360 research outputs found
Worst case analysis for a general class of on-line lot-sizing heuristics.
In this paper we analyze the worst case performance of heuristics for the classical economic lot-sizing problem with time-invariant cost parameters. We consider a general class of on-line heuristics that is often applied in a rolling horizon environment. We develop a procedure to systematically construct worst case instances for a fixed time horizon and use it to derive worst case problem instances for an infinite time horizon. Our analysis shows that any on-line heuristic has a worst case ratio of at least 2. Furthermore, we show how the results can be used to construct heuristics with optimal worst case performance for small model horizons.
Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches
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 combinational 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
Relax-and-fix heuristics applied to a real-world lot-sizing and scheduling problem in the personal care consumer goods industry
This paper addresses an integrated lot-sizing and scheduling problem in the
industry of consumer goods for personal care, a very competitive market in
which the good customer service level and the cost management show up in the
competition for the clients. In this research, a complex operational
environment composed of unrelated parallel machines with limited production
capacity and sequence-dependent setup times and costs is studied. There is also
a limited finished-goods storage capacity, a characteristic not found in the
literature. Backordering is allowed but it is extremely undesirable. The
problem is described through a mixed integer linear programming formulation.
Since the problem is NP-hard, relax-and-fix heuristics with hybrid partitioning
strategies are investigated. Computational experiments with randomly generated
and also with real-world instances are presented. The results show the efficacy
and efficiency of the proposed approaches. Compared to current solutions used
by the company, the best proposed strategies yield results with substantially
lower costs, primarily from the reduction in inventory levels and better
allocation of production batches on the machines
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