A Hybrid Approach to the Optimization of Multiechelon Systems

Table 1

Description of CLP predicates.

Predicate	Description
P1; CLP environment	The implementation of the model in CLP, the term representation of the problem in the form of predicates.
P2; CLP environment	The transformation of the original problem aimed at extending the scope of constraint propagation. The transformation uses the structure of the problem. The most common effect is a change in the representation of the problem by reducing the number of decision variables and the introduction of additional constraints and variables, changing the nature of the variables, and so forth.
P3; CLP environment	Constraint propagation for the model: constraint propagation is one of the basic methods of CLP. As a result, the variable domains are narrowed, and in some cases, the values of variables are set, or even the solution can be found.
P4; CLP environment	Generation by the AG: (i) the model for mathematical programming: generation performed automatically using CLP predicate; (ii) additional constraints on the basis of the results obtained by predicate P3; (iii) domains for different decision variables and other parameters based on the propagation of constraints. Transmission of this information in the form of fixed value of certain variables and/or additional constraints to the MP.
	Merging files generated by predicate AG into one file. It is a model file format in MP format.
P5; EPLEX environment	Finding the consistent area based on information from the CLP.
P6; EPLEX environment	The solution of the model from the P4 by MP solver.
P7; EPLEX environment	Solution transfer from EPLEX to CLP (predicate eplex_get(vars,Zm))