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I have to work on some real world data and come up with an optimization technique to handle cargo.

To make thing simpler let's assume that there are 2 types of resources

  • Manpower (150 ton / 8 hour)
  • Fork lifter (1 ton / 1 hour / 1 man)

So each person can work a max of 8 hours and within those 8 hours he can handle 150 tons. In case of fork lifter a fork lifter can handle 1 ton per hour and also requires a person to operate it. (Note: The person operating the fork lifter should not be confused with the manpower.)

Assuming that we want to handle X tons of cargo in h Hours and find the optimal number of resources required to handle the cargo. What algorithms can be used to tackle such problems? Is there any literature for such problem?

Alternatively, if we are provided with cost against these resources such that

  • Manpower cost per hour is 20$

  • Fork lifter cost per hour is 30$.

If we want to minimize the cost of handling what will be algorithms that can help in such kind of problems? Any literature reference would be helpful.

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  • $\begingroup$ Would you explain more about the problem? From what you mentioned, it is a simple resource planning problem that does not need any optimization method/model. You can easily calculate the needed capacity with the trade-off between the available hours/resources per day and the required capacity of resources to do tasks. Also, the cost would be calculated too. This sounds like rough-cut capacity planning that could be found in the literature. Is this what you are looking for? $\endgroup$
    – A.Omidi
    Sep 7 at 13:12
  • $\begingroup$ @A.Omidi yes, this is what I am looking for but I need some research papers or book that would help understand how to approach such problems. However, I think I would need some optimization technique to minimize the cost function. Can you help with that? Any book, research paper would be helpul. $\endgroup$
    – Lopez
    Sep 8 at 5:07
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Rough-cut capacity planning is an essential tool for rapidly calculating the needed capacity and trade-off between the available and required resources which is frequently used in the planning software. As a reference:

RCCP is a long-term plan capacity planning tool that marketing and production use to balance required and available capacity and to negotiate changes to the master schedule and/or available capacity. You can change your master schedules by changing master schedule dates and increasing or decreasing master schedule quantities. You can change your available capacity by adding or removing shifts, using overtime or subcontracted labor, and adding or removing machines.

It would be calculated either based on the heuristic methods like, vary workforce, Constant workforce/overtime, etc, or by mathematical modeling approach. Some useful resources are:

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