Uncertain Activity Durations Research Articles

A matheuristic-oriented iterated greedy algorithm for multi-mode resource-constrained project scheduling problem under uncertainty

Multi-mode resource-constrained project scheduling problem is one of the most important branches of combinatorial optimization problems. The aim is to find a feasible solution consisting of activity start time and execution mode so that the project makespan is minimized. However, there are a lot of uncertain events, that bring great challenges to project scheduling. We first propose a mixed integer linear programming model where the activity duration is uncertain. Then two uncertain parameters are introduced to describe the disturbance degree of uncertain activity duration and the allowable violation degree of constraints respectively, and the MILP model with uncertain activity duration is converted to its deterministic robust counterpart model. A matheuristic local optimization approach is proposed to balance computational time with the optimization of the computational result. A matheuristic-oriented iterated greedy algorithm that combines a matheuristic local optimization approach and an iterated greedy algorithm is proposed to solve this problem in this paper. Experimental results indicate that the robust counterpart model can obtain robust optimal solutions for small-scale instances in accepted computational time. Meanwhile, the proposed matheuristic-oriented iterated greedy algorithm can obtain robust near-optimal solutions for large-scale instances and is superior to other compared algorithms.

Short-term underground mine planning with uncertain activity durations using constraint programming

Short-term underground mine planning with uncertain activity durations using constraint programming

A two‐layer approach for solving robust decentralized multiproject scheduling problem with multi‐skilled staff

AbstractUncertain activity durations and multi‐skilled staff allocation are two practical factors that are difficult to cope with in real project management. This paper studies a new decentralized resource‐constrained multiproject scheduling problem with uncertain activity durations and multi‐skilled staff allocation. The robust project scheduling is employed to tackle uncertainty. We name it the robust decentralized resource‐constrained multiproject scheduling problem with multi‐skilled staff (RDMPSP‐MS). To formulate this problem, a two‐layer model containing local scheduling and global coordination decision‐making is established based on the multiagent system. To solve this model, a two‐layer approach (TLA) is developed. In the TLA, a starting time criticality heuristic method is adopted to handle the local scheduling problem, and a global resource allocation heuristic algorithm is designed to allocate multi‐skilled staff. The computational experiments are conducted on the adapted Multi‐Project Scheduling Problem LIBrary (MPSPLIB) data set. The results show that the proposed TLA outperforms seven heuristic algorithms based on priority rules regarding solution quality and efficiency on most problem subsets. It is further verified that the robustness of the baseline schedule deteriorates with the increase in problem size and activity duration variability level. Additionally, the results of this research provide practical guidance for managers who expect to determine reasonable project deadlines in a decentralized multiproject environment.

Balancing Project Schedule, Cost, and Value under Uncertainty: A Reinforcement Learning Approach

Industrial projects are plagued by uncertainties, often resulting in both time and cost overruns. This research introduces an innovative approach, employing Reinforcement Learning (RL), to address three distinct project management challenges within a setting of uncertain activity durations. The primary objective is to identify stable baseline schedules. The first challenge encompasses the multimode lean project management problem, wherein the goal is to maximize a project’s value function while adhering to both due date and budget chance constraints. The second challenge involves the chance-constrained critical chain buffer management problem in a multimode context. Here, the aim is to minimize the project delivery date while considering resource constraints and duration-chance constraints. The third challenge revolves around striking a balance between the project value and its net present value (NPV) within a resource-constrained multimode environment. To tackle these three challenges, we devised mathematical programming models, some of which were solved optimally. Additionally, we developed competitive RL-based algorithms and verified their performance against established benchmarks. Our RL algorithms consistently generated schedules that compared favorably with the benchmarks, leading to higher project values and NPVs and shorter schedules while staying within the stakeholders’ risk thresholds. The potential beneficiaries of this research are project managers and decision-makers who can use this approach to generate an efficient frontier of optimal project plans.

