The Simple Plant Location Problem is a well-known (andNP-hard) combinatorial optimisation problem, with applications in logistics. We present a new family of valid inequalities for the associated family of polyhedra, and show that it contains an exponentially large number of new facet-defining members. We also present a new procedure, called facility augmentation, which enables one to derive ev...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

In this paper we consider the problem of assigning transmission powers to the nodes of a wireless network in such a way that all the nodes of the network are connected and the total power consumption is minimized. A mixed integer programming formulation is presented together with some new valid reinforcing inequalities. Computational results show the effectiveness of the new valid inequalities ...

We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood’s [19] integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally, we provide an approximation-factor-pres...

Metric inequalities, cutset inequalities and Benders feasibility cuts are three families of valid inequalities that have been widely used in different algorithms for network design problems. This article sheds some light on the interrelations between these three families of inequalities. In particular, we show that cutset inequalities are a subset of the Benders feasibility cuts, and that Bende...

In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a lineariz...

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, su...

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is pre...

We give new facets and valid inequalities for the separable piecewise linear optimization knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. In a companion paper [12] we demonstrate the efficiency of the inequalities when used as cuts in a branch-and-cut scheme.

In this paper, we consider the polyhedral structure of the integrated minimum-up/-downtime and ramping polytope, which has broad applications in power generation scheduling prob-lems. The generalized polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. We derive strong validinequalities for this...