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.

Design of nest access grids and perches in front of the nests: Influence on the behavior of laying hens.

In aviary systems for laying hens, it is important to provide suitable nest access platforms in front of the nests, allowing hens to reach and explore each of the nests easily. This access platform is needed to achieve good nest acceptance by the hens and thereby prevent mislaid eggs. In the present experiment, the behavior of hens using 2 different nest access platforms, a plastic grid and 2 wooden perches, was examined. Furthermore, the nests were placed on both sides of the aviary rack (corridor side and outdoor side), either integrated into the aviary rack itself (integrated nest; IN) or placed on the walls of the pens (wall nest; WN), resulting in a 2 × 2 factorial design Four thousand five hundred white laying hens were housed in 20 test pens. The eggs in the nests and mislaid eggs were collected daily, and the behavior of hens on the nest accesses was filmed during wk 25 and 26, using focal observation and scan sampling methods. More balancing, body contact, and agonistic interactions were expected for nests with perches, whereas more walking and nest inspections were expected for nests with grids. There were more mislaid eggs and balancing found in pens equipped with nests with wooden perches. More agonistic interactions and balancing, less standing, and a longer duration of nest inspection were found with the WN compared with the IN. Interactions between platform design and position of the nests were found for duration of nest visits, body contact, and walking, with the highest amount for WN equipped with plastic grids. Nests on the corridor side were favored by the hens. Nest-related behaviors, such as nest inspection, standing, and walking, decreased over time as did the number of hens on the nest accesses, whereas sitting increased. These results indicate that the hens had more difficulties in gripping the perches as designed. The lower number of hens on the nest access platforms in front of IN may be due to a better distribution around nests and tier changes within the aviary rack. Based on these results, grids rather than perches provide for improved nesting behavior.

Batch scheduling in process industries: an application of resource-constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time.

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