Fixed-Charge Transportation with Product Blending

Authors:
Dimitri J. Papageorgiou;Alejandro Toriello;George L. Nemhauser;Martin W. P. Savelsbergh
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;School of Mathematical and Physical Sciences, University of Newcastle, Callaghan NSW 2308, Australia
Venue:
Transportation Science
Year:
2012

Citing 8
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Abstract

Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in distribution networks so they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) studied in this paper captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program, and we derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Furthermore, we prove that, in certain situations, these classes of facets along with the continuous relaxation of the original constraints yield a description of the convex hull. Finally, we present a computational study that demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB with arc capacities and multiple consumers.