Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We present the components of a branch-and-cut solution approach, including new branching rules that exploit the structure of the corresponding conflict hypergraph. We also investigate valid … Read more
We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem in an attempt to find the globally optimum solution. As objective functions in UAV path optimization problems typically tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the … Read more
We study the polyhedral structure of a generalization of a mixing set described by the intersection of two mixing sets with two shared continuous variables, where one continuous variable has a positive coefficient in one mixing set, and a negative coefficient in the other. Our developments are motivated from a key substructure of linear joint … Read more
We study a multiechelon supply chain model that consists of a production level and several transportation levels, where the demands can exist in the production echelon as well as any transportation echelons. With the presence of stationary production capacity and general cost functions, our model integrates production, inventory and transportation decisions and generalizes existing literature … Read more
This paper considers the problem of cyclic ow shop robotic cell scheduling deploying several single and dual gripper robots. In this problem, dierent part types are successively processed on multiple machines with dierent pickup criteria including free pickup, pickup within time-windows and no-waiting times. The parts are transported between the machines by the robots. We … Read more
The design of hub-and-spoke transport networks is a strategic planning problem, as the choice of hub locations has to remain unchanged for long time periods. However, strikes, disasters or traffic breakdown can lead to the unavailability of a hub for a short period of time. Therefore it is important to consider such events already in … Read more
We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more
Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more
We study robust versions of the uncapacitated lot sizing problem, where the demand is subject to uncertainty. The robust models are guided by three parameters, namely, the total scaled uncertainty budget, the minimum number of periods in which one would like the demand to be protected against uncertainty, and the minimum scaled protection level per … Read more
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with n nodes. The best known lower bound is \Omega(n^2), the best known upper bound is O(n^3). In this note … Read more