We address the multi container loading problem of a company that has to serve its customers by first putting the products on pallets and then loading the pallets into trucks. We approach the problem by developing and solving integer linear models. To be useful in practice, our models consider three types of constraints: geometric constraints, … Read more
“Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex.” This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of … Read more
Christofides and Hadjiconstantinou introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably … Read more
We present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in … Read more
Demand for healthcare services is growing rapidly in Australia and across the world, and rising healthcare expenditure is increasing pressure on sustainability of government-funded healthcare systems. In Australia, elective surgery waiting lists are growing and hospitals are struggling with a capacity shortage. To keep up with the rising demand, we need to be more efficient … Read more
In conservation planning, the data related to size, growth and diffusion of populations is sparse, hard to collect and unreliable at best. If and when the data is readily available, it is not of sufficient quantity to construct a probability distribution. In such a scenario, applying deterministic or stochastic approaches to the problems in conservation … Read more
Integer programming formulations describe optimization problems over a set of integer points. A fundamental problem is to determine the minimal size of such formulations, in particular, if the size of the coefficients or sparsity of the constraints is bounded. This article considers lower and upper bounds on these sizes both in the original and in … Read more
We present a branch-and-cut algorithm for solving discrete bilevel linear programs where the upper-level variables are binary and the lower-level variables are either pure integer or pure binary. This algorithm performs local search to find improved bilevel feasible solutions. We strengthen the relaxed node subproblems in the branch-and-cut search tree by generating cuts to eliminate … Read more
In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development … Read more
A regular timetable is a collection of events that repeat themselves every specific time span. This even structure, whenever applied at a whole network, leads to several benefits both for users and the company, although some issues are introduced, especially about dimensioning the service. It is therefore fundamental to properly consider the interaction between the … Read more