Stochastic Project Scheduling Research Articles

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.

Risk assessment and optimal scheduling of serial projects

The valuation and planning of complex projects are becoming increasingly challenging with rising market uncertainty and the deregulation of many industries, which have also raised the need for efficient risk management. We take the perspective of a private firm interested in sequential capacity expansion of a project and develop a framework for measuring the downside risk of the serial project and optimising the sequence of the stages. Under general distributional assumptions for the duration of each stage, we present an accurate representation of the project’s net present value (NPV) distribution based on a Pearson curve fit, leading to closed-form expressions for the associated risk measures. We then assess the impact of duration variability on the value at risk and demonstrate its role in stochastic project scheduling. We also account for the trade-off between maximising the expected NPV and minimising the risk exposure, and obtain the optimal schedule for risk-averse decision-makers. It becomes obvious that both the duration variability of each stage and the decision-makers’ risk preferences can significantly affect the optimal sequence of the stages and that high duration variability is not always undesirable, even for risk-averse decision-makers.

A stochastic bi-objective project scheduling model under failure of activities

A stochastic bi-objective project scheduling model under failure of activities

Stochastic Project Scheduling Optimization for Multi-stage Prefabricated Building Construction with Reliability Application

This study investigates a project scheduling problem of prefabricated building (PB) construction in an uncertain environment. Different from the traditional scheduling models in PB construction, we consider a complex multi-stage cooperation system including the production, transportation and assembly (PTA) phases. In this system, both activity durations and resource amounts are stochastic variables. By applying the reliability theory to the stochastic scheduling model innovatively, we formulate a duration reliability model to maximize the probability of non-delayed project completion, within the resource constraints. As the proposed model is a non-deterministic polynomial hard (NP-hard) problem, a hybrid meta-heuristic differential evolution particle swarm optimization (DEPSO) algorithm is developed, which is utilized the mutation factor of the differential evolution (DE) algorithm in the framework of the particle swarm optimization (PSO). Finally, a real-life example of a PB construction project is used to explore the performance of the proposed DEPSO algorithm. The result shows that the hybrid algorithm DEPSO can better find the global optimal solution in the multi-dimensional optimization problem.

Relative Average Deviation as Measure of Robustness in the Stochastic Project Scheduling Problem

In the Project Scheduling Problem (PSP), the solution robustness can be understood as the capacity that a baseline has to support the disruptions generated by unplanned events (risks). A robust baseline of the project can be obtained from redundancy based methods, which are considered proactive methods to solve the stochastic project scheduling problem. In this research, three redundancy based methods are evaluated and their performance is compared in terms of robustness. These methods add extra time to the original activities duration in order to face the eventualities that may appear during the project execution. In this article a new indicator to analyze the solution robustness to the Project Scheduling Problem with random duration of activities is proposed. This indicator called Relative Average Deviation (RAD) is defined as the margin of deviation of the activities’ start times in relation to their durations. The RAD is based in a traditional concept that seeks to minimize the value of the differences between the planned start times and the real executed start times. The planned start times were obtained from the project baseline generated by each redundancy based method and the real executed start times were obtained from a simulation process based on Monte Carlo technique. The new indicator was used to evaluate the robustness of three baselines generated by different methods but applied to the same case study. Finally, the results suggest that the Relative Average Deviation (RAD) facilitates the interpretation of the robustness concept because it focuses on analyzing the deviation margin associated with an activity.

A Proactive Robust Scheduling Method for Aircraft Carrier Flight Deck Operations with Stochastic Durations

The operations on the aircraft carrier flight deck are carried out in a time-critical and resource-constrained environment with uncertainty, and it is of great significance to optimize the makespan and obtain a robust schedule and resource allocation plan for a greater sortie generation capacity and better operational management of an aircraft carrier. In this paper, a proactive robust optimization method for flight deck scheduling with stochastic operation durations is proposed. Firstly, an operation on node-flow (OONF) network is adopted to model the precedence relationships of multi-aircraft operations, and resource constraints categorized into personnel, support equipment, workstation space, and supply resource are taken into consideration. On this basis, a mathematical model of the robust scheduling problem for flight deck operation (RSPFDO) is established, and the goal is to maximize the probability of completing within the limitative makespan (PCLM) and minimize the weighted sum of expected makespan and variance of makespan (IRM). Then, in terms of proactive planning, both serial and parallel schedule generation schemes for baseline schedule and robust personnel allocation scheme and equipment allocation adjustment scheme for resource allocation are designed. In terms of executing schedules, an RSPFDO-oriented preconstraint scheduling policy (CPC) is proposed. To optimize the baseline schedule and resource allocation, a hybrid teaching-learning-based optimization (HTLBO) algorithm is designed which integrates differential evolution operators, peak crossover operator, and learning-automata-based adaptive variable neighborhood search strategy. Simulation results shows that the HTLBO algorithm outperforms both some other state-of-the-art algorithms for deterministic cases and some existing algorithms for stochastic project scheduling, and the robustness of the flight deck operations can be improved with the proposed resource allocation schemes and CPC policy.

