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

Table 3

Description of the facts, lists, and parameters for the illustrative example.

Facts	Keys	Parameters
Facts about structure of the problem
F_product; (#id_pro, #id_wer, #)	#id_pro: problem ID; #id_wer: version of the data instances; #: product ID
F_machine; (#id_pro, #id_wer, #)	#id_pro: problem ID; #id_wer: version of the data instances; #: machine ID
F_technology; (#id_pro, #id_wer, #, #, parameters)	#id_pro: problem ID; #id_wer: version of the data instances; #: product ID; #: machine ID	: the execution time of the product on the machine
F_precedence; (#id_pro, #id_we, #, #, #)	#id_pro: problem ID; #id_wer: version of the data instances; #: product ID; #: machine ID
F_resources; (#id_pro, #id_we, #, parameters)	#id_pro: problem ID; #id_wer: version of the data instances; #: additional resource ID	: the total number of additional resources
F_allocation; (#id_pro, #id_we, #, #, #, parameters)	#id_pro: problem ID; #id_wer: version of the data instances; #: additional resource ID; #: machine ID; #: product ID	: the number of additional resources needed to execute a product on the machine
F_model; (#id_pro, #id_wer, #, parameters)	#id_pro: problem ID; #id_wer: version of the data instances; #: model ID	: line of code for model ID
F_order; (#id_pro, #id_we, #, parameters)	#id_pro: problem ID; #id_wer: version of the data instances; #: product ID	: the size of the order for product
Lists
L_precedence; (#, #, #)	#: machine ID; #: product ID
L_technology; (#, #, parameters)	#: product ID; #: machine ID	: the execution time of the product on the machine ; : if the product is executed on the machine ,   = 1; otherwise, = 0; : the size of the order for product
L_allocation; (#, #, #, parameters)	#: additional resource ID; #: machine ID; #: product ID	: the number of additional resources needed to execute a product on the machine ; : the total number of additional resources
L_model; (#, parameters)	#: model ID	: line of code for model ID
L_index_; (#, #, parameters)	#: product ID; #: machine ID	: the new index after transformation
L_data_; (#, parameters)	#: the new index after transformation (combination of # and #)	: the execution time of the product on the machine ; : if the product is executed on the machine, ; otherwise, ; : the size of the order for product
L_precedence_; (#, #)	#: the new index after transformation (combination of # and #)