Project Scheduling Problem Research Articles

The Use of Meta-Heuristic Methods to Solve Resource-Constrained Project Scheduling and Different Administrative Situations and Allowance to Cut Activities with Cut Costs

In this research, a modeling for problem of project scheduling is presented with cut allowance and multiple administrative methods for each activity considering costs of earliness and tardiness. Genetic algorithm was used to solve this problem, and finally in order to prove algorithm’s capability solving mentioned problem, the results were compared with absolute and exact results by LINGO software for small problems and evaluation indicators of algorithm for big ones, respectively. In the end, a proper algorithm with desired efficiency is presented to solve the above problem.

A multi-objective multi-agent optimization algorithm for the multi-skill resource-constrained project scheduling problem with transfer times

This paper addresses the Multi-Skill Resource-Constrained Project Scheduling Problem with Transfer Times (MSRCPSP-TT). A new model has been developed that incorporates the presence of transfer times within the multi-skill RCPSP. The proposed model aims to minimize project’s duration and cost, concurrently. The MSRCPSP-TT is an NP-hard problem; therefore, a Multi-Objective Multi-Agent Optimization Algorithm (MOMAOA) is proposed to acquire feasible schedules. In the proposed algorithm, each agent represents a feasible solution that works with other agents in a grouped environment. The agents evolve due to their social, autonomous, and self-learning behaviors. Moreover, the adjustment of environment helps the evolution of agents as well. Since the MSRCPSP-TT is a multi-objective optimization problem, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used in different procedures of the MOMAOA. Another novelty of this paper is the application of TOPSIS in different procedures of the MOMAOA. These procedures are utilized for: (1) detecting the leader agent in each group, (2) detecting the global best leader agent, and (3) the global social behavior of the MOMAOA. The performance of the MOMAOA has been analyzed by solving several benchmark problems. The results of the MOMAOA have been validated through comparisons with three other meta-heuristics. The parameters of algorithms are determined by the Response Surface Methodology (RSM). The Kruskal–Wallis test is implemented to statistically analyze the efficiency of methods. Computational results reveal that the MOMAOA can beat the other three methods according to several testing metrics. Furthermore, the impact of transfer times on project’s duration and cost has been assessed. The investigations indicate that resource transfer times have significant impact on both objectives of the proposed model.

Modified multi-objective evolutionary programming algorithm for solving project scheduling problems

Though the Genetic Algorithm (GA) has received considerable attention recently in solving multi-objective optimization problems, inefficiency regarding performance has been reported in applications related to project scheduling. The degradation in efficiency was magnificent in applications of highly epistatic objective functions, including scheduling problems wherein the parameters being optimized are highly correlated. Furthermore, the crossover, being the dominant operator in GA, added significantly to the observed inefficiency for causing violations in the dependency between activities. Unlike GA, the Evolutionary Programming (EP) algorithm employs only a mutation operator which makes it less vulnerable to the dependency violation issue. This study proposes a modified Multi-Objective Evolutionary Programming (MOEP) algorithm to model and solve scheduling problems of multi-mode activities, including time–cost trade-off and finance-based scheduling with resource levelling. The modification involves the implementation of a new mutation operator to accommodate the scheduling problems in hand. Furthermore, the modified MOEP algorithm is benchmarked against the two multi-objective algorithms of SPEA-II and NSGA-II which have been used extensively in the literature to solve project scheduling problems. The results indicated that the modified MOEP algorithm outperformed SPEA-II and NSGA-II in terms of the diversity and quality of the Pareto optimal set.

