Abstract
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). TheECLiPSesystem 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.
Highlights
A supply chain (SC) is a system of producers, distributors, suppliers networks, customers, retailers, activities, resources, and information involved in moving services and/or products from producers to customers
This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints
A contribution of this paper is to propose a declarative method for hybrid modeling and solving of the supply chain optimization problems using multidimensional transformation as a presolving method
Summary
A supply chain (SC) is a system of producers, distributors, suppliers networks, customers, retailers, activities, resources, and information involved in moving services and/or products from producers to customers. Simultaneous consideration of distribution, production, and transport planning and control problems greatly advances the effectiveness of the processes and operations of all of these problems These problems are characterized by high complexity due to the large number of different activities of the SC (plants, vehicles, distribution centers, retailers, etc.) and due to many interactions and different restrictions among these activities (i.e., capacity, modes of transportation, relocation of distribution centers, nature of demand, balance, environmental, etc.). Very often discussed problems become overconstrained (the problem where solution does not exist, i.e., valuation of variables that satisfies all the constraints) For this reason, the main motivation behind this study was to develop an alternative approach, highly effective in optimization and far more flexible in problem modeling than mathematical programming methods, especially when modeling logical and soft constraints.
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