Stochastic Activity Durations Research Articles

Surrogate-assisted cooperative learning genetic programming for the resource-constrained project scheduling problem with stochastic activity durations and transfer times

For the project scheduling problem with transfer times under an uncertain environment, not only the activity durations are stochastic, but transfer times are often also stochastic. Therefore, we propose a resource-constrained project scheduling problem with stochastic activity durations and transfer times (RCPSP-SDT), which requires complex activity sequencing and resource transfer decisions with an activity priority rule (APR) and a resource transfer priority rule (RTPR) under unpredicted dynamic factors. However, manually designed combination rules of APRs and RTPRs are time-consuming and only for specific scenarios. Therefore, we develop a hyper-heuristic approach based on genetic programming (GP), which has been successfully applied to evolve activity priority rules for project scheduling problems. A new representation of GP individuals was designed to evolve the APR and the RTPR simultaneously. In order to improve the efficiency and solution quality of the approach, we propose surrogate-assisted cooperative learning genetic programming (SCLGP) based on GP. Based on the benchmark data set, computer experiments were conducted under nine variance levels of stochastic distributions. The results show that the proposed algorithm SCLGP performs significantly better than the classical priority rule (PR)-based heuristics. Furthermore, the effectiveness and efficiency of SCLGP were verified by comparing it to four other GP-based algorithms. Finally, the impact of the parameters on the algorithm was investigated, proving that these parameters affect the algorithm’s performance.

Co-evolution genetic programming-based hyper-heuristics for the stochastic project scheduling problem with resource transfer and idle costs

In this paper, we study the stochastic resource-constrained project scheduling problem with transfer and idle costs (SRCPSP-TIC) under uncertain environments, where the resource transfer and idle take time and costs. Priority rule (PR) based heuristics are the most commonly used approaches for project scheduling under uncertain environments due to their simplicity and efficiency. For PR-based heuristics of the SRCPSP-TIC, activity priority rules (APRs) and transfer priority rules (TPRs) are necessary to decide the activity sequence and resource transfer. Traditionally, APRs and TPRs need to be manually designed, which is time-consuming and difficult to adapt to different scheduling scenarios. Therefore, based on two individual representation methods, we propose two co-evolution genetic programming (CGP) based hyper-heuristics to evolve APRs and TPRs automatically. Furthermore, a fitness function surrogate-assisted method and a transfer learning mechanism are designed to improve the efficiency and solution quality of the CGP. Based on the instances with different stochastic activity duration distributions, we test the performance of different CGP-based hyper-heuristics and compare the evolved PRs with the classical PRs to demonstrate the effectiveness of evolved PRs. Experimental results show that the proposed algorithms can automatically evolve efficient PRs for the SRCPSP-TIC.

Stochastic resource leveling in projects with flexible structures

In project management, efficient utilization of resources plays a key role in project success, and resource leveling is an effective technique to optimize resource usage. During project execution, there are often uncertainties that complicate resource leveling. Furthermore, existing research on resource leveling typically assumes a fixed project structure. However, this is not always the case in practice, because there may be a variety of optional technical solutions for some activities, leading to a flexible project structure. Therefore, considering both stochastic activity durations and flexible project structures, we propose and study the stochastic resource leveling problem with flexible project structures (SRLP-PS). The solution of the SRLP-PS is in the form of a scheduling policy. We design two algorithms for solving the NP-hard SRLP-PS: (a) an exact algorithm based on stochastic programming, in which we formulate a scenario-based non-linear stochastic programming model and linearize it into an equivalent deterministic mixed-integer linear programming model that can be directly solved by CPLEX; and (b) an improved differential evolution algorithm, which is equipped with several problem-specific components, such as two mutation operators balancing exploration and exploitation, initialization, and local improvement search. Extensive computational experiments on a large number of benchmark instances are performed to validate our algorithms, which are also compared with state-of-the-art meta-heuristics. The computational results reveal the effectiveness and competitiveness of our algorithms. We also analyze the value of stochastic information based on the exact algorithm and the meta-heuristics, respectively.