Optimal Hedging: Managing Time and Cost Uncertainty in the Stochastic Time-Cost-Quality Tradeoff Project Scheduling Problem

Optimal Hedging: Managing Time and Cost Uncertainty in the Stochastic Time-Cost-Quality Tradeoff Project Scheduling Problem

Airline ground operations: Schedule recovery optimization approach with constrained resources

Most airlines have established integrated hub and operations control centers for the monitoring and adjustment of tactical operations. However, decisions in such a control center are still elaborated manually on the basis of expert knowledge held by several agents representing the interests of different airline departments and local stakeholders. This article studies a concept which incorporates the situational awareness gained by airport-collaborative decision making into an airline-internal decision support system, such that it integrates all available schedule recovery options during aircraft ground operations. The developed mathematical optimization model is an adaptation of the Resource-Constrained Project Scheduling Problem (RCPSP) and incorporates key features from turnaround target time prediction, passenger connection management, tactical stand allocation and ground service vehicle routing into the airline hub control problem. The model is applied in a case study consisting of 20 turnarounds during a morning peak at Frankfurt airport. Schedule recovery performance (resilience) is analyzed for a set of key performance indicators within multiple scenario instances which contain different resource availability and aim at solving various arrival delay situations. Results highlight that a minimization of tactical cost concurrently reduces average departure delay for flight and passengers while recovery performance is substantially affected when some options are not included in the evaluation process. Thus, our concept provides airlines with an optimization approach for constrained airport resources so that total cost and delay resulting from schedule deviations are reduced, which may benefit strategic schedule planning and improve predictability of operations for local collaborators, such as airport, ground handlers and ATM performance.

Towards Finding Robust Execution Strategies for RCPSP/max with Durational Uncertainty

Resource Constrained Project Scheduling Problems with minimum and maximum time lags (RCPSP/max) have been studied extensively in the literature. However, the more realistic RCPSP/max problems — ones where durations of activities are not known with certainty – have received scant interest and hence are the main focus of the paper. Towards addressing the significant computational complexity involved in tackling RCPSP/max with durational uncertainty, we employ a local search mechanism to generate robust schedules. In this regard, we make two key contributions: (a) Introducing and studying the key properties of a new decision rule to specify start times of activities with respect to dynamic realizations of the duration uncertainty; and (b) Deriving the fitness function that is used to guide the local search towards robust schedules. Experimental results show that the performance of local search is improved with the new fitness evaluation over the best known existing approach.

A variable neighborhood search approach for the resource-constrained multi-project collaborative scheduling problem

Multi-mode and multi-skill project scheduling problems widely exist in the real-world industry. Many efforts have been devoted to the multi-mode project scheduling problem and the multi-skill project scheduling problem. However, the integrated multi-mode and multi-skill project scheduling problem was seldom considered. This paper studies the resource-constrained multi-project scheduling problem in the development of high-end equipment and develops an integrated multi-mode and multi-skill scheduling model with different employee abilities. Based on the characteristics of high-end equipment development, we propose several optimal properties and design an effective heuristic algorithm. Since the resource-constrained project scheduling problem is NP-hard, three neighborhoods for the problem are constructed and a Variable Neighborhood Search Algorithm (VNS) is developed to solve the problem in a reasonable time. Finally, computational experiments are carried out to validate the performance of the proposed algorithm.

Constraint Logic Programming for Real-World Test Laboratory Scheduling

The Test Laboratory Scheduling Problem (TLSP) and its subproblem TLSP-S are real-world industrial scheduling problems that are extensions of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, TLSP includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. For TLSP-S such a grouping is already part of the input. In this work, we show how TLSP-S can be solved by Answer-set Programming extended with ideas from other constraint solving paradigms. We propose a novel and efficient encoding and apply an answer-set solver for constraint logic programs called clingcon. Additionally, we utilize our encoding in a Very Large Neighborhood Search framework and compare our methods with the state of the art approaches. Our approach provides new upper bounds and optimality proofs for several existing benchmark instances in the literature.

