Home/ Questions/Q 8492329
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-06-10T22:41:13+00:00

I have such a problem with organizing a non-automated warehouse (with forklifts). In the

  • 0

I have such a problem with organizing a non-automated warehouse (with forklifts). In the start of the day, there are some pallets in pallet racks in warehouse and during the day there are some specific number of lorries importing / exporting pallets to / from warehouse. And I want to minimize travel distances of forklifts during the day and (or) minimize waiting time of lorries that are processing outgoing deliveries (they are waiting for filling up their lorry with pallets).

I have suggested some quite intuitive algorithms, but they are not producing good results if I compare them to most intuitive method – putting imported pallets to the nearest free rack in warehouse. I tried to convert this problem to linear programming, but I didnt succeed – I know how to find minimized forklift paths for individual lorry, but then I dont know how to put it together because each time lorry export/import some pallets the warehouse state is changed (different pallet layout in warehouse). I also tried brute-force method for finding the best result by systematically checking every possibility, but this isnt producing results in a reasonable time…

Does anyone have some idea please (about converting the problem to linear programming)?

Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    Some ideas.

    It sounds like you may not be able to cast this problem into LP canonical form. Recall, the canonical form of a LP is

    LP Equation

    If you want to optimize the travel distance of the forklifts, then –c is a vector of costs for operating each forklift, A will be the matrix of size #lorries x #forklifts that contain the optimal distances that you are able to calculate, and the solution x will assign some fraction of the work to each forklift.

    You will have to figure out the vector b based on system constraints, i.e. b[i] could be the maximum distance a forklift can drive based on its average speed.

    Hopefully you can convert the real number solutions to some reasonable integer solution, otherwise you will need to use Integer Linear Programming, which is a much more difficult optimization problem.

    Finally, if moving the palettes around in the warehouse changes the cost of the system, then LP will not be applicable and you will have to use some sort of state-space search (best-first, A*, or some other variant) where the state is defined by the location of the palettes, forklifts and lorries.

    • 0