Simulation-based hybrid genetic algorithms for the stochastic multi-mode resource-constrained project scheduling problem with minimized financial risk

Projects face uncertainties during implementation, and these uncertainties often lead to risk factors that disrupt successful project execution and cause a loss of profit. The stochastic project scheduling technique has been an effective avenue for reducing the risks in project management. Nevertheless, previous studies often neglected resource limits for minimizing the financial risks of projects in stochastic project scheduling problems. This study aims to optimize the conditional net present value at risk (CNPVaR), which measures a project’s expected loss of net present value (NPV) in a stochastic multi-mode resource-constrained project scheduling problem (SMRCPSP). Accordingly, considering the stochastic activity duration and cash flow, we construct a scenario-based optimization model for the SMRCPSP, where the solution (strategy) of the SMRCPSP is represented by a policy that includes an activity list and execution mode list; a scheduling policy is then employed to map the start times of activities at each decision time based on the solution. Three simulation-based hybrid genetic algorithms embedded with different iteration alternatives according to activity-based (AB) or resource-based (RB) scheduling policies are used. Furthermore, computational experiments are conducted to evaluate the proposed procedures through 480 instances. With respect to the CNPVaR, expected NPV, and algorithm stability metrics, the results of the experiments demonstrate that the genetic algorithm (GA) with local search based on the RB scheduling policy performed best compared with two other hybrids of the GA, the existing vibration damping optimization (VDO) method and a pure GA for large-sized projects. However, the VDO outperforms the other approaches according to the AB scheduling policy for small-scale projects. Additionally, a case study is conducted; the findings demonstrate that the risk attitude (confidence level) of project managers and the discount factor have impacts on the CNPVaR and expected NPV, but the CNPVaR is insensitive to the number of simulations.

Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies

We study a project with stochastic activity durations and cash flows; we model the uncertainty using discrete scenarios. The project entails precedence-related activities, each of which incurs a cash flow that may be positive (inflow) or negative (outflow). The problem is to find a scheduling policy that maximizes the expected net present value of the project. A scheduling policy decides the starting time of each activity under every possible realization of the unknown parameters. Ideally, one wants to expedite the inflows (e.g., incoming payments), while delaying the outflows (e.g., costs) as much as possible, without violating the project deadline. In this article, we devise an exact and a heuristic method to define policies within two new classes of scheduling policies. The first policy class generalizes all existing static policies in the literature and further illustrates the importance of intentional activity delays from both a theoretical as well as an empirical point of view. Whereas the literature on project scheduling has mainly focused on static policies, we also propose a second class of dynamic policies. We show that dynamic policies outperform static policies by means of extensive computational experiments.

BUFFERING POLICIES FOR PREFABRICATED CONSTRUCTION SUPPLY CHAIN SUBJECT TO MATERIAL LEAD TIME AND ACTIVITY DURATION UNCERTAINTIES

Supply chain management plays a pivotal role in the smooth execution of prefabricated construction. One key aspect involves strategically placing and sizing buffers to handle uncertainties (e.g., stochastic material lead-times and activity durations) within the prefabricated construction supply chain (PCSC). This study examines three buffering policies based on varying combinations of time and inventory buffers to mitigate stochastic material delays and activity prolongs in PSCS, namely, pure inventory buffering policy, pure time buffering policy, and mixed inventory-time buffering policy. To enable this analysis, we characterize how stochastic material delays originating from off-site supply chains impact project schedules, and then develop mathematical procedures for sizing inventory and/or time buffers under the three buffering policies. Case application and numerical analysis are conducted to investigate the performance of these buffering policies and the impact of the project characteristics on them (e.g., due date and arrival rate). Finally, insights are extracted to assist managers in choosing appropriate policies for projects with different characteristics. In general, combining inventory and time buffers results in better performance, particularly under tight project deadlines and high arrival rates. The pure time buffering policy can also be a viable option in specific situations, allowing managers to have more choices.

