TY - JOUR
T1 - Polyhedral results for discrete-time production planning MIP formulations for continuous processes
AU - Maravelias, Christos T.
AU - Papalamprou, Konstantinos
N1 - Funding Information:
Christos Maravelias would like to gratefully acknowledge financial support from the National Science Foundation, under Grant No. CTS-0547443. Konstantinos Papalamprou was partially supported by the Greek State Scholarships Foundation. Appendix A
PY - 2009/11/12
Y1 - 2009/11/12
N2 - We derive polyhedral results for discrete-time mixed-integer programming (MIP) formulations for the production planning of multi-stage continuous chemical processes. We express the feasible region of the LP-relaxation as the intersection of two sets. The constraints describing the first set yield the convex hull of its integer points. For the second set, we show that for integral data the constraint matrix is κ-regular, and that the corresponding polyhedron is integral if the length of the planning period is selected appropriately. We use this result to show that for rational data, integer variables can also assume integral values at the vertices of the polyhedron. We also discuss how these results provide insight and can be used to effectively address large-scale problems. Finally, we present computational results for a series of example problems.
AB - We derive polyhedral results for discrete-time mixed-integer programming (MIP) formulations for the production planning of multi-stage continuous chemical processes. We express the feasible region of the LP-relaxation as the intersection of two sets. The constraints describing the first set yield the convex hull of its integer points. For the second set, we show that for integral data the constraint matrix is κ-regular, and that the corresponding polyhedron is integral if the length of the planning period is selected appropriately. We use this result to show that for rational data, integer variables can also assume integral values at the vertices of the polyhedron. We also discuss how these results provide insight and can be used to effectively address large-scale problems. Finally, we present computational results for a series of example problems.
KW - Mixed-integer programming
KW - Polyhedral results
KW - Production planning
KW - Scheduling
KW - κ-Regularity
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U2 - 10.1016/j.compchemeng.2009.05.015
DO - 10.1016/j.compchemeng.2009.05.015
M3 - Article
AN - SCOPUS:70249129347
SN - 0098-1354
VL - 33
SP - 1890
EP - 1904
JO - Computers and Chemical Engineering
JF - Computers and Chemical Engineering
IS - 11
ER -