Paweł Sitek

A hybrid framework for the modelling and optimisation of decision problems in sustainable supply chain management

This paper describes the hybrid framework for the modelling and optimisation of decision problems in sustainable supply chain management. The constraint-based environments used so far to model and solve the decision-making problems have turned out to be ineffective in cases where a number of interbound variables are added up in multiple constraints. The hybrid approach proposed here combines the strengths of mathematical programming and constraint programming. This approach allows a significant reduction in the search time necessary to find the optimal solution, and facilitates solving larger problems. Two software packages, LINGO and ECLiPSe, were employed to solve optimisation problems. The hybrid method appears to be not only as good as either of its components used independently, but in most cases it is much more effective. Its advantages are illustrated with simplified models of cost optimisation, for which optimal solutions are found ten times faster. The application of the proposed framework has contributed to more than 20 fivefold reduction in the size of the combinatorial problem.

A Hybrid Approach to the Optimization of Multiechelon Systems

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in the system using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets.

A hybrid CP/MP approach to supply chain modelling, optimization and analysis

The paper presents a concept and implementation of a novel hybrid approach to the modelling, optimization and analysis of the supply chain problems. Two environments, mathematical programming (MP) and constraint programming (CP), in which constraints are treated in different ways and different methods are implemented, were combined to use the strengths of both. This integration and hybridization, complemented with an adequate transformation of the problem, facilitates a significant reduction of the combinatorial problem. The whole process takes place at the implementation layer, which makes it possible to use the structure of the problem being solved, implementation environments and the very data. The superiority of the proposed approach over the classical scheme is proved by considerably shorter search time and example-illustrated wide-ranging possibility of expanding the decision and/or optimization models through the introduction of new logical constraints, frequently encountered in practice. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. The presented approach will be compared with classical mathematical programming on the same data sets.

A Hybrid Programming Framework for Modeling and Solving Constraint Satisfaction and Optimization Problems

This paper proposes a hybrid programming framework for modeling and solving of constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). Two paradigms, CLP (constraint logic programming) and MP (mathematical programming), are integrated in the framework. The integration is supplemented with the original method of problem transformation, used in the framework as a presolving method. The transformation substantially reduces the feasible solution space. The framework automatically generates CSP and COP models based on current values of data instances, questions asked by a user, and set of predicates and facts of the problem being modeled, which altogether constitute a knowledge database for the given problem. This dynamic generation of dedicated models, based on the knowledge base, together with the parameters changing externally, for example, the user?s questions, is the implementation of the autonomous search concept. The models are solved using the internal or external solvers integrated with the framework. The architecture of the framework as well as its implementation outline is also included in the paper. The effectiveness of the framework regarding the modeling and solution search is assessed through the illustrative examples relating to scheduling problems with additional constrained resources.

Hybrid Solution Framework for Supply Chain Problems

The paper presents application and implementation aspects of a hybrid approach to modeling and optimization for supply chain problems. Two environments of mathematical programming (MP) and constraint programming (CP) were integrated into Hybrid Solution Framework (HSF). The strengths of MP and CP, in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models in logistic and supply chain management, where an objective function and many discrete decision variables added up in multiple constraints.

A Declarative Framework for Constrained Search Problems

Constrained search problems (eg. scheduling, planning, resource allocation, placement, routing etc.) appear frequently at different levels of decisions. They are usually characterized by many types of constraints, which make them unstructured and difficult to solve (NP-complete). Traditional mathematical programming approaches are deficient because their representation of constraints is artificial (using 0-1 variables). Unlike traditional approaches, constraint logic programming (CLP) provides for a natural representation of heterogeneous constraints. In CLP we state the problem requirements by constraints; we do not need to specify how to meet these requirements. In this paper we propose a declarative framework for decision support system (DSS) for constrained search problems implemented by CLP and relational SQL database. We illustrate this concept by the implementation of a DSS for scheduling problems with external resources in different production organization environments.

A hybrid approach to modeling and optimization for supply chain management with multimodal transport

The paper presents the concept and the outline of the implementation of a hybrid approach to supply chain optimization. In this approach, integration of two environments of integer programming (IP) and constrain logic programming (CLP) is proposed. The idea behind the new solution is to use the strengths of both environments, in which optimization constraints are differently treated and different methods are used to solve them. This is particularly important for models in which there is the objective function and various constraints that sum many discrete decision variables. To verify the proposed approach, the optimization models and their implementation in traditional (IP) and hybrid approaches are presented.

A Hybrid Approach to the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP)

The paper presents a concept and application of a hybrid approach to modeling and optimization the Two-Echelon Capacitated Vehicle Routing Problem. Two environments of mathematical programming (MP) and constraint logic programming (CLP) were integrated. The strengths of MP and CLP, in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) is an extension of the classical Capacitated Vehicle Routing Problem (CVRP) where the delivery depot-customers pass through intermediate depots (called satellites). Multi-echelon distribution systems are quite common in supply-chain and logistic systems. The presented approach will be compared with classical mathematical programming on the same data sets.

A Multi-Agent Approach to the Multi-Echelon Capacitated Vehicle Routing Problem

The paper presents a concept and application of a multi-agent approach to modeling and optimization the Multi-Echelon Capacitated Vehicle Routing Problem. Two environments (mathematical programming (MP) and constraint logic programming (CLP)) and two types of agents were integrated. The strengths of MP and CLP, in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) is an extension of the classical Capacitated Vehicle Routing Problem (CVRP) where the delivery depot-customers pass through intermediate depots (called satellites). Multi-echelon distribution systems are quite common in supply-chain and logistic systems. The presented multi-agent approach will be compared with classical mathematical programming on the same data sets.

A novel integrated approach to the modelling and solving of the Two-Echelon Capacitated Vehicle Routing Problem

The paper presents a concept and implementation of a novel approach to the modelling and solving of the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP). Multi-echelon distribution systems are quite common in supply-chain and logistic systems. Two environments, mathematical programming (MP) and constraint logic programming, in which constraints are treated in different ways and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. The 2E-CVRP is an extension of the classical Capacitated Vehicle Routing Problem (CVRP) where the delivery depot-customers pass through intermediate depots (called satellites). The 2E-CVRP was selected as a known and documented example for verification and evaluation of the effectiveness of the proposed approach. The presented approach will be compared with classical MP on the same data-sets in computational tests. The proposed approach will be used also for extensions of the modelled problem beyond the standard.