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Hello I am new to operational research and would like help classify the following transport problem.

I have a model which simulates a taxi like service, it a has a range of inputs that can be changed (no. vehicles, starting times, vehicle capacity etc) and then the model spits out a set of outputs (time spent idol, time spent travelling with passengers, time passengers spend waiting) which I apply some kind of associated cost to both the inputs and the outputs.

What kind of techniques would you apply to this problem so that I can minimise the total cost?

I imagine some algorithm would iteratively run the model and adjust the inputs and measure the outputs to form the data. However this is just my uneducated guess.

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Exactly, you probably want to use local search methods: begin with an arbitrary initial input (preferably good); then modify the current input with some random changes (change a vehicle, add one, remove one...), keep the best result and loop. You could look into simulated annealing.

If you need the best solution and your search space is large (and it probably is), a blackbox model should be inefficient. If you can have access to the model, you can formulate it as an optimization problem (minimize cost subject to constraints), for example with integer linear programming, or use more clever heuristics.

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  • $\begingroup$ On the other hand, for a large model integer linear programming can be very slow, while local search methods may be able to get very good (if not optimal) solutions in a reasonable amount of time. $\endgroup$ Commented Jul 24, 2015 at 21:01
  • $\begingroup$ You're right: I saw a scheduling problem and got carried away. Without mentioning integer programming, however, improving the basic local search process will be beneficial. The first improvement you may add is to not evaluate the full model each time but calculate the effect of a change incrementally. $\endgroup$
    – Ggouvine
    Commented Jul 26, 2015 at 19:53

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