Problem-specific multi-objective invasive weed optimization algorithm for reconnaissance mission scheduling problem

With the progress of technology, the multi-agent system is successfully applied in many applications. In this paper, we investigate the problem of multi-agent system reconnaissance mission scheduling, which is the core of the reconnaissance decision support system and can be modeled as an extension of Multi-Mode Multi-Skill Resource-Constrained Project Scheduling Problem. Three objectives are considered in this paper: (1) minimizing the reconnaissance mission’s makespan, (2) minimizing the total cost of allocating reconnaissance agents, and (3) maximizing the total quality of all reconnaissance tasks. An effective problem-specific multi-objective invasive weed optimization algorithm (PS-MOIWO) is proposed for solving the problem. Firstly, a new chromosome structure guaranteeing the feasibility of solutions and an initialization method are proposed. Secondly, we propose a self-adaptive penalty-based constraint handling technique to describe the fitness of each individual and adopt a novel non-dominated sorting method to rank the population. Thirdly, by using the problem-specific knowledge, a local search procedure is developed and incorporated into the PS-MOIWO framework to enhance the exploitation ability. Based on the Taguchi method, algorithm’s suitable parameter combinations are determined. Simulation results based on a set of newly generated reconnaissance instances and the comparisons with some existing algorithms demonstrate the proposed algorithm’s effectiveness.

Pattern mining‐based pruning strategies in stochastic local searches for scheduling problems

AbstractScheduling problems are a subclass of combinatorial problems consisting of a set of tasks/activities/jobs to be processed by a set of resources usually to minimize a time criterion. Some optimization methods used to solve these problems are hybridized with knowledge discovery techniques to extract information during the optimization process and enhance it. However, most of these hybrid techniques are custom‐designed and lack generalization. In this paper, a module for knowledge extraction in Stochastic Local Searches is designed, aiming to be problem independent and plugged into optimization methods that relies on multiple Stochastic Local Search replications. The objective is to prune parts of the search space for which the exploration is likely to lead to poor solutions. This is performed through the extraction of high‐quality patterns occurring in locally optimal solutions. Benchmarked on two well‐known scheduling problems, the Job‐shop Problem and the Resource Constrained Project Scheduling Problem, the results show both a speed up in the convergence and the reaching of better local optima solutions.

A novel non-dominated sorting genetic algorithm for solving the triple objective project scheduling problem

Multi-objective project scheduling has attracted wide attention for approximately two decades. However, most of the existing research has focused on the double-objective project scheduling problem, while literature on project scheduling problems with more than two objectives is rather scarce. In this paper, the typical multi-mode resource-constrained project scheduling problem is extended to a new triple-objective multi-mode project scheduling problem (TOMPSP) with the objectives of minimizing the project duration, minimizing the resource investment and maximizing the robustness of the schedule. To solve the presented triple-objective problem, we resort to the latest version of the multi-objective genetic algorithm, the non-dominated sorting genetic algorithm III (NSGA-III). In the decoding process of the NSGA-III, a modified SSGS (serial schedule generation scheme), in which resource constraints are relaxed, is suggested by considering the delays of activities. Although the NSGA-III shows excellent performance in numerous multi-objective optimization problems with more than two objectives, it has a potential disadvantage in that it occasionally cannot find the intercept during the adaptive normalization process, and thus, the population cannot be normalized as expected. Since a case without an intercept is impossible in the NSGA-II, we adopt the NSGA-II normalization process rather than that of NSGA-III. The standard instances in PSPLib are modified to serve as the instances of the TOMPSP, and a computational experiment is conducted to test the algorithms. The results show that the presented algorithm not only greatly simplifies the implementation of the NSGA-III but also significantly improves the execution efficiency and calculation quality.

A TYPE-2 FUZZY OPTIMIZATION MODEL FOR PROJECT PORTFOLIO SELECTION AND SCHEDULING INCORPORATING PROJECT INTERDEPENDENCY AND SPLITTING

This paper presents a new optimization model and a new interval type-2 fuzzy solution approach for project portfolio selection and scheduling (PPSS) problem, in which split of projects and re-execution are allowable. Afterward, the approach is realized as a multi-objective optimization that maximizes total benefits of projects concerning economic concepts by considering the interest rate and time value of money and minimizes the tardiness value and total number of interruptions of chosen projects. Besides, budget and resources limitation, newfound relations are proposed to consider dependency relationships via a synergy among projects to solve PPSS problem hiring interval type-2 fuzzy sets. For validation of the model, numerical instances are provided and solved by a new extended procedure based on fuzzy optimistic and pessimistic viewpoints regarding several situations. In the end, their results are studied. The results show that it is more beneficial when projects are allowed to be split.

