Heuristic branch-and-price for building long term trainee schedules.

Branch-and-price is an increasingly important technique for solving large integer programming models. Staff scheduling has been a particularly fruitful area since these problems typically exhibit a decomposable structure. Beside computational efficiency branch-and-price produces two other important advantages in comparison with pure integer programming. Firstly, it often allows for a more accurate problem statement since many constraints which are hard to formulate in the integer program could be easily incorporated in the column generator. Secondly, a branch-and-price algorithm can easily be turned into an effective heuristic when optimality is no major concern. We illustrate these advantages for a medical trainee scheduling problem encountered at Oogziekenhuis Gasthuisberg Leuven and present some computational results together with implementation issues.Advantages; Area; Branch-and-price; Constraint; Efficiency; Heuristic; Integer programming; Model; Models; Problems; Research; Scheduling; Staff scheduling; Structure;

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

Decision-based genetic algorithms for solving multi-period project scheduling with dynamically experienced workforce

The importance of the flexibility of resources increased rapidly with the turbulent changes in the industrial context, to meet the customers’ requirements. Among all resources, the most important and considered as the hardest to manage are human resources, in reasons of availability and/or conventions. In this article, we present an approach to solve project scheduling with multi-period human resources allocation taking into account two flexibility levers. The first is the annual hours and working time regulation, and the second is the actors’ multi-skills. The productivity of each operator was considered as dynamic, developing or degrading depending on the prior allocation decisions. The solving approach mainly uses decision-based genetic algorithms, in which, chromosomes don’t represent directly the problem solution; they simply present three decisions: tasks’ priorities for execution, actors’ priorities for carrying out these tasks, and finally the priority of working time strategy that can be considered during the specified working period. Also the principle of critical skill was taken into account. Based on these decisions and during a serial scheduling generating scheme, one can in a sequential manner introduce the project scheduling and the corresponding workforce allocations

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table

Multi-skill resource-constrained project scheduling problems : models and algorithms

