Optiplan: A Planning System That Unifies

Integer Programming with Planning Graph.

Co and Araar (1988) present a 0/1

integer programming model to minimize the deviation between the workload assigned to each machine and the capacity of each machine.

The

integer programming formulation consists of about 700 binary variables and 300 constraints.

Papadimitriou, "On the Complexity of

Integer Programming," Journal of the ACM (JACM), 28(4): 765-768, 1981.

Because that optimal solution of the linear program is also a feasible solution to the original integer program, it represents an optimal solution to the original

integer programming problem.

Paredes, "A hybrid approach using an Artificial Bee algorithm with mixed

integer programming applied to a large-scale capacitated facility location problem," Mathematical Problems in Engineering, vol.

Intended for students in management and industrial engineering as well as supply chain management professionals, this volume examines the use of mixed

integer programming to design supply chain systems and to model complex scheduling problems.

The proposed base station clustering problem is formulated as a binary

integer programming problem that has a stronger LP relaxation bound than other general

integer programming problems.

This third edition include more extensive modeling exercises and detailed

integer programming examples, illustrating how mathematics can be used in real-world applications in the social, life, and managerial sciences.

Van Roy, "Cross decomposition for mixed

integer programming," Mathematical Programming, vol.

Some specific topics explored include lattice reformulation of

integer programming problems, Ehrhart polynomial roots and Stanley's non-negativity theorem, enumeration of integer solutions to linear inequalities defined by digraphs, and perfect Delaunay polytopes and perfect quadratic functions on lattices.