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.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient. We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

Predicting adverse events in children with fever and chemotherapy-induced neutropenia: the prospective multicenter SPOG 2003 FN study

PURPOSE To develop a score predicting the risk of adverse events (AEs) in pediatric patients with cancer who experience fever and neutropenia (FN) and to evaluate its performance. PATIENTS AND METHODS Pediatric patients with cancer presenting with FN induced by nonmyeloablative chemotherapy were observed in a prospective multicenter study. A score predicting the risk of future AEs (ie, serious medical complication, microbiologically defined infection, radiologically confirmed pneumonia) was developed from a multivariate mixed logistic regression model. Its cross-validated predictive performance was compared with that of published risk prediction rules. Results An AE was reported in 122 (29%) of 423 FN episodes. In 57 episodes (13%), the first AE was known only after reassessment after 8 to 24 hours of inpatient management. Predicting AE at reassessment was better than prediction at presentation with FN. A differential leukocyte count did not increase the predictive performance. The score predicting future AE in 358 episodes without known AE at reassessment used the following four variables: preceding chemotherapy more intensive than acute lymphoblastic leukemia maintenance (weight = 4), hemoglobin > or = 90 g/L (weight = 5), leukocyte count less than 0.3 G/L (weight = 3), and platelet count less than 50 G/L (weight = 3). A score (sum of weights) > or = 9 predicted future AEs. The cross-validated performance of this score exceeded the performance of published risk prediction rules. At an overall sensitivity of 92%, 35% of the episodes were classified as low risk, with a specificity of 45% and a negative predictive value of 93%. CONCLUSION This score, based on four routinely accessible characteristics, accurately identifies pediatric patients with cancer with FN at risk for AEs after reassessment.

The effects of cardiac output and pulmonary arterial hypertension on volumetric capnography derived-variables during normoxia and hypoxia

The aim of this study was to test the effect of cardiac output (CO) and pulmonary artery hypertension (PHT) on volumetric capnography (VCap) derived-variables. Nine pigs were mechanically ventilated using fixed ventilatory settings. Two steps of PHT were induced by IV infusion of a thromboxane analogue: PHT25 [mean pulmonary arterial pressure (MPAP) of 25 mmHg] and PHT40 (MPAP of 40 mmHg). CO was increased by 50 % from baseline (COup) with an infusion of dobutamine ≥5 μg kg(-1) min(-1) and decreased by 40 % from baseline (COdown) infusing sodium nitroglycerine ≥30 μg kg(-1) min(-1) plus esmolol 500 μg kg(-1) min(-1). Another state of PHT and COdown was induced by severe hypoxemia (FiO2 0.07). Invasive hemodynamic data and VCap were recorded and compared before and after each step using a mixed random effects model. Compared to baseline, the normalized slope of phase III (SnIII) increased by 32 % in PHT25 and by 22 % in PHT40. SnIII decreased non-significantly by 4 % with COdown. A combination of PHT and COdown associated with severe hypoxemia increased SnIII by 28 % compared to baseline. The elimination of CO2 per breath decreased by 7 % in PHT40 and by 12 % in COdown but increased only slightly with COup. Dead space variables did not change significantly along the protocol. At constant ventilation and body metabolism, pulmonary artery hypertension and decreases in CO had the biggest effects on the SnIII of the volumetric capnogram and on the elimination of CO2.

Scheduling in service systems: an application in the event-tourism industry

This paper deals with an event-bus tour booked by Bollywood film fans. During the tour, the participants visit selected locations of famous Bollywood films at various sites in Switzerland. Moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour; for organizational reasons, two or more buses cannot stay at the same location simultaneously. The planning problem is how to compute a feasible schedule for each bus such that the total waiting time (primary objective) and the total travel time (secondary objective) are minimized. We formulate this problem as a mixed-integer linear program, and we report on computational results obtained with the Gurobi solver.

Migration background is associated with caries in Viennese school children, even if parents have received a higher education.

BACKGROUND A low level of education and the migration background of parents are associated with the development of caries in children. The aim of this study was to evaluate whether a higher educational level of parents can overcome risks for the development of caries in immigrants in Vienna, Austria. METHODS The educational level of the parents, the school type, and the caries status of 736 randomly selected twelve-year-old children with and without migration background was determined in this cross sectional study. In children attending school in Vienna the decayed, missing, and filled teeth (DMFT) index was determined. For statistical analysis, a mixed negative-binomial-model was used. RESULTS The caries status of the children with migration background was significantly worse compared to that of the native Viennese population. A significant interaction was found between migration background and the educational level of the parents (p = 0.045). No interaction was found between the school type and either the migration background (p = 0.220) or the education level of the parents (p = 0.08). In parents with a higher scholarly education level, migration background (p < 0.01) and school type (p = 0.018) showed an association with DMFT values. In parents with a low education level, however, migration background and school type had no significant association with DMFT values. CONCLUSION These data indicate that children with a migration background are at higher risk to acquire caries than other Viennese children, even when the parents have received a higher education.

Handrub Consumption Mirrors Hand Hygiene Compliance

We assessed handrub consumption as a surrogate marker for hand hygiene compliance from 2007 to 2014. Handrub consumption varied substantially between departments but correlated in a mixed effects regression model with the number of patient-days and the observed hand hygiene compliance. Handrub consumption may supplement traditional hand hygiene observations. Infect. Control Hosp. Epidemiol. 2016;1-4.

PSPLINE: Stata module providing a penalized spline scatterplot smoother based on linear mixed model technology

Pspline uses xtmixed to fit a penalized spline regression and plots the smoothed function. Additional covariates can be specified to adjust the smooth and plot partial residuals.

Projected 21st century decrease in marine productivity: a multi-model analysis

Changes in marine net primary productivity (PP) and export of particulate organic carbon (EP) are projected over the 21st century with four global coupled carbon cycle-climate models. These include representations of marine ecosystems and the carbon cycle of different structure and complexity. All four models show a decrease in global mean PP and EP between 2 and 20% by 2100 relative to preindustrial conditions, for the SRES A2 emission scenario. Two different regimes for productivity changes are consistently identified in all models. The first chain of mechanisms is dominant in the low- and mid-latitude ocean and in the North Atlantic: reduced input of macro-nutrients into the euphotic zone related to enhanced stratification, reduced mixed layer depth, and slowed circulation causes a decrease in macro-nutrient concentrations and in PP and EP. The second regime is projected for parts of the Southern Ocean: an alleviation of light and/or temperature limitation leads to an increase in PP and EP as productivity is fueled by a sustained nutrient input. A region of disagreement among the models is the Arctic, where three models project an increase in PP while one model projects a decrease. Projected changes in seasonal and interannual variability are modest in most regions. Regional model skill metrics are proposed to generate multi-model mean fields that show an improved skill in representing observation-based estimates compared to a simple multi-model average. Model results are compared to recent productivity projections with three different algorithms, usually applied to infer net primary production from satellite observations.