A bi-objective optimization for finance-based and resource-constrained robust project scheduling

Numerous finance-based projects encounter disturbances from a variety of uncertain factors during their execution, under which both the original baseline schedule and financing alternative become infeasible. However, many previous studies on the finance-based project scheduling problem (FBSP) neglected a potential feature of stochastic activity durations. In this paper, we address the issue of generating a robust project schedule that not only satisfies financing credit and renewable resource limits, but also tackles disruptions due to activity uncertainty. A bi-objective model for finance-based and resource-constrained robust project scheduling problem (FBRCRPSP) is constructed, where the trade-off between profit and robustness is considered. Based on the transformed integer programming model, an exact procedure of ε- constraints is proposed to obtain Pareto-optimal solutions for small-sized instances. For large-scale projects, a non-dominated sorting genetic algorithm with local search (NSGA-II-LS) that deeply explores the neighboring solution space is developed, in which a generic procedure with two new recursion policies is proposed to determine the robustness of schedules. Benchmarking is conducted to evaluate the efficiency of the algorithms via some performance criteria. The results show that all developed approaches have good performance in small-sized instances, and the NSGA-II-LS outperforms the non-dominated sorting genetic algorithm without local search (NSGA-II) in terms of the spread, convergence, and diversity of Pareto-optimal solutions significantly. In addition, some managerial insights are summarized to enlighten project managers.

Tabu search for dedicated resource-constrained multiproject scheduling to minimise the maximal cash flow gap under uncertainty

Maintaining a positive balance between cash outflow and inflow is very important for contractors to smoothly implement projects. Based on this fact, with the objective of minimising the maximal cash flow gap, this paper investigates a dedicated resource-constrained multiproject scheduling problem with stochastic activity duration where renewable resources are dedicated to individual projects in advance, and the schedule of each project is then arranged independently. First, we construct an optimisation model for the problem and propose properties for it. Second, for the NP-hardness of the problem, we design a tabu search algorithm consisting of two modules and develop the measures according to the proposed properties to improve the searching efficiency of the algorithm. Finally, we conduct a computational experiment on a randomly generated dataset to evaluate the performance of the developed algorithm and analyse the effects of key parameters on the objective function value. The conclusions are as follows. The developed tabu search algorithm with the improvement measures is the most promising algorithm for solving the studied problem, and the contribution of the improvement measures may vary as the project parameters change. The maximal cash flow gap increases along with the resource factor, required robustness of project schedule, and discount rate per period of cash flows, and decreases with the increase in the project deadline, resource strength, number of milestone activities, advance payment proportion, or progress payment proportion. The interactions among the resource strength, resource factor, and project deadline may also generate an effect on the maximal cash flow gap.

A two-stage genetic programming framework for Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project Insertions

This study proposes a novel hyper-heuristic based two-stage genetic programming framework (HH-TGP) to solve the Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project Insertions (SRCMPSP-NPI). It divides the evolution of genetic programming into generation and selection stages, and then establishes a multi-state combination scheduling mode with multiple priority rules (PRs) for the first time to realize resource constrained project scheduling under both stochastic activity duration and new project insertion. In the generation stage, based on a modified attribute set for multi-project scheduling, NSGA-II is hybridized to evolve a non-dominated PR set for forming a selectable PR set. While in the selection stage, the whole decision-making process is divided into multiple states based on the completion activity duration, and a weighted normalized evolution process with two crossovers, two mutations and four local search operators to match the optimal PR for each state from the PR set. Under the existing benchmark, HH-TGP is compared with the existing methods to verify its effectiveness.

