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.

Transport of iodide in structured clay–loam soil under maize during irrigation experiments analyzed using HYDRUS model

Transport of radioactive iodide 131I− in a structured clay loam soil under maize in a final growing phase was monitored during five consecutive irrigation experiments under ponding. Each time, 27 mm of water were applied. The water of the second experiment was spiked with 200 MBq of 131I− tracer. Its activity was monitored as functions of depth and time with Geiger-Müller (G-M) detectors in 11 vertically installed access tubes. The aim of the study was to widen our current knowledge of water and solute transport in unsaturated soil under different agriculturally cultivated settings. It was supposed that the change in 131I− activity (or counting rate) is proportional to the change in soil water content. Rapid increase followed by a gradual decrease in 131I− activity occurred at all depths and was attributed to preferential flow. The iodide transport through structured soil profile was simulated by the HYDRUS 1D model. The model predicted relatively deep percolation of iodide within a short time, in a good agreement with the observed vertical iodide distribution in soil. We found that the top 30 cm of the soil profile is the most vulnerable layer in terms of water and solute movement, which is the same depth where the root structure of maize can extend.

Experimental evidence for the immediate impact of fertilization and irrigation upon the plant and invertebrate communities of mountain grasslands

The response of montane and subalpine hay meadow plant and arthropod communities to the application of liquid manure and aerial irrigation – two novel, rapidly spreading management practices – remains poorly understood, which hampers the formulation of best practice management recommendations for both hay production and biodiversity preservation. In these nutrient-poor mountain grasslands, a moderate management regime could enhance overall conditions for biodiversity. This study experimentally assessed, at the site scale, among low-input montane and subalpine meadows, the short-term effects (1 year) of a moderate intensification (slurry fertilization: 26.7–53.3 kg N·ha−1·year−1; irrigation with sprinklers: 20 mm·week−1; singly or combined together) on plant species richness, vegetation structure, hay production, and arthropod abundance and biomass in the inner European Alps (Valais, SW Switzerland). Results show that (1) montane and subalpine hay meadow ecological communities respond very rapidly to an intensification of management practices; (2) on a short-term basis, a moderate intensification of very low-input hay meadows has positive effects on plant species richness, vegetation structure, hay production, and arthropod abundance and biomass; (3) vegetation structure is likely to be the key factor limiting arthropod abundance and biomass. Our ongoing experiments will in the longer term identify which level of management intensity achieves an optimal balance between biodiversity and hay production.

Resource-Constrained Project Scheduling with Project Management Information Systems

Most commercial project management software packages include planning methods to devise schedules for resource-constrained projects. As it is proprietary information of the software vendors which planning methods are implemented, the question arises how the software packages differ in quality with respect to their resource-allocation capabilities. We experimentally evaluate the resource-allocation capabilities of eight recent software packages by using 1,560 instances with 30, 60, and 120 activities of the well-known PSPLIB library. In some of the analyzed packages, the user may influence the resource allocation by means of multi-level priority rules, whereas in other packages, only few options can be chosen. We study the impact of various complexity parameters and priority rules on the project duration obtained by the software packages. The results indicate that the resource-allocation capabilities of these packages differ significantly. In general, the relative gap between the packages gets larger with increasing resource scarcity and with increasing number of activities. Moreover, the selection of the priority rule has a considerable impact on the project duration. Surprisingly, when selecting a priority rule in the packages where it is possible, both the mean and the variance of the project duration are in general worse than for the packages which do not offer the selection of a priority rule.

The Resource-Constrained Project Scheduling Problem with Work-Content Constraints

For executing the activities of a project, one or several resources are required, which are in general scarce. Many resource-allocation methods assume that the usage of these resources by an activity is constant during execution; in practice, however, the project manager may vary resource usage by individual activities 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 precedence and various work-content-related constraints are met.

Irrigation development in Eritrea: potentials and constraints: Proceedings of the workshop of AEAS and SLM Programme Eritrea

Development of irrigation, which is of crucial importance in Eritrea, is perceived by many as the main technique for improving the precarious food security situation in this Sahelian country in the Horn of Africa. The present publication presents the outcome of a nationwide workshop held in 2003, which brought together administrators, scientists, and members of public development agencies and NGOs. These workshop participants presented experiences, lessons learnt, and ideas about how to move forward in relation to development of irrigation in Eritrea. Specifically, the publication deals with the following broad themes, lessons learnt, and experiences in Eritrea: · spate irrigation systems and measurement of performance, as well as experience with modernisation of spate irrigation systems in Eritrea · small-scale irrigation systems and their potentials and pitfalls, including development of low-cost micro irrigation · climate and irrigation, including rainfall forecasts · socio-economic aspects of irrigation, including gender questions, institutional requirements, and irrigation and livelihoods The publication contains an extensive summary in the Tigrinya language, in order to facilitate access to the key findings by local non-English-speaking stakeholders in irrigation development.

On an Application of Microsoft Excel’s Evolutionary Solver to the Resource-Constrained Project Scheduling Problem RCPSP

The Solver Add-in of Microsoft Excel is widely used in courses on Operations Research and in industrial applications. Since the 2010 version of Microsoft Excel, the Solver Add-in comprises a so-called evolutionary solver. We analyze how this metaheuristic can be applied to the resource-constrained project scheduling problem (RCPSP). We present an implementation of a schedule-generation scheme in a spreadsheet, which combined with the evolutionary solver can be used for devising good feasible schedules. Our computational results indicate that using this approach, non-trivial instances of the RCPSP can be (approximately) solved to optimality.

An MILP-based heuristic for staff scheduling problems with acceptance levels

We present a real-world staff-assignment problem that was reported to us by a provider of an online workforce scheduling software. The problem consists of assigning employees to work shifts subject to a large variety of requirements related to work laws, work shift compatibility, workload balancing, and personal preferences of employees. A target value is given for each requirement, and all possible deviations from these values are associated with acceptance levels. The objective is to minimize the total number of deviations in ascending order of the acceptance levels. We present an exact lexicographic goal programming MILP formulation and an MILP-based heuristic. The heuristic consists of two phases: in the first phase a feasible schedule is built and in the second phase parts of the schedule are iteratively re-optimized by applying an exact MILP model. A major advantage of such MILP-based approaches is the flexibility to account for additional constraints or modified planning objectives, which is important as the requirements may vary depending on the company or planning period. The applicability of the heuristic is demonstrated for a test set derived from real-world data. Our computational results indicate that the heuristic is able to devise optimal solutions to non-trivial problem instances, and outperforms the exact lexicographic goal programming formulation on medium- and large-sized problem instances.

Efficient list-generation techniques for scheduling assessment centers

Human resources managers often conduct assessment centers to evaluate candidates for a job position. During an assessment center, the candidates perform a series of tasks. The tasks require one or two assessors (e.g., managers or psychologists) that observe and evaluate the candidates. If an exercise is designed as a role-play, an actor is required who plays, e.g., an unhappy customer with whom the candidate has to deal with. Besides performing the tasks, each candidate has a lunch break within a prescribed time window. Each candidate should be observed by approximately half the number of the assessors; however, an assessor may not observe a candidate if they personally know each other. The planning problem consists of determining (1) resource-feasible start times of all tasks and lunch breaks and (2) a feasible assignment of assessors to candidates, such that the assessment center duration is minimized. We present a list-scheduling heuristic that generates feasible schedules for such assessment centers. We propose several novel techniques to generate the respective task lists. Our computational results indicate that our approach is capable of devising optimal or near-optimal schedules for real-world instances within short CPU time.