Enhanced method to plan the operations of vertical supply systems of high-rise projects

Logistics planning and management are integral to the successful management of construction projects. Although on-site logistics are critical to efficient project delivery, they receive less attention in terms of research. This research introduces a new method for planning on-site logistics operations utilizing vertical supply systems (VSS) in high-rise projects. This method challenges the limitations of using critical path method and Resource Constrained Project Scheduling Problem in scheduling high-rise projects. The presented method treats lifting operations as activities with durations. The method presents a new classification of lifting activities based on their relation to other works, and it prioritizes the assignment of VSS to lifting activities based on the flexibility of VSS choice for each task. These two novel contributions allow planning construction works to match the capacity of available VSS, and it allows an efficient distribution of lifting tasks among available VSS. This method was applied to two towers in an ongoing project. The application to the first tower was during construction which allowed measuring tangible improvements on site and the other applied during the planning stage. The application of this method resulted in shorter floor cycles by 20% to 30%, less idle workers and more efficient cost control.

A local search framework for industrial test laboratory scheduling

In this paper we introduce a complex scheduling problem that arises in a real-world industrial test laboratory, where a large number of activities has to be performed using qualified personnel and specialized equipment, subject to time windows and several other constraints. The problem is an extension of the well-known Resource-Constrained Project Scheduling Problem and features multiple heterogeneous resources with very general availability restrictions, as well as a grouping phase, where the jobs have to be assembled from smaller units. We describe an instance generator for this problem and publicly available instance sets, both randomly generated and real-world data. Finally, we present and evaluate different metaheuristic approaches to solve the scheduling subproblem, where the assembled jobs are already provided. Our results show that Simulated Annealing can be used to achieve very good results, in particular for large instances, where it is able to consistently find better solutions than a state-of-the-art constraint programming solver within reasonable time.

Dominance-based linear formulation for the Anchor-Robust Project Scheduling Problem

In project scheduling under processing times uncertainty, the Anchor-Robust Project Scheduling Problem is to find a baseline schedule of bounded makespan and a max-weight subset of jobs whose starting times are guaranteed. The problem was proven NP-hard even for budgeted uncertainty. In the present work we design mixed-integer programming (MIP) formulations that are valid for a variety of uncertainty sets encompassing budgeted uncertainty. A new dominance among solutions is proposed, resulting into an MIP formulation. We further study the combinatorial structure of the problem. Non-trivial polynomial cases under budgeted uncertainty are exhibited, where the dominance-based formulation yields a polyhedral characterization of integer solutions. In more general cases, the dominance-based formulation is shown to be tighter than all previously known formulations. In numerical experiments we investigate how the formulation performs on instances around the polynomial cases, for both budgeted uncertainty sets and more elaborate uncertainty sets involving several budgets.

Negotiation mechanisms for the multi-agent multi-mode resource investment problem

Carrying out complex projects often involves several collaborating parties (agents) with conflicting goals. We consider project scheduling problems, where each activity belongs to one of several agents, with a given deadline on the project completion while one aims at a schedule with an efficient use of resources. As there are precedence relations among activities and the activity execution requires varying amounts of resources, the need for coordination among the agents arises. For the execution of activities, an agent can choose from several modes that determine the processing time and resource usage. Each agent aims to minimise his/her individual resource costs associated with the project. Hence, the problem at hand is the multi-agent generalisation of the multi-mode resource investment problem. Here, we consider local as well as global resources. The latter ones are shared among the agents, thus the problem involves the need for a suitable allocation of respective resource costs. As agents are unwilling to share critical and sensitive information (or are not expected to always provide truthful information), the employed solution procedure should not rely on such information under consideration of the agents’ incentives. We propose and extend such decentralised negotiation mechanisms which facilitate the allocation of global resources. We analyse their potential to overcome information asymmetry and yield high quality solutions utilising a distributed scheduling procedure and a representation which aids in learning effective mode decisions.

