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.

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.

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 ECL i PS e , 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.

The paper presents an optimization model and its implementation using a hybrid approach for the Capacitated Vehicle Routing Problem with Pick-up and Alternative Delivery (CVRPPAD). The development of the CVRPPAD was motivated by postal items distribution issues. The model proposed combines various features of Vehicle Routing Problem variants. The novelty of this model lies in the introduction of alternativeness of item delivery points, differentiation of delivery point types in terms of their capacity (parcel lockers) and possibility of collecting the items during the execution of delivery routes. The model also takes into account a possibility of introducing time windows related to delivery time. The proposed data structure in the form of sets of facts facilitates the implementation of the model in all environments, Constraint Logic Programming (CLP), Mathematical Programming (MP), metaheuristics, databases, etc. The model is implemented in the MP, hybrid CLP/MP, and hybrid CLP/heuristic environments. The hybrid CLP/MP approach is the authors' original solution, which has already been used to solve Supply Chain Management problems, scheduling problems, routing problems etc. For large size problems, considering their combinatorial character, the proposed CLP/MP approach is ineffective. Its effectiveness will improve when MP is replaced by a heuristic. All implementations were performed on the same data instances (facts), which made it possible to compare them according to the solution search time, number of decision variables and number of constraints. The directions into which the model can be further developed were also presented.

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 exampleillustrated 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.