Narrow Results

In this paper, we introduce a new project scheduling problem with multiple milestones and completely ordered activities. The characteristic of our problem lies in the activity durations, which are determined by the unique attributes of each activity and the worker assigned to it. The objective is to identify the optimal assignment of workers to activities that minimizes the weighted number of tardy activities. We show that the problem is strongly NP-hard by reducing it from the 3-partition problem even for two cases with a special structure of durations. Furthermore, we identify two cases that can be solved in polynomial time.

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

Scheduling multi-project is a complex decision making process. It involves the effective and timely allocation of resources to different projects. In the case of multi-project, resources are often transferred between the projects. It consumes both time and cost, when projects are situated in different geographic locations. As a result, the net present value (NPV) of multi-projects is significantly impacted by the resource transfer time. In this paper, a new genetic algorithm (GA) approach to the multi-project scheduling problem with resource transfer times is presented, where the NPV of all projects is maximized subject to renewable resource constraints. The paper also presents a heuristic approach using two phase priority rules for the same problem. We conduct a comprehensive analysis of 60 two-phase priority rules. The proposed GA approach is compared to the heuristic approach using the well-known priority rules. An extensive computational experiment is reported.

In order to identify critical activities and critical sequences under resource availability constraints, resource dependencies need to be established. By doing this, project managers and practitioners can focus their limited energy on specific activities and paths during the execution of a project schedule, thus guaranteeing that the project gets finished on time and with the available resources. This study proposes various rules to judge the superiority or inferiority of the methods of dependencies’ creation. The total number of critical sequences which is one of these rules, directly influences the degree of difficulty in controlling the whole project — a major concern for project managers. This study classifies activities in a resource-constrained project schedule on the basis of the relationships between activities and develops the basic idea behind the optimization of resource dependencies. Specifically, two mathematical models to minimize the total number of critical sequences and that of resource links through the table translation method are proposed. A computation example shows great improvement in the number of critical sequences, critical activities and resource links and gives effective results while solving the problems in the previous research. Moreover, simulations using J30, J60, and J120 instances by Kolisch highlight the high computing speed when searching for the actual minimum number of critical sequences and resource links thanks to the table translation method.

We investigate a project scheduling problem in which cash flows are periodically variable, and we aim to maximize the net present value (NPV). For each activity, a set of cash flows is considered where each one pertains to a particular period. This setting is compatible with inflation rates that may well occur in some countries with unstable economic situations where the occurrence times of inflation are sometimes known in advance. In this case, the project can be scheduled more suitably to abate probable pitfalls. In this paper, we investigate the problem in two settings: deterministic and stochastic cash flows. In the deterministic case, in each period we consider the expected value of cash flows of each activity as a constant and develop an integer linear programming model in conjunction with a branch-and-bound algorithm to solve the problem optimally. Moreover, we develop a multi-stage stochastic programming (MSSP) model to formulate the stochastic version of the problem. Using a set of randomly generated test instances and extensive computational results, we analyze the performance of our developed solution approaches. In addition, we compare the deterministic and stochastic models and analyze the sensitivity of the most important parameters.

In this paper, we study the well-known resource availability cost problem with stochastic resource availability. The objective is to determine the initial levels of all renewable resources and establish a schedule corresponding to each scenario such that the expected resource availability cost is minimized. We assume that resource shortfalls can be compensated externally but at a noticeable higher cost. We formulate the problem as a two-stage stochastic programming model (TSSPM). We also develop an exact decomposition-based algorithm (DBA) for the particular case of the problem with at most two resources, which also functions as a heuristic for the original problem. Since the number of scenarios influences the performance of the developed solution approaches, we utilize a fast scenario reduction method to reduce the number of scenarios. Computational results indicate that the DBA outperforms the TSSPM formulation in solution quality and CPU runtime.