Optimal Delays, Safe Floats, or Release Dates? Applications of Simulation Optimization in Stochastic Project Scheduling

Abstract In the field of project scheduling, the application of activity floats is often the subject of researches that seek to maximize the net present value (NPV) of project networks. However, NPV-based scheduling in stochastic projects may result in a conflict with the primary objective of scheduling, i.e. minimizing the makespan. The main objective of this study is to improve the financial gain while respecting the makespan (i.e. applying safe floats) in stochastic projects. Next, instead of the traditional use of float which prescribes a fixed delay in the start of activity in any condition, we use release dates as the by-product of above-mentioned method to reduce the variation in time and NPV of the project with less computational effort. The project models are simulated in SAS Simulation Studio. Response Surface Methodology (RSM) is used to design the experiments, interpret the results and predict the solution. The focus is on the temporal analysis of stochastic networks, and no resource constraint is considered.

Bi-Objective Multi-Mode Project Scheduling Under Risk Aversion

The paper proposes a model for stochastic multi-mode resource-constrained project scheduling under risk aversion with the two objectives makespan and cost. Activity durations and costs are assumed as uncertain and modeled as random variables. For the scheduling part of the decision problem, the class of early-start policies is considered. In addition to the schedule, the assignment of execution modes to activities has to be selected. To take risk aversion into account, the approach of optimization under multivariate stochastic dominance constraints, recently developed in other fields, is adopted. For the resulting bi-objective stochastic integer programming problem, the Pareto frontier is determined by means of an exact solution method, incorporating a branch-and-bound technique based on the forbidden set branching scheme from stochastic project scheduling. Randomly generated test instances, partially derived from a test case from the PSPLIB, are used to show the computational feasibility of the approach.

A two-stage stochastic programming project scheduling approach to production planning

In engineering-to-order (ETO) or manufacturing-to-order (MTO) systems producing highly customized items, the high level of customization, together with long flow times, forces the production plan to be defined before information on items customization, and details on the manufacturing activities are completely disclosed. Due to the partial available information, the production plan must provide a robust schedule of the activities and of the resources utilization, trying to incorporate a certain degree of anticipation of uncertainty. This paper proposes a two-stage stochastic programming project scheduling approach to support production planning in ETO/MTO system. The approach provides a baseline production plan together with a set of revisions of the plan to react to the occurrence of uncertain events. A scenario-based approach is used to model the changes affecting the characteristics of the activities to be processed. The proposed approach is tested on random-generated instances and on a real manufacturing system producing machining centers.

Multi-resource allocation in stochastic project scheduling

We propose a resource allocation model for project scheduling. Our model accommodates multiple resources and decision-dependent activity durations inspired by microeconomic theory. First, we elaborate a deterministic problem formulation. In a second stage, we enhance this model to account for uncertain problem parameters. Assuming that the first and second moments of these parameters are known, the stochastic model minimises an approximation of the value-at-risk of the project makespan. As a salient feature, our approach employs a scenario-free formulation which is based on normal approximations of the activity path durations. We extend our model to situations in which the moments of the random parameters are ambiguous and describe an iterative solution procedure. Extensive numerical results are provided.

Berth management in container terminal: the template design problem

One of the foremost planning problems in container transshipment operation concerns the allocation of home berth (preferred berthing location) to a set of vessels scheduled to call at the terminal on a weekly basis. The home berth location is subsequently used as a key input to yard storage, personnel, and equipment deployment planning. For instance, the yard planners use the home berth template to plan for the storage locations of transshipment containers within the terminal. These decisions (yard storage plan) are in turn used as inputs in actual berthing operations, when the vessels call at the terminal. In this paper, we study the economical impact of the home berth template design problem on container terminal operations. In particular, we show that it involves a delicate trade-off between the service (waiting time for vessels) and cost (movement of containers between berth and yard) dimension of operations in the terminal. The problem is further exacerbated by the fact that the actual arrival time of the vessels often deviates from the scheduled arrival time, resulting in last-minute scrambling and change of plans in the terminal operations. Practitioners on the ground deal with this issue by building (capacity) buffers in the operational plan and to scramble for additional resources if needs be. We propose a framework to address the home berth design problem. We model this as a rectangle packing problem on a cylinder and use a sequence pair based simulated annealing algorithm to solve the problem. The sequence pair approach allows us to optimize over a large class of packing efficiently and decomposes the home berth problem with data uncertainty into two smaller subproblems that can be readily handled using techniques from stochastic project scheduling. To evaluate the quality of a template, we use a dynamic berth allocation package developed recently by Dai et al. (unpublished manuscript, 2004) to obtain various berthing statistics associated with the template. Extensive computational results show that the proposed model is able to construct efficient and robust template for transshipment hub operations.

