A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints

This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful...

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Bibliographic Details
Published in:Mathematical Problems in Engineering Vol. 2016; no. 2016; pp. 686 - 701
Main Authors: Sitek, Paweł, Wikarek, Jarosław, Bzdyra, Krzysztof
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Limiteds 01.01.2016
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Subjects:
Algorithms
Combinatorial analysis
Constraint modelling
Hybrid systems
Integer programming
Linear programming
Logic programming
Mathematical models
Mathematical programming
Methods
Mixed integer
Operations research
Optimization
Optimization models
Project management
Searching
Supply chain management
Supply chains
Variables
Poland
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary:This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP) and constraint logic programming (CLP), were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method) helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems). The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2016/1532420