Multi-objective stochastic project scheduling with alternative execution methods: An improved quantum-behaved particle swarm optimization approach

This paper addresses the multi-objective resource-constrained project scheduling problems with stochastic activity durations and alternative execution methods. Three objectives are considered: minimizing expected makespan, expected cost and robustness. Chance constrained programming is applied for formulating this stochastic problem. A hybrid approach that integrates sample average approximation (SAA) and an improved multi-objective chaotic quantum-behaved particle swarm optimization (MOCQPSO) algorithm is proposed. To improve the diversity of solutions and enhance the global search ability, a two-stage learning strategy that balances the exploration and the exploitation is proposed for MOCQPSO. In addition, chaotic operators including chaotic initialization, crossover and mutation are also introduced. Six benchmark functions and an instance generator based on the RCPSP dataset of PSPLIB are designed to validate the performance of the proposed algorithm. The experimental results demonstrate that our proposed method outperforms the original algorithms in solution diversity and quality.

A filtering genetic programming framework for stochastic resource constrained multi-project scheduling problem under new project insertions

Multi-project management and uncertain environment are very common factors, and they bring greater challenges to scheduling due to the increase of problem complexity and response efficiency requirements. In this paper, a novel hyper-heuristic based filtering genetic programming (HH-FGP) framework is proposed for evolving priority rules (PRs) to deal with a multi-project scheduling problem considering stochastic activity duration and new project insertion together, namely the Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project Insertions (SRCMPSP-NPI), within heuristic computation time. HH-FGP is designed to divide traditional evolution into sampling and filtering evolution for simultaneously filtering two kinds of parameters constituting PRs, namely depth range and attribute, to obtain more effective PRs. Based on this, the existing genetic search and local search are improved to meet the depth constraints, and a multi-objective evaluation mechanism is designed to achieve effective filtering. Under the existing benchmark, HH-FGP is compared and analysed with the existing methods to verify its effectiveness.

Scheduling project with stochastic durations and time-varying resource requests: A metaheuristic approach

This paper studies a resource constrained project scheduling problem (RCPSP) under dynamic environments. Along with stochastic activity-durations, resource requests and resource availabilities are also prone to vary with time (i.e., that is, dynamic). To account for stochastic activity durations and the resource dynamic, a chance constrained based mathematical model is proposed. To solve the developed model, an efficient genetic algorithm (GA) based memetic algorithm (MA) is proposed. The proposed algorithm has shown excellent performance for solving 2880 30-activity and 3600 120-activity instances for RCPSP with predefined but time-varying resource requests and availabilities (i.e., RCPSP/t setting). The proposed algorithm has also demonstrated an excellent performance for the extended RCPSP/t setting with stochastic activity durations (i.e., RCPSP/td). Due to the unavailability of any real benchmark instances for this extended RCPSP, this work proposes a pragmatic approach to generate simulated benchmark instances. Numerous time-dependent benchmark instances from the project scheduling library (PSPLIB) are solved to validate the proposed MA. Rigorous experimental analysis with a standard set of 2448 newly generated problem instances for 30, 60, 90, and 120 activities indicates that the proposed meta-heuristic can solve large projects with a reasonable computational burden.

The combined impact of stochastic and correlated activity durations and design uncertainty on project plans

Most model based studies on project uncertainty investigate a single source of uncertainty, with a dominant focus on stochastic activity durations. However, another major uncertainty facing engineering projects is that of changes in design troughout the project delivery. This may come from uncertainty in the market, technology, or regulations, leading to changes in design and implementation paths, with alterations in the project network itself. This comes on top of stochastic and correlated activity durations for a given design. In this paper we develop a stochastic program to investigate how uncertainty in design and activity durations, together, affect planning, and their relationships. The findings suggest that when design uncertainty is modelled by multiple alternatives and delayed decisions on the final alternative, stochastic and correlated activity durations have limited impact. In situations with alternative and subtitutable solutions available for a given design, correlations drive a certain learning behaviour.

