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.

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.

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.

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.

Progression of age-related geographic atrophy: role of the fellow eye

PURPOSE. To evaluate the role of fellow eye status in determining progression of geographic atrophy (GA) in patients with age-related macular degeneration (AMD). METHODS. A total of 300 eyes with GA of 193 patients from the prospective, longitudinal, natural history FAM Study were classified into three groups according to the AMD manifestation in the fellow eye at baseline examination: (1) bilateral GA, (2) early/intermediate AMD, and (3) exudative AMD. GA areas were quantified based on fundus autofluorescence images using a semiautomated image-processing method, and progression rates (PR) were estimated using two-level, linear, mixed-effects models. RESULTS. Crude GA-PR in the bilateral GA group (mean, 1.64 mm(2)/y; 95% CI, 1.478-1.803) was significantly higher than in the fellow eye early/intermediate group (0.74 mm(2)/y, 0.146-1.342). Although there was a significant difference in baseline GA size (P = 0.0013, t-test), and there was a significant increase in GA-PR by 0.11 mm(2)/y (0.05-0.17) per 1 disc area (DA; 2.54 mm(2)), an additional mean change of -0.79 (-1.43 to -0.15) was given to the PR beside the effect of baseline GA size. However, this difference was only significant when GA size was ?1 DA at baseline with a GA-PR of 1.70 mm(2)/y (1.54-1.85) in the bilateral and 0.95 mm(2)/y (0.37-1.54) in the early/intermediate group. There was no significant difference in PR compared with that in the fellow eye exudative group. CONCLUSIONS. The results indicate that the AMD manifestation of the fellow eye at baseline serves as an indicator for disease progression in eyes with GA ? 1 DA. Predictive characteristics not only contribute to the understanding of pathophysiological mechanisms, but also are useful for the design of future interventional trials in GA patients.

Counterbalancing effects of competition for resources and facilitation against grazing in alpine snowbed communities

Alpine snowbeds are habitats where the major limiting factors for plant growth are herbivory and a small time window for growth due to late snowmelt. Despite these limitations, snowbed vegetation usually forms a dense carpet of palatable plants due to favourable abiotic conditions for plant growth within the short growing season. These environmental characteristics make snowbeds particularly interesting to study the interplay of facilitation and competition. We hypothesised an interplay between resource competition and facilitation against herbivory. Further, we investigated whether these predicted neighbour effects were species-specific and/or dependent on ontogeny, and whether the balance of positive and negative plant–plant interactions shifted along a snowmelt gradient. We determined the neighbour effects by means of neighbour removal experiments along the snowmelt gradient, and linear mixed model analyses. The results showed that the effects of neighbour removal were weak but generally consistent among species and snowmelt dates, and depended on whether biomass production or survival was considered. Higher total biomass and increased fruiting in removal plots indicated that plants competed for nutrients, water, and light, thereby supporting the hypothesis of prevailing competition for resources in snowbeds. However, the presence of neighbours reduced herbivory and thereby also facilitated survival. For plant growth the facilitative effects against herbivores in snowbeds counterbalanced competition for resources, leading to a weak negative net effect. Overall the neighbour effects were not species-specific and did not change with snowmelt date. Our finding of counterbalancing effects of competition and facilitation within a plant community is of special theoretical value for species distribution models and can explain the success of models that give primary importance to abiotic factors and tend to overlook interrelations between biotic and abiotic effects on plants.

Coping personality type and environmental enrichment affect aggression at weaning in pigs

