Mathematical Programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of Mathematical Programming to … Read more
This paper investigates problems of disease prevention and epidemic control (DPEC), in which we optimize two sets of decisions: (i) vaccinating individuals and (ii) closing locations, given respective budgets with the goal of minimizing the expected number of infected individuals after intervention. The spread of diseases is inherently stochastic due to the uncertainty about disease … Read more
Two dimensional cutting problems are about obtaining a set of rectangular items from a set of rectangular stock pieces and are of great relevance in industry, whenever a sheet of wood, metal or other material has to be cut. In this paper, we consider the 2-stage two-dimensional knapsack (2TDK) problem which requires finding the maximum … Read more
In this work, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear … Read more
In recent years, decision rules have been established as the preferred solution method for addressing computationally demanding, multistage adaptive optimization problems. Despite their success, existing decision rules (a) are typically constrained by their a priori design and (b) do not incorporate in their modeling adaptive binary decisions. To address these problems, we first derive the … Read more
Directional sensors are gaining importance due to applications, in- cluding surveillance, detection, and tracking. Such sensors have a limited fi eld-of-view and a discrete set of directions they can be pointed to. The Directional Sensor Control problem (DSCP) consists in assigning a direction of view to each sensor. The location of the targets is known with … Read more
Schedule disruptions require airlines to intervene through the process of recovery; this involves modifications to the planned schedule, aircraft routings, crew pairings and passenger itineraries. Passenger recovery is generally considered as the final stage in this process, and hence passengers experience unnecessarily large impacts resulting from flight delays and cancellations. Most recovery approaches considering passengers … Read more
The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are either uncertain or hard to estimate so recently robust optimization approaches have been considered for CNP. In this article, we address very general uncertainty sets, only requiring a linear … Read more
We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in Thörnblad et … Read more
We investigate the efficiency of a discretization procedure utilizing a time-indexed mathematical optimization model for finding accurate solutions to flexible job shop scheduling problems considering objectives comprising the makespan and the tardiness of jobs, respectively. The time-indexed model is used to find solutions to these problems by iteratively employing time steps of decreasing length. The … Read more