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I have a picking list(list of items to pick in a warehouse) already ordered following a desired sequence. Every item has a width, length and height. When I report a picking list first of all I have to choose a package in order to put these items somewhere. A package aswell has a width, length and height(assuming a fill rate=100%). The item quantity on the picking list is only divisible by whole numbers. The questions to answer are; If I want to minimize the number of packages, how many packages should I use? How do I know the package sequence?(so I know what package to pick everytime I begin reporting a picking list or begin a new package?

To me, these are some variables and fixed numbers.

Item    FIXED
Item Quantity   FIXED
Item Width  FIXED
Item Lenght FIXED
Item Height FIXED
Item volume FIXED
Package VARIABLE
Package Quantity    VARIABLE
Package Width   FIXED
Package Lenght  FIXED
Package Height  FIXED
Package Volume  FIXED
Package fill rate   FIXED
Package sequence    VARIABLE

Anyone who can solve it?

Murmel
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Gerard Cepero Abad
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1 Answers1

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This is a general problem known as the Bin packing problem. There are many solutions for it, but overall is an NP-hard problem, meaning no polynomial solution. Also you might not be able to fill packages 100%.

Most algorithms try not to find the best solution, but the fastest one, using heuristics. These are greedy algorithms, and produce moderately effective results (for example no box will remain less then half empty if there are items remaining).

A book titled The Algorythm Design Manual writes the following about this problem:

Analytical and empirical results suggest that ‘first fit decreasing’ is the best heuristic. Sort the objects in decreasing order of size, so that the biggest object is first and the smallest last. Insert each object one by one in to the first bin that has room for it.

Máthé Endre-Botond
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