Integer Programming Models and Parameterized Algorithms for Controlling Palletizers

TL;DR

This paper models and solves the FIFO Stack-Up problem, a combinatorial challenge in palletizing bins from conveyor sequences, using graph-based algorithms and integer programming, demonstrating practical solution methods for large instances.

Contribution

Introduces a decision graph model and a BFS-based solution for the FIFO Stack-Up problem, along with integer programming approaches and a realistic instance generator.

Findings

Breadth-first search on the decision graph effectively solves large practical instances.

Integer programming with CPLEX outperforms GLPK in solving the problem.

The proposed methods handle thousands of bins efficiently.

Abstract

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.