Robust decision trees for the multi-mode project scheduling problem with a resource investment objective and uncertain activity duration

In this paper, we advocate the use of robust decision trees for a multi-mode resource constrained project scheduling problem with uncertain activity duration and a resource investment objective, coming from an industrial assembly line scheduling application. This work takes place in the context of multi-stage optimization where uncertainty is revealed progressively across a succession of decision time points. In a robust decision tree, a node represents a robust partial schedule from the time origin to a specific decision time point. At this point, the decision maker has access to some information, which partitions the uncertainty scenario set, yielding for each scenario subset a child node and an associated extended partial robust schedule up to the next decision point. Considering that the level of uncertainty is lowered, the new partial schedule is less conservative and improves the robustness guarantee. However, since all accessible information may not be relevant, we turned the information selection part into an optimization problem. An algorithm is proposed to solve the robust decision tree problem. Experimentation is provided to study the influence of decision tree parameters as well as highlighted recommendations. The interest of the decision tree is shown through an experimental comparison with classical approaches of the literature on benchmark instances and industrial instances.

Optimizing workforce allocation under uncertain activity duration

Even though warehouses are becoming increasingly automated, humans remain their central and most important resource. Every day, various activities must be carried out by workers. The assignment of individual workers to specific tasks has a major impact on the overall efficiency of a warehouse. The problem of finding an efficient assignment is not trivial and is complicated by task durations being unknown in advance, operational constraints, and the fact that employee well-being must be taken into consideration to maintain employee satisfaction. The method proposed in this paper uses work profiles: ordered lists of task properties such as type and work zone. Each worker is assigned exactly one profile and tasks are dynamically allocated to workers based on their profile. Finding a good profile assignment is crucial, yet the profiles are usually assigned manually by shift supervisors. This paper proposes a framework for automating the assignment of profiles to employees under uncertain task durations. The proposed approach applies a metaheuristic algorithm together with discrete-event simulation to evaluate the quality of a solution. The simulation component is used to address uncertainty of the task durations either by considering multiple scenarios or by using mean task durations. Possible values for task durations originate from distributions which are assumed to be given or learned from historical data. The contributions of this paper are threefold: (1) we propose a profile-assignment framework that deals with uncertainty of the task durations, (2) we study the trade-offs between run time and accuracy within this framework, and (3) we analyze our main design decisions and demonstrate how our method outperforms reconstructed solutions produced by a human expert.

A Two-Stage Algorithm Based on 12 Priority Rules for the Stochastic Distributed Resource-Constrained Multi-Project Scheduling Problem With Multi-Skilled Staff

In practical multi-skilled resource-constrained multi-project management, the activity duration is often affected by some factors (e.g., rework, increased workload), leading to uncertainty. Moreover, multiple projects are often managed under a distributed decision-making environment. To deal with uncertain activity durations in distributed multi-project management with multi-skilled staff, this paper studies a stochastic distributed resource-constrained multi-project scheduling problem with multi-skilled staff (MS-SDRCMPSP). In a distributed decision-making environment, a two-stage model with local scheduling and global coordination stages is established to describe MS-SDRCMPSP. A two-stage algorithm with 12 priority rules (TSA-12PRs) is proposed, these 12 priority rules are composed of 4 activity priority rules and 3 resource priority rules. In the local schedule stage, 4 activity priority rules (PRs) are applied to obtain the local schedule plan. In the global coordination phase, we develop 3 resource PRs based on variable neighborhood search (VNS), of which VNS is used to solve the execution order of conflicting projects, and 3 resource PRs are developed to formulate multi-skilled resource assignment strategies. Based on the multi-skilled instances adapted from benchmark instances, we evaluate the performance of the 12 PRs on different instances. The experiment results show that two PRs among 12 PRs perform better than other PRs in all-size instances. Comparing the two-stage algorithm with better two PRs with other approaches in literatures, we find that our method performs better than other approaches, especially in large-size instances. In addition, further experiments show that our method is more conducive to shortening the CPU runtime on distributed problems than centralized methods.

