scholarly journals SOLVING THE POLYTECHNIC CLASS SCHEDULING PROBLEM USING INTEGER LINEAR PROGRAMMING MODEL

2020 ◽  
Vol 5 (10) ◽  
Author(s):  
ABDULLAHI A. A ◽  
RAJI I. I. ◽  
OYENIYI R. B
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Programming Model ◽  
Scheduling Problem ◽  
Integer Linear Programming Model ◽  
Class Scheduling

scholarly journals Equivalent Transformation of Nonlinear Constraints to Linear Constraints in Petri Nets

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
YuFeng Chen ◽  
Abdulrahman Al-Ahmari ◽  
Chi Tin Hon ◽  
NaiQi Wu
Keyword(s):  
Linear Programming ◽  
Petri Nets ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Linear Constraints ◽  
Linear Programming Model ◽  
Equivalent Transformation ◽  
Nonlinear Constraints ◽  
Nonlinear Constraint ◽  
Integer Linear Programming Model

This paper focuses on the enforcement of nonlinear constraints in Petri nets. An integer linear programming model is formulated to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same admissible marking space as the nonlinear one does in Petri nets. The obtained linear constraints can be easily enforced to be satisfied by a set of control places with a place invariant based method. The control places make up a supervisor that can enforce the given nonlinear constraint. For a case that the admissible marking space decided by a nonlinear constraint is nonconvex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint with respect to the reachable markings. Finally, a number of examples are provided to demonstrate the proposed approach.

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