Automated Statistical Analysis in Stochastic Project Scheduling Simulation

This paper describes a stochastic simulation-based scheduling system (S3) that: (1) integrates the deterministic critical path method (CPM), the probabilistic program evaluation and review technique (PERT), and the stochastic discrete event simulation (DES) approaches into a single system and lets the scheduler make an informed decision as to which method is better suited to the company’s risk-taking culture; (2) automatically determines the minimum number of simulation runs in DES mode and therefore optimizes the simulation process; and (3) provides a terminal method that tests the statistical significance of the differences between simulations, hence eliminating outliers and therefore increasing the accuracy of the DES process. The system is based on an earlier version of the system called stochastic project scheduling simulation and makes use of all the capabilities of this system. The study is of value to practitioners because S3 produces a realistic prediction of the probability of completing a proje...

Project scheduling under uncertainty: Survey and research potentials

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, which is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling under uncertainty projects with deterministic network evolution structure.

Probability of Project Completion Using Stochastic Project Scheduling Simulation

This paper introduces a software, Stochastic Project Scheduling Simulation (SPSS), developed to measure the probability to complete a project in a certain time specified by the user. To deliver a project by a completion date committed to in a contract, a number of activities need to be carried out. The time that an entire project takes to complete and the activities that determine total project duration are always questionable because of the randomness and stochastic nature of the activities' durations. Predicting a project completion probability is valuable, particularly at the time of bidding. The SPSS finds the longest path in a network and runs the network a number of times specified by the user and calculates the stochastic probability to complete the project in the specified time. The SPSS can be used by a contractor: (1) to predict the probability to deliver the project in a given time frame and (2) to assess its capabilities to meet the contractual requirement before bidding. The SPSS can also be used by a construction owner to quantify and analyze the risks involved in the schedule. The benefits of the tool to researchers are: (1) to solve program evaluation and review technique problems; (2) to complement Monte Carlo simulation by applying the concept of project network modeling and scheduling with probabilistic and stochastic activities via a web based Java Simulation which is operateable over the Internet, and (3) to open a way to compare a project network having different distribution functions.

Linear preselective policies for stochastic project scheduling

In the context of stochastic resource-constrained project scheduling we introduce a novel class of scheduling policies, the linear preselective policies. They combine the benefits of preselective policies and priority policies; two classes that are well known from both deterministic and stochastic scheduling. We study several properties of this new class of policies which indicate its usefulness for computational purposes. Based on a new representation of preselective policies as and/or precedence constraints we derive efficient algorithms for computing earliest job start times and state a necessary and sufficient dominance criterion for preselective policies. A computational experiment based on 480 instances empirically validates the theoretical findings.

The role of the nonanticipativity constraint in commercial software for stochastic project scheduling

Recently announced commercial project scheduling products address the stochastic project scheduling problem. Their solution methods do not consider the nonanticipativity constraint and thus provide potentially unattainable solutions to stochastic resource constrained project scheduling problems. The nonanticipativity constraint of multiperiod stochastic problems imposes the requirement that solutions be based only on information known at the time of decisions. Users should use the results from these programs with extreme care.

A Stochastic Dynamic Programming model for scheduling of offshore petroleum fields with resource uncertainty

Norwegian deliveries of natural gas to Europe have grown considerably over the last years. Additionally, plans involve even greater supplies, introducing major gas fields as the Troll field. The market for natural gas may to a large extent be viewed as a contractual market. This is normally explained by the big investments involved in development and transport. In such a perspective, the supplier's planning problem of scheduling fields and pipes may prove important in order to be able to meet contractual agreements. This paper describes a model of Stochastic Dynamic Programming type which may be viewed as a first attempt in solving this type of problem. The main focus in this model is on project scheduling and resource uncertainty. Each project's production profile is viewed as a stochastic variable. Then a possible goal could be to minimize expected deviation from a given predicted contract profile. We use the term SPSP (Stochastic Project Scheduling Problem) to refer to our problem. Besides a simplified description of the mathematical model, the paper also describes some tests with model-examples. These examples are constructed to obtain some interesting (non-intuitive) effects. The paper concludes with some remarks on complexity and speedup possibilities.

Bounding Distributions for Stochastic Logic Networks

A stochastic logic network is defined as a connected set of logic and time delay elements. Each of the latter elements has an associated probability distribution describing the nature of that element's delay. When used, for example, in project planning and scheduling, combinations of logic and time delay elements in such networks may represent conditions for the starting of project activities which are themselves represented by time delay elements. It is at present not known how to calculate the probability distributions for the events in such a network. This paper shows how to obtain upper and lower bounds for these probability distributions. The method is not a simulation technique; rather, it is a straightforward computational scheme derived from elementary probability theory. An example is given where the method is applied to a stochastic project scheduling network in which alternative ways exist for carrying out one of the jobs in the network.