Resource conflicts

Overview

In this article, the project scheduling problem in project management will be introduced and followed with a discussion on the Resource-constrained project scheduling problem (RCPSP) will be discussed. Key concepts of the RCPSP and practical applications will be addressed, without getting into the technical details of the mathematical models and optimization algorithms used to solve the RCPSP. Instead, the focus will be placed on explaining the problem formulation, the assumptions and constraints, and the practical implications of the scheduling decisions.

Relevance of Project Scheduling / Resource Conflicts

Broader context of the problem for example:

• Importance of efficient project scheduling
• The challenges of resource allocation
• Performance Criteria (Potential reference: Herroelen et al., 1996)
• The trade-offs between project completion time, resource utilization, and cost

Potential Reference (Chapter 1): (Demeulemeester & Herroelen, 2006)

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The allocation of limited resources over a period of time is the primary focus of scheduling and sequencing in project management. Scheduling pertains to the determination of when specific activities should take place, while sequencing deals with the arrangement of these activities in a particular order. Research on how to optimally allocate scarce resources over time has been a significant area of interest since the inception of operations research in the mid-1950s (Herroelen et al., 1996).

The effective and accurate management of extensive projects is purported to result in successful project implementation, increased revenues, and reduced costs and lost profits. Scheduling is therefore, a crucial responsibility of project management, but it has become increasingly challenging due to resource limitations and the need to account for precedence relationships. As a result, project scheduling is a widely recognized and fundamental issue that researchers have extensively studied from different angles. The development of standard solutions for this issue has been a major focus in the field of project management.

Resource-constrained project scheduling problem (RCPSP)

• Discuss various project scheduling techniques, such as Gantt charts, Critical Path Method (CPM), and Program Evaluation and Review Technique (PERT)
• Explain how each technique works and its advantages and disadvantages

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The problem of project scheduling involves determining the time required to complete a project's activities to achieve a specific objective. Early research on project scheduling focused on describing activities solely in terms of their duration, leading to the development of methods like the critical path method (CPM) and program evaluation and review technique (PERT), which account for precedence relationships between activities. However, treating precedence relationships as independent is an unrealistic assumption, prompting the introduction of constraints to better model their impact. One notable constraint is resource availability, which is a pervasive issue in project scheduling and is commonly referred to as the Resource-Constrained Project Scheduling Problem (RCPSP).

Basic form of the RCPSP / Basic concept of RCPSP / Standard RCPSP

This problem pertains to a project consisting of J activities labeled j=1,…,J. The duration of each activity j is represented by dj, which signifies that once an activity begins, it must be completed without interruption. Generally, there are technological requirements that establish precedence relationships between the activities, which are denoted by sets of immediate predecessors Pj. This means that an activity j cannot commence until all its predecessors (i∈Pj) have been completed.

Furthermore, these precedence relationships can be depicted in the form of a network. To perform each activity, a certain quantity of resources is required, with the resources being considered renewable due to full capacity being available in each period. A total of K types of renewable resources are available, labelled k=1,…,K, with Rk being the constant amount of resource available at the start of each period for resource k. In each period where activity j is processed, rjk units of resource k are required. Two additional activities, j=0 and j=J+1, represent the beginning and end of the project, respectively, and are both considered dummy activities with a processing time and resource consumption of zero. All parameters in the problem are assumed to be deterministic, definite, and non-negative integers. The objective of the problem is to determine the start time (Sj) for activities j=0,1,…,J+1 in such a way that the project's completion time is minimized.

Given the vast differences encountered in practice, researchers have modified the original form of the RCPSP over time. Moreover, it has been demonstrated that the RCPSP problem is classified as a strongly NP-hard problem. As a consequence, different solutions are employed based on the variations in the fundamental assumptions (Habibi et al., 2018).

Types of RCPSP

• See if it is relevant to discuss the different types of RCPSP i.e., single-mode, multi-mode, time-dependent, resource-dependent, precedence-constrained, time-cost trade-off, and multi-project RCPSP

RCPSP Modelling and Solution Techniques

• Explain how to model RCPSP and the different solution techniques available, such as mathematical programming, heuristic algorithms, and metaheuristics
• Discuss the advantages and disadvantages of each technique

Real-world Application

• Provide example of how RCPSP has been applied in real-world scenarios, such as construction projects, manufacturing processes, and software development
• Explain how RCPSP has helped improve project efficiency and reduce costs

Challenges and Limitations of RCPSP

• Discuss some of the challenges and limitations of RCPSP, such as the need for accurate data and the difficulty of solving large-scale problems
• Explain how these challenges can be overcome, such as through data analytics and optimization algorithms

References

Herroelen, W., Demeulemeester, E., & De Reyck, B. (1996). Resource-constrained project scheduling: A survey of recent developments. Katholieke Universiteit Leuven. https://www.researchgate.net/publication/46430164_Resource-constrained_project_scheduling

Habibi, F., Barzinpour, F., & Sadjadi, S. J. (2018). Resource-constrained project scheduling problem: review of past and recent developments. Journal of Project Management, 55–88. https://doi.org/10.5267/j.jpm.2018.1.005

Demeulemeester, E. L., & Herroelen, W. S. (2006). Project Scheduling: A Research Handbook. Springer Science & Business Media.