Emergency Repair Scheduling Model for Road Network Integrating Rescheduling Feature

When a natural disaster occurs, road maintenance departments always face the challenge of how to assign repair resources properly to recover damaged road segments as soon as possible. From the literature review, most studies treat such problems as a vehicle routing problem (VRP). In those studies, repair resources are always dispatched as complete crews, and cannot be divided into smaller scales. Furthermore, each disaster point is only allowed one group of resources to recover it, without considering the possibility of accelerating the production rate subjected to specific objectives. Such limitation restricts required resources in an inflexible manner. Therefore, this study defines all repair works as an emergency repair project and adopts the framework of the Resource-Constrained Project Scheduling Problem (RCPSP), which can resolve such complicated resource assignment issue. A novel emergency repair scheduling model for the road network is proposed based on Constraint Programming (CP) as the searching algorithm to facilitate model formulation. According to the RCPSP concepts, disaster points are set as repair activities and resource travel routes between disaster points are set as transit activities. All the repair activities are linked by transit activities and the required resources are assigned accordingly. In order to consider the second-wave hazard events of where new disaster points may occur, and new resources may be added into emergency repair projects, a rescheduling feature is integrated into the proposed model. Through two case studies, research findings show that this model can be easily modulated to adapt to different situations satisfying practical disaster management goals and solving emergency repair scheduling problems for road networks efficiently.

Underground mine scheduling under uncertainty

Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value; constraints enforce geotechnical precedence between activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic schedules address these start dates at a coarse level, whereas tactical schedules must account for the day-to-day variability of underground mine operations, such as unanticipated equipment breakdowns and ground conditions, both of which might slow production. At the time of this writing, the underground mine scheduling literature is dominated by a deterministic treatment of the problem, usually modeled as a Resource Constrained Project Scheduling Problem (RCPSP), which precludes mine operators from reacting to unforeseen circumstances. Therefore, we propose a stochastic integer programming framework that: (i) characterizes uncertainty in duration and economic value for each underground mining activity; (ii) formulates a new stochastic variant of the RCPSP; (iii) suggests an optimization-based heuristic; and, (iv) produces implementable, tactical schedules in a practical amount of time and provides corresponding managerial insights.

Financial Optimization of the Resource-Constrained Project Scheduling Problem with Milestones Payments

This article presents the resource-constrained project scheduling problem with the discounted cash flow maximization criterion from the perspective of a contractor. Cash flows are considered as the contractor’s expenses related to the execution of activities and client’s payments (revenue to the contractor) after the completion of contractual stages. To solve the problem, dedicated techniques to generate solutions and a simulated annealing algorithm are proposed. Finally, the proposed procedures are examined using the test library, Project Scheduling Library (PSPLIB). An experimental analysis identified the efficient moves and techniques for creating solutions, that is backward scheduling with optimization of completion times of project stages and triple justification.

Integrating Schedule Risk Analysis with Multi-Skilled Resource Scheduling to Improve Resource-Constrained Project Scheduling Problems

Construction projects are planned in a complex and dynamic environment characterized by high risks and uncertainties amidst resource constraints. Assessing construction schedule risk facilitates informed decision-making, especially in a resource-constrained situation, and allows proactive actions to be taken so that project objectives are not jeopardized. This study presents a stochastic multiskilled resource scheduling (SMSRS) model for resource-constrained project scheduling problems (RCSPSP) considering the impact of risk and uncertainty on activity durations. The SMSRS model was developed by integrating a schedule risk analysis (SRA) model (developed in MS Excel) with an existing multiskilled resource scheduling (MSRS) algorithm for the development of a feasible and realistic schedule. The computational experiment carried out on three case projects using the proposed SMSRS model revealed an average percentage deviation of 10.50%, indicating the inherent risk and uncertainty in activity durations of the project schedule. The core contribution of the proposed SMSRS model is that it: (1) presents project practitioners with a simple tool for assessing the risks and uncertainty associated with resource-constrained project schedules so that necessary response actions can be taken to ensure project success; (2) provides the small-scale construction businesses with an affordable tool for evaluating schedule risk and developing a feasible and realistic project schedule.