On the multi-mode, multi-skill resource constrained project scheduling problem : computational results

This paper is concerned with an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) which belongs to the class of the optimization scheduling problems with multi-level (or multi-mode) activities. We developed a practical tool, useful to represent multi-mode projects, and to find a solution for the problem on hand – select the best mode for each resource in each activity in order to minimize the total cost, considering the resource cost, a penalty for tardiness and a bonus for early completion. We implemented an adaptation of a filtered beam search (FBS) algorithm to this problem, using the C# programming language. A “filtered beam” search is a heuristic Branch and Bound (BaB) procedure that uses breadth first search but only the top “best” nodes are kept. We give some of the most important solution details and we report on further computational results, by testing the application for different problem sizes

Exact/heuristic hybrids using rVNS and hyperheuristics for workforce scheduling

In this paper we study a complex real-world workforce scheduling problem. We propose a method of splitting the problem into smaller parts and solving each part using exhaustive search. These smaller parts comprise a combination of choosing a method to select a task to be scheduled and a method to allocate resources, including time, to the selected task. We use reduced Variable Neighbourhood Search (rVNS) and hyperheuristic approaches to decide which sub problems to tackle. The resulting methods are compared to local search and Genetic Algorithm approaches. Parallelisation is used to perform nearly one CPU-year of experiments. The results show that the new methods can produce results fitter than the Genetic Algorithm in less time and that they are far superior to any of their component techniques. The method used to split up the problem is generalisable and could be applied to a wide range of optimisation problems

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

Resource assignment in short life technology intensive (SLTI) new product development (NPD)

Enterprises managing multiple concurrent New Product Development (NPD) projects face significant challenges assigning staff to projects in order to achieve launch schedules that maximize financial returns. The challenge is increased with the class of Short Life Technology Intensive (SLTI) products characterized by technical complexity, short development cycles and short revenue life cycles. Technical complexity drives the need to assign staffing resources of various technical disciplines and skill levels. SLTI products are rapidly developed and launched into stationary market windows where the revenue life cycle is short and decreasing with any time-to-market delay. The SLTI-NPD project management decision is to assign staff of varying technical discipline and skill level to minimize the revenue loss due to product launch delays across multiple projects. This dissertation considers an NPD organization responsible for multiple concurrent SLTI projects each characterized by a set of tasks having technical discipline requirements, task duration estimates and logical precedence relationships. Each project has a known potential launch date and potential revenue life cycle. The organization has a group of technical professionals characterized by a range of skill levels in a known set of technical disciplines. The SLTI-NPD resource assignment problem is solved using a multi-step process referred to as the Resource Assignment and Multi-Project Scheduling (RAMPS) decision support tool. Robust scheduling techniques are integrated to develop schedules that consider variation in task and project duration estimates. A valuation function provides a time-value linkage between schedules and the product revenue life cycle for each product. Productivity metrics are developed as the basis for prioritizing projects for resources assignment. The RAMPS tool implements assignment and scheduling algorithms in two phases; (i) a constructive approach that employs priority rule heuristics to derive feasible assignments and schedules and (ii) an improvement heuristic that considers productivity gains that can be achieved by interchanging resources of differing skill levels and corresponding work rates. An experimental analysis is conducted using the RAMPS tool and simulated project and resource data sets. Results show significant productivity and efficiency gains that can be achieved through effective project and resource prioritization and by including consideration of skill level in the assignment of technical resources

Multi-mode resource constrained project scheduling problem including multi-skill labor (MRCPSP-MS): model and a solution method

The problem that we address in this chapter is an extension of the Resource-Constrained Project Scheduling Problem (RCPSP). It belongs to the class of project scheduling problems with multi-level (or multi-mode) activities, that permit an activity to be processed by resources operating at appropriate modes, where each mode belongs to a different resource level and incurs different cost and duration. Each activity must be allocated exactly one unit of each required resource, and the resource unit may be used at any of its specified levels. The processing time of an activity is given by the maximum of the durations that would result from different resources allocated to that activity. The objective is to find an optimal solution that minimizes the overall project cost, given a delivery date. A penalty is incurred for tardiness beyond the specified delivery date, or a bonus is accrued for early completion. We present a mathematical programming formulation as an accurate problem definition. A Filtered Beam Search (FBS)-based method is used to solve the problem. It was implemented using the C# language. Results of our experimentations on the use of this method are also presented.(undefined

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

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

Multi-Mode Resource-Constrained Project-Scheduling Problem With Renewable Resources: New Solution Approaches

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP) with renewable resources.  In MRCPSP, an activity can be executed in one of many possible modes; each mode having different resource requirements and accordingly different activity durations.  We assume that all resources are renewable from period to period, such as labor and machines.  A solution to this problem basically involves two decisions – (i) The start time for each activity and (ii) the mode for each activity.  Given the NP-Hard nature of the problem, heuristics and metaheuristics are used to solve larger instances of this problem.  A heuristic for this type of problem involves a combination of two priority rules - one for each of the two decisions.  Heuristics generally tend to be greedy in nature.  In this study we propose two non-greedy heuristics for mode selection which perform better than greedy heuristics.  In addition, we study the effect of double justification and backward/forward scheduling for the MRCPS.  We also study the effect of serial vs. parallel scheduling.  We found that all these elements improved the solution quality.  Finally we propose an adaptive metaheuristic procedure based on neural networks which further improves the solution quality.  The effectiveness of these proposed approaches, compared to existing approaches in the literature, is demonstrated through empirical testing on two well-known sets of benchmark problems