A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method

In this study the intuitionistic fuzzy version of the critical path method has been proposed to solve networking problems with uncertain activity durations. Intuitionistic fuzzy set [1] is an extension of fuzzy set theory [2] unlike fuzzy set, it focuses on degree of belonging, the degree of nonbelonging or non-membership function and the degree of hesitancy which helps the decision maker to adopt the best among the worst cases. Trapezoidal and the triangular intuitionistic fuzzy numbers are utilized to describe the uncertain activity or task durations of the project network. Here trapezoidal and triangular intuitionistic fuzzy numbers are converted into their corresponding parametric form and applying the proposed intuitionistic fuzzy arithmetic operations and a new method of ranking based on the parametric form of intuitionistic fuzzy numbers, the intuitionistic fuzzy critical path with vagueness reduced intuitionistic fuzzy completion duration of the project has been obtained. The authentication of the proposed method can be checked by comparing the obtained results with the results available in pieces of literature.

A faster exact method for solving the robust multi-mode resource-constrained project scheduling problem

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions that minimise the worst-case project makespan, whilst assuming that activity durations lie in a budgeted uncertainty set. Computational experiments show that this easy-to-implement formulation is many times faster than the current state-of-the-art solution approach for this problem, whilst solving over 40% more instances to optimality over the same benchmarking set.

Developing a Heuristic Algorithm to Solve Uncertainty Problem of Resource Allocation in a Software Project Scheduling

In project management process, the objective is to define and develop a model for planning, scheduling, controlling, and monitoring different activities of a particular project. Time scheduling plays an important role in successful implementation of various activities and general outcome of project. In practice, various factors cause projects to suffer from time delay in accomplishing the activities. One important reason is imprecise knowledge about time duration of activities. This study addresses the problem of project scheduling in uncertain resource environments, which are defined by uncertain activity durations. The study presents a solution of the levelling and allocation problems for projects that have some uncertain activities. The resources are minimised using resource levelling based on a proposed heuristic algorithm with limited duration. The algorithm performs the resource scheduling (levelling and allocation) for minimum moments. The efficiency of the proposed algorithm is indicated by the resource improvement coefficient and rate of resource utilisation.

Evaluation of VaR and CVaR for the makespan in interval valued blocking job shops

The paper deals with the job shop scheduling problem with complex blocking constraints (BJSS) under uncertainties. It proposes a method for the evaluation of the risk that the makespan of a deterministic feasible schedule assumes worse extreme values, considering uncertain activity durations represented by intervals. An interval-valued network approach is proposed to model the feasible solutions characterized by uncertain values for jobs’ releases, processing and setup times. The study assumes the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR) as risk measures for the makespan of the feasible solutions, and addresses both modeling and computational issues. They include the implementation and test of a network-based model used with an innovative algorithm for the first time applied to complex BJSS problems to provide an accurate, rapid and viable computation of both risk indices. The impact of different sources of uncertainty (including setups, releases and processing times) on the overall performance of the proposed approach are analyzed. The results of a wide experimental campaign show that the method, for both the computational time and the quality of the evaluations, has broad applicability. It can support the decision-makers for a wide range of practical scheduling cases taking into account their risk sensibility.

New closed-loop approximate dynamic programming for solving stochastic decentralized multi-project scheduling problem with resource transfers

Resource transfers and uncertain activity durations are two practical factors that are difficult to cope with in real project management. This paper studies a new decentralized multi-project scheduling problem with both resource transfers and uncertain activity durations, we name it the stochastic decentralized multi-project scheduling problem with resource transfers (SDRCMPSPTT). To tackle the curse-of-dimensionality of an exact solution approach, we develop a new and effective rollout policy-based approximate dynamic programming (ADP) algorithm for SDRCMPSPTT. Based on the benchmark instances, we build a new data set and examine the performance of 12 priority rule heuristics, then select the two best ones as the base policy for our rollout algorithm. The proposed approach is verified under a stochastic environment by assessing different base heuristic policies, computational results show that the rollout algorithm can further improve the solution quality of the base heuristics. Compared with the state-of-the-art algorithm for solving the decentralized multi-project scheduling problem under a deterministic environment, our rollout policy-based ADP algorithm can also obtain competitive solutions.

