Open Journal of Mathematical Optimization

Exact optimization algorithms for an order picking problem
Nicola Bianchessi1; Dario Ostuni1; Giovanni Righini1
1Department of Computer Science, University of Milan, Via Celoria 18, 20133 Milan, Italy
Open Journal of Mathematical Optimization, Volume 7 (2026), article no. 3, 18 p.

We consider a combinatorial optimization problem arising when a set of pick-up and delivery orders must be satisfied within an Automated Storage/Retrieval System. The computational complexity of the problem is still open, but it is conjectured to be $NP$-hard. We point out some of its relevant properties and we describe three exact optimization algorithms to solve it, one based on dynamic programming and the other two on branch-and-bound. We also present a mixed-integer linear programming model to solve the problem by general purpose mathematical programming solvers. Computational results are provided to assess the effectiveness of these methods.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/ojmo.51
Classification: 90C27
Keywords: Order picking, Integer linear programming, Dynamic programming, Branch-and-bound

Nicola Bianchessi  1 ; Dario Ostuni  1 ; Giovanni Righini  1

1 Department of Computer Science, University of Milan, Via Celoria 18, 20133 Milan, Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Nicola Bianchessi; Dario Ostuni; Giovanni Righini. Exact optimization algorithms for an order picking problem. Open Journal of Mathematical Optimization, Volume 7 (2026), article  no. 3, 18 p.. doi: 10.5802/ojmo.51
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