Trade-off problems concentrate on balancing the main parameters of a project as completion time, total cost and quality of activities. In this study, the problem of project time-cost-quality trade-off is formulated and solved from a new standpoint. For this purpose, completion time and crash cost of project are illustrated as fuzzy goals, also the dependency of implementing time of each activity and its execution-quality is described by a fuzzy number. The overall quality of the project execution is defined as the minimum execution-quality of the project activities that should be maximized. Based on some real assumptions, a three-objective programming problem associated with the time-cost-quality trade-off problem is formulated; then with the aim of identifying a fair and appropriate trade-off, the research problem is reformulated as a single objective linear programming by utilizing a fuzzy decision-making methodology. Generating a final preferred solution, rather than a set of Pareto optimal solutions, and having a reasonable interpretation are two most important advantages of the proposed approach. To explain the practical performance of the proposed models and approach, a time-cost-quality trade-off problem for a project with real data is solved and analyzed.

The paper defines four fuzzy project scheduling models under inflation condition without or with budget limit. The activity time is described by fuzzy relation or fuzzy variables. The models can be solved in the forms of crisp LP or NLP after using the concept of α-cut.

Traditional project scheduling methods inherently assume that the decision makers (DMs) are a unique entity whose acts are based on group rationality. However, in practice, DMs’ reliance on individual rationality and the wish to optimize their own objectives skew negotiations towards their preferred solutions. This makes conventional project scheduling solutions unrealistic. Here, a new two-step method is proposed that seeks to increase the overall efficiency of project schedules without violating individual rationality criteria, to find scheduling solutions that are acceptable to all DMs. First, a genetic algorithm is combined with evidential reasoning (ER) to obtain near optimal project schedule alternatives with respect to the priorities of each DM, separately. Second, the fallback bargaining method is used to help the DMs reach a consensus on an alternative with the highest group satisfaction. The proposed model is tested on a benchmark project scheduling problem with over 3.6 billion possible project scheduling alternatives. The results show that the model helps DMs when appointing their preferences using a well-organized procedure to provide a transparent view of each project schedule performance solution. Furthermore, the model is able to absorb the maximum support from the DMs, not necessarily a unique entity, by collecting all the self-optimizing DMs’ preferences and fairly allocating the benefits.

In the environment of scientific and technological innovation, the human and material resources that can reach the project threshold are often limited. For enterprise projects that require high R&D and production level to produce rapid emergency resources, they often face the problem of difficult effective allocation of emergency resources, resulting in project delay. Therefore, in the process of high-tech projects, it is necessary to deal with the lack of emergency scientific and technological resources. Therefore, based on the particle swarm optimization algorithm which is easy to be realized by scientific and technological innovation enterprises, this study improves its two shortcomings of easy local optimization and low performance, constructs the CD-PSO project scheduling model, verifies the performance of the improvement points, and tests the performance of the model in the actual project case of enterprise rapid emergency resource scheduling. The results show that the optimal solution of CD-PSO model in the three sample sets is higher than that of D-PSO model in the same group, and the average scheduling duration is the shortest, which is 350 days, and the proportion of reaching the optimal duration is 100%. The operation effect is obviously better than other scheduling models. The CD-PSO project scheduling model designed in this study is easier to implement and can calculate the optimal solution of the first project more efficiently. It not only has excellent performance, but also has a strong popularization foundation.

By using a recursive method, we determine the project completion time when the activity times are distributed according to a beta distribution. The $k$th moment of the maximum of non-identical independent random variables following this distribution-type is evaluated. Applicability and appropriateness of the beta model are illustrated by some examples, which show that the suggested estimate program evaluted and review technique of the project completion time is located between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski An upper bound on the expected completion time of PERT networks, Eur. J. Oper. Res.21(2) (1985b) 206–212. Moreover, this estimate gives less values of the approximation errors than most of the other known estimates.

In projects with generalized precedence relations (GPRs), a typical problem of resource-constrained project scheduling with GPRs is that 2n parallel activities are adjusted to n sequence activities pairs. In order discuss the theory and to tackle this problem, this paper studies the optimal sequence of parallel activities with GPRs and proposes an algorithm to adjust 6 parallel activities to 3 activity pairs with minimum effective on project duration under GPRs.