Stochastic radiotherapy appointment scheduling

When scheduling the starting times for treatment appointments of patients in hospitals or outpatient clinics such as radiotherapy centers, minimizing patient waiting time and simultaneously maximizing resource usage is crucial. Significant uncertainty in the treatment durations makes scheduling those activities particularly challenging. In addition to the treatments themselves, also preparation times and exiting times have to be considered, which are uncertain as well. To address and analyze this type of problems, the current study develops a model for planning appointment times under uncertain activity durations for a medical unit with a single “core resource” (in our application case a radiotherapy beam device), several treatment rooms, and required preparation and exiting phases for each patient. We employ a novel buffer concept based on quantiles of duration distributions and introduce a reactive procedure that adapts a pre-determined baseline schedule to the actual patient flow. For heuristically solving the resulting stochastic optimization model, a combination of a Genetic Algorithm and Monte Carlo simulation is proposed. A case study uses real-world data on activity durations gathered from an ion beam therapy facility in Austria. Experimental results comparing different variants of the method are carried out. In particular, comparisons of the stochastic optimization approach to a simpler deterministic approach are given.

A compact reformulation of the two-stage robust resource-constrained project scheduling problem

This paper considers the resource-constrained project scheduling problem with uncertain activity durations. We assume that activity durations lie in a budgeted uncertainty set, and follow a robust two-stage approach, where a decision maker must resolve resource conflicts subject to the problem uncertainty, but can determine activity start times after the uncertain activity durations become known.We introduce a new reformulation of the second-stage problem, which enables us to derive a compact robust counterpart to the full two-stage adjustable robust optimisation problem. Computational experiments show that this compact robust counterpart can be solved using standard optimisation software significantly faster than the current state-of-the-art algorithm for solving this problem, reaching optimality for almost 50% more instances on the same benchmark set.

Managing Uncertainty and Disruptions in Resource Constrained Project Scheduling Problems: A Real-Time Reactive Approach

Resource constrained project scheduling problems (RCPSPs) are complex optimization problems that aim to minimize project completion time after considering limited resources and precedence-related activities with known durations. However, due to the dynamic nature of real-world applications, activity durations are vulnerable to change. In addition, resource demands along with resource availability at any stage of a project can also vary due to disruptions, which compel practitioners to re-think existing scheduling methodologies. Consequently, to mitigate the conjoint effect of those uncertainties and/or disruptions, this paper proposes a real-time reactive scheduling approach. To deal with uncertain activity durations, a chance constrained based approach is followed, which is later solved by an advanced meta-heuristic based approaches called IGFBIS and IGFBID. After solving an exhaustive list of stochastic RCPSP instances, this paper proves the efficacy of the proposed approaches, which is proven to be more useful to mitigate uncertainty or disruption while executing real-life projects.

A robust optimization approach for the multi-mode resource-constrained project scheduling problem

This paper suggests a robust optimization approach for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. The objective is to minimize the worst-case project duration by deciding on activity modes, resource allocations and a schedule baseline. The problem is solved by a Benders decomposition approach with specialized cuts. We consider polyhedral uncertainty sets in which the level of conservatism can be adjusted. Using a computational study in which various problem instances are explored under varying levels of uncertainty, conservatism and several types of duration distributions, we provide insights about the price of robustness and the performance of the approach. The hope is that these insights can guide future multi-mode project scheduling implementations when there is partial information about the distribution of activity durations.