This study investigated the effects of different environmental treatments and personality types on aggression at mixing of newly weaned domestic piglets. From birth to weaning, 16 litters were housed with their dams in either barren (B) or larger, substrate-enriched (E) environments. At 15 days old, piglets were classified as 'high' (HR) or low resistant' (LR) in a manual restraint test (backtest), which is thought to identify proactive (HR) and reactive (LR) stress coping strategies that may reflect different personality types. At 30 days old, 128 piglets were weaned, relocated and mixed into 32 pens comprising two HR and two LR unfamiliar pigs, balanced for sex and weaning weight. Eight B and eight E groups changed environmental condition whereas the others remained in the same type of environment. Number and duration of fights. fight outcomes and unilateral fighting were scored for 5 h post-mixing and skin lesions were counted before and 5 h, 1 day and 2 days after mixing. On the day following weaning, fighting and also exploratory and oral manipulative behaviours were measured for 6 h. Generalized Linear Mixed Model analyses suggested interactions between pre-weaning environment, post-weaning environment and personality type. Overall, pre-weaning E pigs had longer fights at weaning and mixing (P=0.01) and fought for longer on the next day (P=0.02) than pre-weaning B pigs, and inflicted more skin lesions (P=0.02). Post-weaning enrichment did not affect fighting at mixing but reduced the time spent fighting the next day (P=0.03). Personality had subtle and environment-dependent effects on fighting, and influenced the "structure" rather than the amount of aggressive behaviour. HR pigs, for instance, bullied (i.e. chased surrendering pigs) more often (P=0.009) and their fighting behaviour was less affected by their relative body weight than that of LR pigs. Post-weaning E pigs showed relatively higher levels of exploratory behaviour (P=0.02) and less oral manipulative behaviour (P=0.04) than post-weaning B pigs. In particular, switching from a good quality environment (E) to a worse quality one (B) at weaning decreased exploratory behaviour on the next day, especially for LR pigs, who also tended to fight with and orally manipulate their pen mates more in that condition, and seemed to be more affected by a deterioration of the environment. Overall, pre-weaning enrichment increased aggression after weaning whereas post-weaning enrichment reduced it, and personality type related to some aspects of fighting behaviour. (C) 2011 Elsevier B.V. All rights reserved.

Mean CD4 cell count changes in patients failing a first-line antiretroviral therapy in resource-limited settings

Background Changes in CD4 cell counts are poorly documented in individuals with low or moderate-level viremia while on antiretroviral treatment (ART) in resource-limited settings. We assessed the impact of on-going HIV-RNA replication on CD4 cell count slopes in patients treated with a first-line combination ART. Method Naïve patients on a first-line ART regimen with at least two measures of HIV-RNA available after ART initiation were included in the study. The relationships between mean CD4 cell count change and HIV-RNA at 6 and 12 months after ART initiation (M6 and M12) were assessed by linear mixed models adjusted for gender, age, clinical stage and year of starting ART. Results 3,338 patients were included (14 cohorts, 64% female) and the group had the following characteristics: a median follow-up time of 1.6 years, a median age of 34 years, and a median CD4 cell count at ART initiation of 107 cells/μL. All patients with suppressed HIV-RNA at M12 had a continuous increase in CD4 cell count up to 18 months after treatment initiation. By contrast, any degree of HIV-RNA replication both at M6 and M12 was associated with a flat or a decreasing CD4 cell count slope. Multivariable analysis using HIV-RNA thresholds of 10,000 and 5,000 copies confirmed the significant effect of HIV-RNA on CD4 cell counts both at M6 and M12. Conclusion In routinely monitored patients on an NNRTI-based first-line ART, on-going low-level HIV-RNA replication was associated with a poor immune outcome in patients who had detectable levels of the virus after one year of ART.

Modeling of red blood cell life-spans in hematologically normal populations

Despite the impact of red blood cell (RBC) Life-spans in some disease areas such as diabetes or anemia of chronic kidney disease, there is no consensus on how to quantitatively best describe the process. Several models have been proposed to explain the elimination process of RBCs: random destruction process, homogeneous life-span model, or a series of 4-transit compartment model. The aim of this work was to explore the different models that have been proposed in literature, and modifications to those. The impact of choosing the right model on future outcomes prediction--in the above mentioned areas--was also investigated. Both data from indirect (clinical data) and direct life-span measurement (biotin-labeled data) methods were analyzed using non-linear mixed effects models. Analysis showed that: (1) predictions from non-steady state data will depend on the RBC model chosen; (2) the transit compartment model, which considers variation in life-span in the RBC population, better describes RBC survival data than the random destruction or homogenous life-span models; and (3) the additional incorporation of random destruction patterns, although improving the description of the RBC survival data, does not appear to provide a marked improvement when describing clinical data.

