can also use project management software to create a detailed schedule and track the progress of tasks.

5. What are the challenges of task dependency modeling?

The main challenge of task dependency modeling is accurately identifying all the dependencies and understanding their impact on the project. It can also be challenging to manage changes in dependencies as the project progresses. Additionally, task dependencies can create a domino effect, where a delay in one task can cause delays in other tasks, making it difficult to meet project deadlines.

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