A multi-objective optimization approach to project scheduling with resiliency criteria under uncertain activity duration

Uncertainty is one of the main parts of the project management environment that can strongly affect the project objectives and cause unpredictable delays. This study presents a multi-objective optimization approach for constructing resilient project schedules under resource constraints to cope with uncertain activity durations. In this paper, the concept of resilient project scheduling is defined to measure the ability of schedules to deal with duration disruption. Since the direct evaluation of resiliency is computationally complicated and time-consuming, a new surrogate resilience measure is introduced. The proposed resiliency criteria measure the floating of activities and the risks associated with the completion of the project. Furthermore, a new model based on a combination of time buffer and float allocation approach is developed. To extend existing project scheduling models with uncertainty, general precedence relationships between activities have been considered. To validate the proposed approach, the construction project of a combined cycle power plant is used as a case study. Due to a large number of project activities in this case study, the non-dominated sorting genetic algorithm (NSGA II) has been used to solve the problem. The results of solving the mathematical model using the proposed method are assessed through extensive simulation experiments and compared with those of the baseline schedule. The results show that by taking the proposed resiliency measure and the optimal allocation of buffer time to activities, the project completed at the same duration with higher reliability.

Robust project scheduling integrated with materials ordering under activity duration uncertainty

This article addresses the project scheduling and the materials ordering problem (PSMOP) with uncertain activity durations. A two-stage optimisation approach is proposed to generate a robust schedule in order to protect the project execution from the duration uncertainty. First of all, a mixed-integer programming model under a deterministic environment is formulated to address this issue, which aims to minimise the corresponding costs and is solved by the genetic algorithm (GA). Second, a robust project scheduling integrated with materials ordering method (RPSMOM) is developed to build a proactive schedule on the basis of the baseline schedule generated by the given deterministic model. In this method, a novel index that measures the risk of activity delay (RAD) is suggested by taking the uncertain activity durations into account. Finally, computational experiments are conducted under different levels of activity duration uncertainty. The results demonstrate that the integrated proactive scheduling method is highly effective in decreasing the total cost and improving the robustness of the project schedule in most circumstances.

The Use of a Multiple Risk Level Model to Tackle the Duration of Risk for Construction Activity

The project evaluation and review technique (PERT) is the most well-known method to handle the risk due to uncertain activity durations, previous studies show that the β-distribution-based PERT estimation tends to be over-optimistic and it offers no control of the project in terms of risk duration. This study proposes a multiple risk-level (MRL) model that uses a site spatial constraint, environmental effects and the “5 Ms” of construction management to tackle the duration of risk during a construction project. A Risk-based Critical Path Scheduling Method (R-CPSM) that uses MRL is developed to calculate the duration of the project. A case study using a project selected from a previous study is used to compare the four estimation methods: two traditional PERT methods (3.2σs and 6σs), a Monte Carlo Simulation and the proposed MRL model. The results show that, compared with traditional approaches to estimate durations of uncertain activity, the proposed R-CPSM method is more systematic that can be combined with a cost estimation process and offers a rectification mechanism that dynamically monitors and adjusts the important factors that affect the risk duration. This method gives a more realistic estimate that is in agreement with the results of previous studies.

Robust Optimization for the Resource Constrained Multi-Project Scheduling Problem with Uncertain Activity Durations

This paper studies the multi-project scheduling problem which involves multiple projects with different importance weight; with predefined assigned due dates; with activities that have uncertain durations; and with renewable resources that are constrained. The resource sharing policy is applied to share the resources among projects. Due to the environmental rapid changes and also the uniqueness of projects, the probability distribution function of uncertain durations cannot be estimated with confidence. Besides, the multi-project scheduling problem with its large scale investment dictates a conservative approach to deal with the existing uncertainty. Therefore, the Robust Resource-Constrained Multi-Project Scheduling Problem (RRCMPSp ) is studied in this paper while the maximum total weighted tardiness of the projects should be minimized. A scenario-relaxation algorithm is implemented which results in optimal solutions for the RRCMPSp . The aim is to find an optimal structure containing all the projects in such a way that it transfers the resources between the activities based on the resource sharing policy while the maximum weighted differences between the projects finish times and their assigned due dates will be minimum.