Alper Atamturk In financial markets high levels of risk are associated with large returns as well as large losses, whereas with lower levels of risk, the potential for either return or loss is small. Therefore, risk management is fundamentally concerned with finding an optimal trade-off between risk and return matching an investor’s risk tolerance. Managing risk is … Read more
Mixed-integer rounding (MIR) is a simple, yet powerful procedure for generating valid inequalities for mixed-integer programs. When used as cutting planes, MIR inequalities are very effective for problems with unbounded integer variables. For problems with bounded integer variables, however, cutting planes based on lifting techniques appear to be more effective. This is not surprising as … Read more
Lifting is a procedure for deriving valid inequalities for mixed-integer sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory … Read more
Lot-sizing problems with inventory bounds and fixed charges have not received much attention in the literature, even though there are many emerging applications in which highly specialized storage is the main activity of interest. The traditional infinite capacity and variable cost assumptions on inventory that have been prevalent in the literature are inappropriate in situations … Read more
A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These … Read more
We describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based on only the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation. Citation Appeared in Operations Research … Read more
The flow set with partial order is a mixed-integer set described by a budget on total flow and a partial order on the arcs that may carry positive flow. This set is a common substructure of resource allocation and scheduling problems with precedence constraints and robust network flow problems under demand/capacity uncertainty. We give a … Read more
We study the design of capacitated survivable networks using directed p-cycles. A p-cycle is a cycle with at least three arcs, used for rerouting disrupted flow during edge failures. Survivability of the network is accomplished by reserving sufficient slack on directed p-cycles so that if an edge fails, its flow can be rerouted along the … Read more
In this paper we study the network design arc set with variable upper bounds. This set appears as a common substructure of many network design problems and is a relaxation of several fundamental mixed-integer sets studied earlier independently. In particular, the splittable flow arc set, the unsplittable flow arc set, the single node fixed-charge flow … Read more
Recent developments in integer-programming software systems have tremendously improved our ability to solve large-scale instances. We review the major algorithmic components of state-of-the-art solvers and discuss the options available to users to adjust the behavior of these solvers when default settings do not achieve the desired performance level. Furthermore, we highlight advances towards integrated modeling … Read more