Association between symptoms and quality of life in patients with schizophrenia: a pooled analysis of changes over time

Quality of life is an important outcome in the treatment of patients with schizophrenia. It has been suggested that patients' quality of life ratings (referred to as subjective quality of life, SQOL) might be too heavily influenced by symptomatology to be a valid independent outcome criterion. There has been only limited evidence on the association of symptom change and changes in SQOL over time. This study aimed to examine the association between changes in symptoms and in SQOL among patients with schizophrenia. A pooled data set was obtained from eight longitudinal studies that had used the Brief Psychiatric Rating Scale (BPRS) for measuring psychiatric symptoms and either the Lancashire Quality of Life Profile or the Manchester Short Assessment of Quality of Life for assessing SQOL. The sample comprised 886 patients with schizophrenia. After controlling for heterogeneity of findings across studies using linear mixed models, a reduction in psychiatric symptoms was associated with improvements in SQOL scores. In univariate analyses, changes in all BPRS subscales were associated with changes in SQOL scores. In a multivariate model, only associations between changes in the BPRS depression/anxiety and hostility subscales and changes in SQOL remained significant, with 5% and 0.5% of the variance in SQOL changes being attributable to changes in depression/anxiety and hostility respectively. All BPRS subscales together explained 8.5% of variance. The findings indicate that SQOL changes are influenced by symptom change, in particular in depression/anxiety. The level of influence is limited and may not compromise using SQOL as an independent outcome measure.

Factors influencing subjective quality of life in patients with schizophrenia and other mental disorders: a pooled analysis

Subjective quality of life (SQOL) is an important outcome in the treatment of patients with schizophrenia. However, there is only limited evidence on factors influencing SQOL, and little is known about whether the same factors influence SQOL in patients with schizophrenia and other mental disorders. This study aimed to identify the factors associated with SQOL and test whether these factors are equally important in schizophrenia and other disorders. For this we used a pooled data set obtained from 16 studies that had used either the Lancashire Quality of Life Profile or the Manchester Short Assessment of Quality of Life for assessing SQOL. The sample comprised 3936 patients with schizophrenia, mood disorders, and neurotic disorders. After controlling for confounding factors, within-subject clustering, and heterogeneity of findings across studies in linear mixed models, patients with schizophrenia had more favourable SQOL scores than those with mood and neurotic disorders. In all diagnostic groups, older patients, those in employment, and those with lower symptom scores had higher SQOL scores. Whilst the strength of the association between age and SQOL did not differ across diagnostic groups, symptom levels were more strongly associated with SQOL in neurotic than in mood disorders and schizophrenia. The association of employment and SQOL was stronger in mood and neurotic disorders than in schizophrenia. The findings may inform the use and interpretation of SQOL data for patients with schizophrenia.

Can a website-delivered computer-tailored physical activity intervention be acceptable, usable, and effective for older people?

Despite the numerous health benefits, population physical activity levels are low and declining with age. A continued increase of Internet access allows for website-delivered interventions to be implemented across age-groups, though older people have typically not been considered for this type of intervention. Therefore, the purpose of this study was to evaluate a website-delivered computer-tailored physical activity intervention, with a specific focus on differences in tailored advice acceptability, website usability, and physical activity change between three age-groups. To mimic "real-life" conditions, the intervention, which provided personalized physical activity feedback delivered via the Internet, was implemented and evaluated without any personal contact for the entire duration of the study. Data were collected online at baseline, 1-week, and 1-month follow-up and analyzed for three age-groups (≤44, 45-59, and ≥60 years) using linear mixed models. Overall, 803 adults received the intervention and 288 completed all measures. The oldest age-group increased physical activity more than the other two groups, spent the most time on the website, though had significantly lower perceived Internet self-confidence scores when compared with the youngest age-group. No differences were found in terms of website usability and tailored advice acceptability. These results suggest that website-delivered physical activity interventions can be suitable and effective for older aged adults.