A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Study of 3D-growth conditions for selective area MOVPE of high aspect ratio GaN fins with non-polar vertical sidewalls

GaN fins are 3D architectures elongated in one direction parallel to the substrate surface. They have the geometry of walls with a large height to width ratio as well as small footprints. When appropriate symmetry directions of the GaN buffer are used, the sidewalls are formed by non-polar {11-20} planes, making the fins particularly suitable for many device applications like LEDs, FETs, lasers, sensors or waveguides. The influence of growth parameters like temperature, pressure, V/III ratio and total precursor flow on the fin structures is analyzed. Based on these results, a 2-temperature-step-growth was developed, leading to fins with smooth side and top facets, fast vertical growth rates and good homogeneity along their length as well as over different mask patterns. For the core-shell growth of fin LED heterostructures, the 2-temperature-step-growth shows much smoother sidewalls and less crystal defects in the InGaN QW and p-GaN shell compared to structures with cores grown in just one step. Electroluminescence spectra of the 2-temperature-step-grown fin LED are demonstrated

Ambient and substrate energy influence decomposer diversity differentially across trophic levels.

The species-energy hypothesis predicts increasing biodiversity with increasing energy in ecosystems. Proxies for energy availability are often grouped into ambient energy (i.e., solar radiation) and substrate energy (i.e., non-structural carbohydrates or nutritional content). The relative importance of substrate energy is thought to decrease with increasing trophic level from primary consumers to predators, with reciprocal effects of ambient energy. Yet, empirical tests are lacking. We compiled data on 332,557 deadwood-inhabiting beetles of 901 species reared from wood of 49 tree species across Europe. Using host-phylogeny-controlled models, we show that the relative importance of substrate energy versus ambient energy decreases with increasing trophic levels: the diversity of zoophagous and mycetophagous beetles was determined by ambient energy, while non-structural carbohydrate content in woody tissues determined that of xylophagous beetles. Our study thus overall supports the species-energy hypothesis and specifies that the relative importance of ambient temperature increases with increasing trophic level with opposite effects for substrate energy

Scheduling reefer mechanics at container terminals

This paper discusses the scheduling of reefer mechanics at container terminals. Reefer mechanics plug and unplug reefer containers such that due times are met. We outline the resulting scheduling problem and two simple heuristics. Subsequently, we present a simulation model to analyze the scheduling methods and the reefer-related processes in a realistic dynamic framework. Some results from the simulation experiments are also presented. They demonstrate the applicability of the heuristic and the use of the simulation model in practice. The simulation study was carried out for a real container terminal in the port of Hamburg, Germany

Project Scheduling with Multiple Modes: A Genetic Algorithm

In this paper we consider the resource-constrained project scheduling problem with multiple execution modes for each activity and makespan minimization as objective. We present a new genetic algorithm approach to solve this problem. The genetic encoding is based on a precedence feasible sequence of activities and a mode assignment. After defining the related crossover, mutation, and selection operators, we describe a local search extension which is employed to improve the schedules found by the basic genetic algorithm. Finally, we present the results of our thorough computational study. We determine the best among several different variants of our genetic algorithm and compare it to three other heuristics that have recently been proposed in the literature. The results that have been obtained using a standard set of instances show that the new genetic algorithm outperforms the other heuristic procedures with regard to a lower average deviation from the optimal makespan

A Competitive Genetic Algorithm for Resource-Constrained Project Scheduling

In this paper we consider the resource-constrained project scheduling problem (RCPSP) with makespan minimization as objective. We propose a new genetic algorithm approach to solve this problem. Subsequently, we compare it to two genetic algorithm concepts from the literature. While our approach makes use of a permutation based genetic encoding that contains problem-specific knowledge, the other two procedures employ a priority value based and a priority rule based representation, respectively. Then we present the results of our thorough computational study for which a standard set of project instances has been used. The outcome reveals that our procedure is the most promising genetic algorithm to solve the RCPSP. Finally, a priority rule based random sampling procedure known from the literature serves as a further benchmark. We show that our genetic algorithm yields better results than this sampling approach

Self-Adapting Genetic Algorithms with an Application to Project Scheduling

This paper introduces a new general framework for genetic algorithms to solve a broad range of optimization problems. When designing a genetic algorithm, there may be several alternatives for a component such as crossover, mutation or decoding procedure, and it may be difficult to determine the best alternative (e.g., the best crossover strategy) a priori. For such cases, we suggest to include alternative components into the genetic algorithm. Indicating the component to be actually used in the genotype, this allows the genetic algorithm to adapt itself. That is, the genetic algorithm learns which of the alternative components is the most successful by means of genetic optimization. In order to demonstrate the potential of the self-adapting genetic algorithm concept, we apply it to the classical resource-constrained project scheduling problem (RCPSP). Motivated by previous computational studies as well as theoretical insight, we employ two different decoding procedures and leave the de..

Scheduling Medical Research Experiments -- An Application of Project Scheduling Methods

We consider a medical research project that was carried out at the University of Kiel (Germany). This paper deals with the task of scheduling this real-world project. The original problem is shown to be an instance of an extension of the well-known resource-constrained project scheduling problem (RCPSP) with makespan minimization as objective. We obtain a moderately sized problem which consists of 62 activities with time-varying resource request and 27 renewable resources with time-varying availabilities. Subsequently, a genetic algorithm that has recently been suggested for the RCPSP is employed to schedule the real-world project. Within less than one minute, a schedule is obtained which is proved to be optimal. Moreover, we compare the schedule found by the genetic algorithm with the hand-made one according to which the original project was performed. The makespan of the computed schedule is more than 10 % shorter than the hand-made one. We conclude that computer based systems are us..