Meta-heuristics for dynamic lot sizing: a review and comparison of solution approaches.

*(English)*Zbl 1102.90002Summary: Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinatorial optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation, neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig-Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples.

##### MSC:

90B05 | Inventory, storage, reservoirs |

90C59 | Approximation methods and heuristics in mathematical programming |

##### Keywords:

meta-heuristics; lot sizing; Dantzig-Wolfe decomposition; Lagrange relaxation; cutting planes
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\textit{R. Jans} and \textit{Z. Degraeve}, Eur. J. Oper. Res. 177, No. 3, 1855--1875 (2007; Zbl 1102.90002)

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