The load balancing nurse-to-patient assignment problem requires the assignment of nurses to patients to minimize the variance of the nurses’ workload. This challenging benchmark is currently best solved exactly with constraint programming (CP) using the spread constraint and a problem-specific heuristic. We show that while the problem is naturally modelled as a mixed integer quadratic programmi...

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 ...

In this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. The constraints are the warehouse capacity and the batch forms of the order placements. The first objective of this problem is to find the order quantities such that the expected ...

Any institution that disseminates data in aggregated form has the duty to ensure that individual confidential information is not disclosed, either by not releasing data or by perturbing the released data, while maintaining data utility. Controlled tabular adjustment (CTA) is a promising technique of the second type where a protected table that is close to the original one in some chosen distanc...

The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...

We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We first derive some basic properties of value functions of quadratic integer programs. We then propose a two-phase solution approach. The first phase constructs the value functions of quadratic integer programs in both stages. The second phase solves...

This paper presents an efficient optimization algorithm for mixed integer nonlinear programming (MINLP) problem resulting from multiple partially linearized (MPL) model based control of nonlinear hybrid dynamical system (NHDS). The algorithm uses structural information of the canonical MPL framework and derives comparatively easier quadratic programming (QP) primal problem as well as an MILP ma...

In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The generalized model is formulated as a mixed integer quadratic programming (MIP) problem. The purpose of this paper is to investigate a continuous approach base...

Answer set programming is a programming paradigm where a given problem is formalized as a logic program whose answer sets correspond to the solutions to the problem. In this paper, we link answer set programming with another widely applied paradigm, viz. mixed integer programming. As a theoretical result, we establish translations from non-disjunctive logic programs to linear constraints used i...

Reduced RLT constraints are a special class of Reformulation-Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform r...