We formulate an integer program to solve a highly constrained academic timetabling problem at the United States Merchant Marine Academy. The IP instance that results from our real case study has approximately both 170,000 rows and columns and solves to near optimality in 12 hours, using a commercial solver. Our model is applicable to both … Read more
The university course timetabling problem deals with the task of scheduling lectures of a set of university courses into a given number of rooms and time periods, taking into account various hard and soft constraints. The goal of the International Timetabling Competitions ITC2002 and ITC2007 was to establish models for comparison that cover the most … Read more
We investigate a robust approach for solving the Capacitated Vehicle Routing Problem (CVRP) with uncertain travel times. It is based on the concept of K-adaptability, which allows to calculate a set of k feasible solutions in a preprocessing phase before the scenario is revealed. Once a scenario occurs, the corresponding best solution may be picked … Read more
Radiation therapy is considered to be one of important treatment protocols for cancers. Radiation therapy employs several beams of ionizing radiation to kill cancer tumors, but such irradiation also causes damage to normal tissues. Therefore, a treatment plan should satisfy dose-volume constraints (DVCs). Intensity-modulated radiotherapy treatment (IMRT) enables to control the beam intensities and gives … Read more
The forest-harvesting and road-construction planning problem basically consists of managing land designated for timber production and divided into harvest cells. For each time period in the given time horizon one must decide which cells to cut and what access roads to build in order to maximize expected net profit under a risk manageable scheme to … Read more
We introduce a new continuous location-allocation problem where the facilities have both a xed opening cost and a coverage distance limitation. The problem might have wide applications especially in the spatial planning of water and/or energy access networks where the coverage distance might be associated with the physical loss constraints. We formulate a mixed integer … Read more
The Min-up/min-down Unit Commitment Problem (MUCP) is to find a minimum-cost production plan on a discrete time horizon for a set of fossil-fuel units for electricity production. At each time period, the total production has to meet a forecasted demand. Each unit must satisfy minimum up-time and down-time constraints besides featuring production and start-up costs. … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded L 1 -costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable s heuristically, we show that there exist optimal policies for the infinite horizon … Read more
SAP’s decision support systems for optimized supply network planning rely on mixed-integer programming as the core engine to compute optimal or near-optimal solutions. The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of a robust and future-proof decision support system for a large and diverse customer base. In this … Read more
In this paper we analyze the rate of local convergence of the augmented Lagrange method for solving optimization problems with equality constraints and the objective function expressed as the sum of a convex function and a twice continuously differentiable function. The presence of the non-smoothness of the convex function in the objective requires extensive tools … Read more