An Introduction to the Resource Constrained Project Scheduling Problem Solving Techniques

Two new continuous-time MILP (Mixed Integer Linear Programming) models are developed for resource constrained project scheduling problems in which activities can be conducted in different (multi) modes. There are efficient and flexible MILP models for this problem in which time is represented by a number of discrete time intervals. However, they require to use large numbers of binary variables as the number of activities increases and time horizon stretches. Hence efforts have been made to formulate MILP models based on continuous-time representation and therefore to speed up the solution process. We propose two novel MILP models based on the event and resource flow concepts. The models are verified by solving benchmark problems in the literature.

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

This paper is concerned with an overview of the Resource-Constrained Project Scheduling Problem (RCPSP) and the conventional meta-heuristic solution techniques that have attracted the attention of many researchers in the field. Therefore, researchers have developed algorithms and methods to solve the problem. This paper addresses the single-mode RCPSP where the objective is to optimize and minimize the project duration while the quantities of resources are constrained during the project execution. In this problem, resource constraints and precedence relationships between activities are known to be the most important constraints for project scheduling. In this context, the standard RCPSP is presented. Then, the classifications of the collected papers according to the year of publication and the different meta-heuristic approaches applied are presented. Five weighted articles and their meta-heuristic techniques developed for RCPSP are described in detail and their results are summarized in the corresponding tables. In addition, researchers have developed various conventional meta-heuristic algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, bee colony optimization, simulated annealing, evolutionary algorithms, and so on. It is stated that genetic algorithms are more popular among researchers than other meta-heuristics. For this reason, the various conventional meta-heuristics and their corresponding articles are also presented to give an overview of the conventional meta-heuristic optimizing techniques. Finally, the challenges of the conventional meta-heuristics are explored, which may be helpful for future studies to apply new suitable techniques to solve the Resource-Constrained Project Scheduling Problem (RCPSP).

Solving resource constrained project scheduling problem (RCPSP) has important role in the context of project scheduling.Considering a single objective RCPSP, the goal is to find a schedule that minimizes the makespan.This is NP-hard problem (Blazewicz et al., 1983) and one may use meta-heuristics to obtain a global optimum solution or at least a near-optimal one.Recently, various meta-heuristics such as ACO, PSO, GA, SA etc have been applied on RCPSP.Bee algorithms are among most recently introduced meta-heuristics.This study aims at adapting artificial bee colony as an alternative and efficient optimization strategy for solving RCPSP and investigating its performance on the RCPSP.To evaluate the artificial bee colony, its performance is investigated against other meta-heuristics for solving case studies in the PSPLIB library.Simulation results show that the artificial bee colony presents an efficient way for solving resource constrained project scheduling problem.

Project scheduling consists of defining and assigning resources to a set of time-scattered activities. Several economic, business and engineering disciplines are considered for practical application: project management, operations research, software development, systems engineering. In Resource-Constrained Project Scheduling (RCPS), task allocation is determined by resource distribution based on a set of constraints. Poor constraint evaluation and its impact on the project schedule, may lead to project baseline disruptions, therefore to cost failover and company loss. The aim of the current research is to provide a solution for the standard Resource Constrained Project Scheduling Problem (RCPSP) through a hybrid heuristic algorithm based on priority rule scheduling (priority rules, schedule generation schemes). We present a conceptual framework for a software engineering context, where activities of concurrent projects are allocated based on employees' skills to optimize a regular objective of estimated activity duration.

In this paper, a renowned metaheuristic algorithm named chemical reaction optimization (CRO) is applied to solve the resource constrained project scheduling problem (RCPSP). This work employed chemical reaction optimization to schedule project tasks to minimize makespan concerning resource and precedence constraints. Chemical reaction optimization is a population-based metaheuristic algorithm. CRO is applied to RCPSP by redesigning its basic operators and taking solutions from the search space using priority-based selection to achieve a better result. The proposed algorithm based on CRO is then tested on large benchmark instances and compared with other metaheuristic algorithms. The experimental results have shown that our proposed method provides better results than other states of art algorithms in terms of both the qualities of result and execution time.

MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing

Passive Optical Network (PON) deployments have recently been aiming to combine the capacity of metro and access networks in the last mile of the Internet service provisioning. Deployment of PONs by running fiber to the premises introduces the advantage of huge capacity but at the same time, it calls for a robust design in order to avoid long service outage durations in case of network failures where survivable network design is mostly limited to the deployment budget. In this paper, we propose three mixed integer linear programming (MILP) models for various survivability policies to deploy reliable long-reach PONs under the budget limitations. Each MILP model aims to place the ONUs in optimal locations so that the covered area is maximized while availability requirements of the users are satisfied within the deployment budget. We solve the MILP models under the uniform and heterogeneous availability requirement scenarios and show that service availability and coverage introduce a trade-off so as the coverage and deployment cost do. Two out of the three survivability policies can guarantee 99.99% service availability while the third one is able to guarantee 99.999% by running the proposed MILP models. However, the first two schemes are able to cover larger area when compared to the third scheme which is the most reliable protection policy.

