A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

Ruler Based Automatic C-Arm Image Stitching Without Overlapping Constraint

In this paper, we propose a new method for stitching multiple fluoroscopic images taken by a C-arm instrument. We employ an X-ray radiolucent ruler with numbered graduations while acquiring the images, and the image stitching is based on detecting and matching ruler parts in the images to the corresponding parts of a virtual ruler. To achieve this goal, we first detect the regular spaced graduations on the ruler and the numbers. After graduation labeling, for each image, we have the location and the associated number for every graduation on the ruler. Then, we initialize the panoramic X-ray image with the virtual ruler, and we “paste” each image by aligning the detected ruler part on the original image, to the corresponding part of the virtual ruler on the panoramic image. Our method is based on ruler matching but without the requirement of matching similar feature points in pairwise images, and thus, we do not necessarily require overlap between the images. We tested our method on eight different datasets of X-ray images, including long bones and a complete spine. Qualitative and quantitative experiments show that our method achieves good results.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.