Tese de doutoramento, Estatística e Investigação Operacional (Otimização), Universidade de Lisboa, Faculdade de Ciências, 2018In this dissertation, project scheduling problems with multi-skill resources are investigated. These problems are commonly found in companies making use of human resources or multi-purpose machinery equipment. The general problem consists of a single project comprising a set of activities. There are precedence relations between the activities. Each activity requires one or several skills for being processed and for each of these skills, more than one resource may be needed. The resources have a unitary capacity per time unit and may master more than one skill. The resources can contribute with at most one skill to at most one activity that requires it, in each time unit. It is usually assumed that the resources are homogeneous, i.e., the proficiency at which each skill is performed is the same across all resources that master that skill. Preemption is not allowed, which implies that once an activity starts being processed it cannot be interrupted. When a resource is assigned to perform a skill for an activity, it remains in that status for the whole processing time of the activity. The objective of the problem is to schedule all the activities, satisfying all constraints such that the makespan of the project is minimized. After introducing a framework to the realm of project scheduling problems with multi-skill resources and highlighting the main objectives and contributes of this thesis, a state-of the-art review on the topic is presented. The particular problem investigated in this document is then described in detail and its specific features are discussed. To that end, a continuous-time mathematical formulation from the literature is revisited, an example of the problem is presented and some aspects related to the computation of feasible solutions are discussed. This last topic is of major relevance when dealing with problems that combine personnel staffing with project scheduling. In order to properly assess the quality of solutions obtained by the methodological developments proposed in this thesis, it became necessary to develop an instance generator to build a set of instances larger than those existing in the literature. After formally proposing such generator, we detail the characteristics of the two sets of instances considered for the computational experiments to be performed. In the next sections of the document, the solution methodologies developed within the scope of this thesis are presented and thoroughly discussed. A wide range of mathematical formulations is studied, two of which are first proposed in this document. From the assessment of their ability both to compute feasible and possibly optimal solutions and to derive good lower bounds (stemming from their linear programming relaxations) to the problem, it will become clear that the so-called discrete-time formulations yield the strongest lower bounds whereas a continuous-time formulation from the literature proved to be the most suitable for solving instances of the problem to optimality. This trend is observed for both sets of instances considered. Two constructive lower bound mechanisms proposed for the resource-constrained project scheduling problem are extended to account for the existence of multi-skill resources and multi skill requirements of the activities. The results reveal that such methods improve the lower bounds achieved by the studied mathematical formulations for some instances. Real-world project scheduling problems usually involve a large number of activities, resources and skills. Hence, the use of exact methods such as the standard techniques for tackling the aforementioned mathematical models, is often impractical. When faced with this kind of situations, a project manager may consider preferable to have a good feasible solution, not necessarily an optimal one, within an admissible time, by means of an approximate method. A close look into the problem being investigated in this thesis reveals that it has some features that are not present in some well-studied particular cases of it, namely the notion of skill—multi skill resources and skill requirements of the activities. Hence, with the objective of developing approximate solution methodologies that better exploit the specific characteristics of the problem at hand, two new concepts are introduced: activity grouping and resource weight. The well-known parallel and serial scheduling schemes, proposed originally for the class of resource-constrained project scheduling problems, are extended to our problem setting and the two above-mentioned concepts are incorporated into these two new frameworks. Such frameworks use well-known activity priority rules for defining the order by which the activities are selected to be scheduled and resource weight rules to determine a set of resources that meets the requirements of all the activities to be scheduled at each time with the least total cost (weight). Thereafter, two heuristic procedures making use of those schedule generation schemes are proposed, namely a multi-pass heuristic built upon the parallel scheduling scheme and a biased random-key genetic algorithm. The idea of computing a feasible solution using the so-called backward planning is also considered in both methods. The multi-pass heuristic retrieves the solution with the minimum makespan after performing a specific number of passes, each associated with a unique combination of the considered activity priority rules, the developed resource weight rules and the two precedence networks: forward and backward. The biased random-key genetic algorithm is a metaheuristic whose developed chromosome structure encodes information related to: (i) the priority values of the activities; (ii) the weights of the resources; (iii) how a chromosome is decoded, i.e., the scheduling scheme and precedence network scheme to be used for computing the associated makespan. By embedding all this information into the chromosomes, it becomes possible to take advantage of the evolutionary framework of the biased random-key genetic algorithm, which tends to allow the evolution of such data (change in their values) over time, towards better makespan valued solutions. Three variants of the biased random-key genetic algorithm are considered with regard to the type of scheduling generation scheme to be used for decoding its chromosomes: (i) all chromosomes are decoded with the parallel scheduling scheme; (ii) all chromosomes are decoded with the serial scheduling scheme; (iii) the scheduling scheme to be used for decoding each chromosome depends on the value of the associated parameter which is embedded in the chromosome. The computational results revealed that the proposed multi-pass heuristic is an efficient algorithm for computing feasible solutions of acceptable quality within a small computational time whereas the biased random-key genetic algorithm is a robust algorithm and a more competitive approximate approach for computing feasible solutions of higher quality, especially for harder instances such as those of medium and large dimensions. We conclude this thesis with an overview of the work done and with some directions for further research in terms of methodological developments and of some potentially interesting extensions of the addressed problem

A greedy heuristic approach for the project scheduling with labour allocation problem

Responding to the growing need of generating a robust project scheduling, in this article we present a greedy algorithm to generate the project baseline schedule. The robustness achieved by integrating two dimensions of the human resources flexibilities. The first is the operators’ polyvalence, i.e. each operator has one or more secondary skill(s) beside his principal one, his mastering level being characterized by a factor we call “efficiency”. The second refers to the working time modulation, i.e. the workers have a flexible time-table that may vary on a daily or weekly basis respecting annualized working strategy. Moreover, the activity processing time is a non-increasing function of the number of workforce allocated to create it, also of their heterogynous working efficiencies. This modelling approach has led to a nonlinear optimization model with mixed variables. We present: the problem under study, the greedy algorithm used to solve it, and then results in comparison with those of the genetic algorithms

A combinatorial approach to multi-skill workforce scheduling

This paper deals with scheduling complex tasks with an inhomogeneous set of resources. The problem is to assign technicians to tasks with multi-level skill requirements. Here the requirements are merely the presence of a set of technicians that possess the necessary capabilities. An additional complication is that a set of combined technicians stays together for the duration of a work day. This typically applies to scheduling of maintenance and installation operations. We build schedules by repeated application of a exible matching model that selects tasks to be processed and forms groups of technicians assigned to combinations of tasks. The underlying mixed integer programming (MIP) model is capable of revising technician-task allocations and performs very well, especially in the case of rare skills