Exact and Asymptotically Exact Solutions for a Class of Assortment Problems

Mass customization requires us to select a few types of resources to produce heterogeneous classes of products. In the assortment problem addressed here, a resource unit of type j yields, at a cost c ij , a batch of a ij product units of type i . The problem, a generalization of the p -median, calls...

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Bibliographic Details
Published in:INFORMS journal on computing 2009-12, Vol.21 (1), p.13-25
Main Authors: Arbib, C, Marinelli, F
Format: Article
Language:English
Subjects:
Algorithms
Customization
cutting stock
deterministic inventory production
Integer programming
Inventory control
Inventory management
Mathematical models
median
Methods
Resource allocation
Scheduling algorithms
Studies
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Summary:Mass customization requires us to select a few types of resources to produce heterogeneous classes of products. In the assortment problem addressed here, a resource unit of type j yields, at a cost c ij , a batch of a ij product units of type i . The problem, a generalization of the p -median, calls for (i) choosing a restricted subset of resource types and (ii) assigning resource units to products so as to fulfill a given demand vector at a minimum cost. For this problem, we develop a branch-and-price scheme that can either be used to find optimal solutions, or tuned by choosing columns in a suitable class so as to get approximate solutions. The solutions obtained in the second case approach the optimum by a ratio that asymptotically reduces to zero as the demand of the least-required product increases. A comparative analysis of the features of the algorithm is discussed for a wide set of large problem instances.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1080.0274