Efficient priority rules for project scheduling under dynamic environments: A heuristic approach

This paper aims to identify an efficient priority rule (PR) for resource constrained project scheduling problems under dynamic environments. Here, the dynamicity comes from the unstable resource availability, time-varying resource demands and stochastic activity durations for each of the project activities. This extended dynamic project scheduling problem is solved by using a proposed Variable Neighbourhood Search Based Local Search Heuristic (VNSLSH). Six PRs are then integrated with the proposed heuristic to identify the best rule. Standard sets of 5760 and 7200 generated test instances with 30 and 120 activities are considered for experimentation. The influence of the variation of activity durations and risk or uncertainty levels on the algorithm’s performance is analysed and discussed. After analysing several PR-based heuristics, this study concludes that no one of the taken PR is dominant over others under this dynamic project scheduling environment.

Analytical models towards explaining the difficulty in efficiently matching site concrete supply resources with placing crew needs

PurposeFor parts of the time on a typical construction site concrete pour, the site placing crew is idle waiting for the arrival of the next truckmixer delivery, whereas for other periods, truckmixers are idle on site waiting to be unloaded. Ideally, the work of the crew should be continuous, with successive truckmixers arriving on site just as the preceding truckmixer has been emptied, to provide perfect matching between site and concrete plant resources. However, in reality, sample benchmark data, representing 118 concrete pours of 69 m3 average volume, illustrate that significant wastage occurs of both crew and truckmixer time. The purpose of this paper is to present and explain the characteristics of the wastage pattern observed and provide further understanding of the effects of the factors affecting the productivity of this everyday routine site concreting system.Design/methodology/approachAnalytical algebraic models have been developed applicable to both serial and circulating truckmixer dispatch policies. The models connect crew idle time, truckmixer waiting time, truckmixer round trip time, truckmixer unloading time and truckmixer numbers. The truckmixer dispatch interval is another parameter included in the serial dispatch model. The models illustrate that perfect resource matching cannot be expected in general, such is the sensitivity of the system to the values applying to those parameters. The models are directly derived from theoretical truckmixer and crew placing time-based flow charts, which graphically depict crew and truckmixer idle times as affected by truckmixer emptying times and other relevant parameters.FindingsThe models successfully represent the magnitudes of the resource wastage seen in real life but fail to mirror the wastage distribution of crew and truckmixer time for the 118 pour benchmark. When augmented to include the simulation of stochastic activity durations, however, the models produce pour combinations of crew and truckmixer wastage that do mirror those of the benchmark.Originality/valueThe basic contribution of the paper consists of the proposed analytical models themselves, and their augmented versions, which describe the site and truckmixer resource wastage characteristics actually observed in practice. A further contribution is the step this makes towards understanding why such an everyday construction process is so apparently wasteful of resources.

A computational experiment to explore better robustness measures for project scheduling under two types of uncertain environments

This paper addresses the proactive resource-constrained project scheduling problem, aiming to explore better surrogate robustness measures for project managers that want to generate robust baseline schedules under uncertain environments. The contribution of this paper is threefold. First, we propose a general framework of slack-based surrogate robustness measures and introduce three parameters to distinguish different alternative calculations of the measure. A computational experiment based on reactive simulation is constructed where the performance of the surrogate measures is evaluated by the reactive cost and two types of uncertain environments, i.e. stochastic resource availabilities and stochastic activity durations, are taken into account. Second, we analyze the impact of the three parameters as well as the two uncertain environments on the surrogate robustness measures and find the best measures for different situations. The proposed surrogate robustness measures are shown to be effective. Compared with benchmark measures, the improvements are respectively 2.67% and 13.79% under the two uncertain environments. Third, we investigate the difference of buffering strategies between the two uncertain environments. For the environment of stochastic resource availabilities, it turns out to be better to have a uniform distribution of time buffers throughout the schedule, while the reverse is true for the environment of stochastic activity durations.