Purpose: The main purpose of the paper is to evaluate the impact of diverse personnel policies around personnel promotion in the design of the strategic staff plan for a public university. The strategic staff planning consists in the determination of the size and composition of the workforce for an organization.Design/methodology/approach: The staff planning is solved using a Mixed Integer Linear Programming (MILP) model. The MILP model represents the organizational structure of the university, the personnel categories and capacity decisions, the demand requirements, the required service level and budget restrictions. All these aspects are translated into a set of data, as well as the parameters and constraints building up the mathematical model for optimization. The required data for the model is adopted from a Spanish public university.Findings: The development of appropriate policies for personnel promotion can effectively reduce the number of dismissals while proposing a transition towards different preferable workforce structures in the university.Research limitations/implications: The long term staff plan for the university is solved by the MILP model considering a time horizon of 8 years. For this time horizon, the required input data is derived from current data of the university. Different scenarios are proposed considering different temporal trends for input data, such as in demand and admissible promotional ratios for workers.Originality/value: The literature review reports a lack of formalized procedures for staff planning in universities taking into account, at the same time, the regulations on hiring, dismissals, promotions and the workforce heterogeneity, all considered to optimize workforce size and composition addressing not only an economic criteria, but also the required workforce expertise and the quality in the service offered. This paper adopts a formalized procedure developed by the authors in previous works, and exploits it to assess the impact of various personnel policies in the staff planning for a particular university case, and this is the principal contribution of the paper.

Effective project management implies the use of advanced planning and scheduling methods that allow to determine feasible sequences of activities and to complete a project on time and on budget. Traditional scheduling tools like fundamental Critical Path Method (CPM) and various methods for Resource Constrained Project Scheduling Problem (RCPSP) and Time Constrained Project Scheduling Problem (TCPSP) have many shortcomings for construction projects where spatial factor plays a critically important role. Previous attempts to interpret space as a specific resource were successful for particular problems of line-of-balance scheduling, space scheduling, dynamic layout planning, horizontal and vertical logic scheduling, workspace congestion mitigating, scheduling multiple projects with movable resources, spatial scheduling of repeated and grouped activities and motion planning. However, none of these methods considers the spatio-temporal requirements in a holistic framework of generic RCPSP problem and provides feasible results accounting for workspace and workflow factors. In this paper we start with the classical RCPSP statement and then present mathematically strong formalisation of the extended generalised problem, taking into account workspace congestion and workflow disturbance constraints specified in practically meaningful and computationally constructive ways. For the generalised RCPSP problem an effective scheduling method is proposed. The method tends to minimise the project makespan while satisfying timing constraints and precedence relations, not exceeding resource utilisation limits, avoiding workspace congestions and keeping workflows continuous. The method reuses so-called serial scheduling scheme and provides for additional computational routines and heuristic priority rules to generate feasible schedules satisfying all the imposed requirements. Advantages of the method and prospects for its application to industrial needs are outlined in the paper too.

Projects represent the principal means of materialization of products. The inherent complexity of product projects is treated through the techniques and approaches project management. Throughout products life cycle the techniques and approaches project management are mainly involved in the planning, programming and control of project activities conducted in context of resource constrained under uncertainties. In addition of scenarios the complexity of the projects, there are some classes of products, typical of industries of the defense, aerospace, telecommunication, software, and biomedicine, which are problematic for current methods of resource constrained project planning and scheduling under uncertainty. The existing methods fail because they suffer from one or more of the following limitations: focused mainly on the basic RCPSP (Resource Constrained Project Scheduling Problem) model; dealing with only one source of uncertainty, mostly in duration of activities; and do not model uncertainties.

This paper introduces a new practical scheduling problem called the resource-constrained project scheduling problem under multiple time constraints, which involves a duration constraint of activity, temporal constraint, and resource calendar constraint. The duration constraint of the activity exists widely in real-life projects, and it is first proposed as a resource-constrained project scheduling problem in this paper. We prove the defects of the traditional temporal constraint and improve it. The new problem combines three types of time constraints for the first time, which makes it closer to the actual scheduling problem. We developed a constraint programming optimization model for the new problem and used the IBM ILOG CPLEX-CP version 12.9.0 optimizer to solve it. Computational experiments are carried out to show that the CP optimizer is fast and provides a near-optimum solution to the new problem for projects with hundreds of activities within minutes compared to other metaheuristic methods. The results reported in this paper can be used as a benchmark for other researchers to compare and improve. The new problem contributes to developing a practical decision support system for resolving real-life constraints in projects.

A GRASP × ILS for the vehicle routing problem with time windows, synchronization and precedence constraints

This paper provides a fast near‐optimum solution to the Multi‐Mode Resource Constrained Project Scheduling Problem (MRCPSP), for projects with activities that have known deterministic renewable and non‐renewable resource requirements. Multi‐modes allows any activity to execute one of many alternative combinations of resource usages and durations, while each activity needs to pick the most feasible one. This type of setting is more prevalent for real‐life project schedules, which necessitates systematic methodologies and advanced solution approaches in harmony with real‐world implementations. This study proposes a Modified Variable Neighbourhood Search Heuristic (MVNSH) algorithm as an advanced optimization technique for scheduling projects. To validate our approach, exhaustive computational tests were carried out by using relevant benchmark instances. The MVNSH algorithm has been shown to be faster and more accurate than many existing heuristic methods. This research also contributes to developing a practical decision support system for resolving real‐life constraints in multi‐mode resource‐constrained projects.

A hybrid scatter search approach for resource-constrained project scheduling problem in PERT-type networks