We show that for any fixed rank, the closure of a set covering problem (and related problems) can be approximated in polynomial time — we can epsilon-approximate any linear program over the closure in polynomial time. CitationCORC report TR-2003-01, Computational Optimization Research Center, Columbia UniversityArticleDownload View PDF
Lagrangian relaxation is a popular technique to solve difficult optimization problems. However, the applicability of this technique depends on having a relatively low number of hard constraints to dualize. When there are many hard constraints, it may be preferable to relax them dynamically, according to some rule depending on which multipliers are active. From the … Read more
We present a simulation-based analytic center cutting plane method to solve a sample average approximation of a call center problem of minimizing staffing costs, while maintaining an acceptable level of service in multiple time periods. We establish convergence of the method when the service level functions are discrete pseudoconcave. An extensive numerical study of a … Read more
We extend a static mixed intger diajunctive (MID) transmission expansion planning model so as to deal with circuit contingency criterion. The model simultaneously represents the network constraints for base case and each selected circuit contingency. The MID approach aloows a commercial optimization solver to achieve and prove solution aptimiality. The proposed approach is applied to … Read more
One of the main issues in the glass industry is the minimization of the trim loss generated when cutting large parts (stocks) into small items. In our application stocks are produced in the plant. Many distinct stock sizes are feasible, and technical constraints limit the variety of cutting patterns to those producing a single type … Read more
We propose a method for optimizing the lift-and-project relaxations of binary integer programs introduced by Lov\’asz and Schrijver. In particular, we study both linear and semidefinite relaxations. The key idea is a restructuring of the relaxations, which isolates the complicating constraints and allows for a Lagrangian approach. We detail an enhanced subgradient method and discuss … Read more
We present the optimization component of a decision support system developed for a sedan service provider. The system assists supervisors and dispatchers in scheduling driver shifts and routing the fleet throughout the day to satisfy customer demands within tight time windows. We periodically take a snapshot of the dynamic data and formulate an integer program, … Read more
In this study, a lifting procedure is applied to some existing formulations of the Diameter Constrained Minimum Spanning Tree Problem. This problem typically models network design applications where all vertices must communicate with each other at minimum cost, while meeting or surpassing a given quality requirement. An alternative formulation is also proposed for instances of … Read more
Given $A \in Z^{m\times n}$, $b \in Z^m, c \in R^n$, we consider the integer program $P_d: \max \{c’x\vert Ax=b;x\in Z^n_+\}$ which has a well-known abstract dual optimization problem stated in terms of superadditive functions. Using a linear program $Q$ equivalent to $P_d$ that we have introduced recently, we show that its dual $Q^*$ can … Read more
We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs from facets of master cyclic group polyhedra. This idea has recently been re-considered by Evans (2002) and Gomory, Johnson and Evans (2003). We compare inequalities generated by this procedure with mixed-integer rounding (MIR) based inequalities discussed in … Read more