Robust resource-constrained max-NPV project scheduling with stochastic activity duration

This study investigates the robust resource-constrained max-NPV project problem with stochastic activity duration. First, the project net present value (NPV) and the expected penalty cost are proposed to measure quality robustness and solution robustness from the perspective of discounted cash flows, respectively. Then, a composite robust scheduling model is proposed in the presence of activity duration variability and a two-stage algorithm that integrates simulated annealing and tabu search is developed to deal with the problem. Finally, an extensive computational experiment demonstrates the superiority of the combination between quality robustness and solution robustness as well as the effectiveness of the proposed two-stage algorithm for generating project schedules compared with three other algorithms, namely simulated annealing, tabu search, and multi-start iterative improvement method. Computational results indicate that the proactive project schedules with composite robustness not only can effectively protect the payment plan from disruptions through allocating appropriate time buffers, but also can achieve a remarkable performance with respect to the project NPV.

Product development network modelling extensions to the cycle elimination method

Abstract This paper considers Product Development (PD) project networks, which are characterized by stochastic activity durations and activity rework or iteration (i.e., potential to repeat some activities several times during PD execution). The Cycle Elimination (CE) approach presented in Nasr et al. (2016) reduces the computational complexity of analyzing iterative PD project networks by considering an approximate network with no iteration. We build on the CE approach to investigate practical scenarios which arise in real world PD projects which are not accounted for by the CE approach. These scenarios include: (i) forward probabilities, (ii) dynamic rework probabilities and proportions, (iii) multiple dependency relationships between activities, and (iv) different rework through indirect connections. We demonstrate these extensions using two case studies. The first case study considers a software development process, where we collected the data by interviewing the managers of the company. The second case study involves a hardware development process (adapted from Pinkett (1998)), where the results show that the proposed method outperformed three existing techniques from the literature. Both cases were solved using the proposed modification to the CE approach, and then simulated to gauge the accuracy of the proposed method showing very promising results.

Stochastic Project Scheduling with Hierarchical Alternatives

In this paper, a resource constrained project scheduling problem with hierarchical alternatives and stochastic activity durations is studied. A stochastic chance constraint is introduced to formulate this problem. A metaheuristic framework called SAA/DAAA through integrating the sampling average approximation (SAA) with the population-based evolutionary artificial algae algorithm (AAA) is developed to solve the problem due to the NP-hardness nature of the problem. The priority-selection list (PSL) and schedule generation scheme (SGS) are introduced for local search. Experiments with different sizes (50-scale, 100-scale, 150-scale) as well as different uncertainty levels (moderate, medium, high) are used as examples to illustrate and validate the proposed method. The influences of sample size, sampling times and confidence level are also analyzed during experiments. In addition, the proposed discrete AAA (DAAA) is compared with classic GA and numerical experiments show that the SAA/DAAA outperforms the SAA/GA in terms of both objectives and solving time.

The Preemptive Stochastic Resource-Constrained Project Scheduling Problem: An Efficient Globally Optimal Solution Procedure

We present a globally optimal solution procedure to tackle the preemptive stochastic resource-constrained project scheduling problem (PSRCPSP). A solution to the PSRCPSP is a policy that allows to construct a precedence- and resource-feasible schedule that minimizes the expected makespan of a project. The PSRCPSP is an extension of the stochastic resource-constrained project scheduling problem (SRCPSP) that allows activities to be interrupted. The SRCPSP and PSRCPSP both assume that activities have stochastic durations. Even though the deterministic preemptive resource-constrained project scheduling problem (PRCPSP) has received some attention in the literature, we are the first to study the PSRCPSP. We use phase-type distributions to model the stochastic activity durations, and define a new Continuous-Time Markov Chain (CTMC) that drastically reduces memory requirements when compared to the well-known CTMC of Kulkarni and Adlakha (1986). In addition, we also propose a new and efficient approach to structure the state space of the CTMC. These improvements allow us to easily outperform the current state-of-the-art in optimal project scheduling procedures, and to solve instances of the PSPLIB J90 and J120 data sets. Last but not least, if activity durations are exponentially distributed, we show that elementary policies are globally optimal for the SRCPSP and the PSRCPSP.