project scheduling

One of the important issues in project management is project scheduling. Since projects are faced with high uncertainty, project scheduling is of high importance under uncertain conditions. The purpose of this research is to present a robust multi-objective model to optimize project scheduling with limited resources by considering uncertainty, in which activities have several execution modes with uncertain duration, costs, and resources.
After reviewing the extant theoretical literature on project scheduling, the assumptions, parameters, and variables of the mathematical model were determined. Then, considering the goals and limitations of the project scheduling problem in deterministic conditions, a mathematical model was developed. This model was transformed into a single-objective model by the epsilon constraint method. To consider the uncertainty in the parameters of the problem, robust optimization, and Bertsimas and Sim's approach were used. Also, Robust optimization of the single-objective model was developed to consider the uncertainty.
According to the obtained results, while the duration of the project increases with the increase in the tolerance of non-deterministic parameters; the percentage of project duration changes decreases for higher values ​​of robust parameters.
The robust parameters are with negative coefficient in the objective function, so their increase leads to a decrease in the objective function value. The highest reduction of the objective function is when the robust parameter is changed from two to one. This coefficient decreases with the increasing value of the corresponding parameter i.e., as the value of stability parameters increases, its effect on changing the value of the objective function decreases. The cost parameter was changed between -40% to +40% for the value of gamma 10 (the state where 10 activities of the project are non-deterministic) for different variation values of parameters of non-deterministic activities. Its effect on the values of the objective function indicated that the variation of the cost parameter in the range of 0 to +40% turns it into an unnecessary constraint and that its change has no effect on the value of the objective function (project duration). Also, in the range of 0 to -40%, the cost reduction caused a decrease in the value of the objective function (increasing the project duration) and the maximum impact of the reduction of the project budget related to the situation where the uncertain parameters of time and cost change by 40% and 50%.

Time and cost are significant factors in every project. By reducing the resources allocated to the project, project costs are reduced, while the reduction of available resources means the inability to simultaneously implement activities or activities in the shortest possible time, which in turn increases the duration of the project. This is although, in all projects, the completion of the projects in the earliest time is considered one of the important parameters of the project. Considering the highly practical application of the examined problem, project scheduling by investing multi-skill resources with the possibility of changing the skill level in fuzzy conditions can be considered a positive step towards creating project scheduling problems.                         
Design/methodology/approach: In this paper, the proposed mathematical model of meta-heuristic genetic algorithms to solve the proposed model is discussed and explained in detail. Several skills are needed to perform each activity. The goal is to optimally determine resource availability and find the best schedule by minimizing investment in resources.              
Considering the activities' need for different skills as well as the expertise of the project members in different skills, it seems obvious that each activity can be done with several different situations in terms of human resources allocation, which might be only for one activity, reaching more than 10 modes. As a result, compared to MRCPSP, this issue has a much higher complexity. The Resource Investment Problem (RIP) is a variant of RCPSP where renewable resource constraints are considered decision variables. In many projects, managers, in addition to making decisions about the time of implementation of activities, should determine the number of resources allocated to activities in each period of the implementation of activities according to the status of the project, which means ignoring the constant pattern of resource consumption for activities during their implementation.                          
Practical implications: By comparing the algorithms with the indicators of maximum extension, distance from the ideal solution, distance, and several Pareto solutions, it was found that the multi-objective genetic algorithm performs far better than the multi-objective Cuckoo algorithm regarding the criteria, distance from the ideal solution, and the largest expansion. However, in terms of the number of Pareto solutions, the algorithm is not superior to the other algorithms. Therefore, it can be concluded that the multi-objective genetic algorithm has relatively a better performance than the multi-objective Cuckoo algorithm.           
Social implications: In this research, each activity can be performed with several different situations in terms of human resource allocation, which may reach more than 10 situations just for one activity. As a result, compared to MRCPSP, this issue has a higher level of complexity. Literature review indicates that being multi-skilled increases the productivity, quality, and consistency of work and gives managers more flexibility in work allocation.              
Originality/value: One of the most important branches of project scheduling knowledge is the problem of project scheduling with limited resources. This new concept has led to the development of one of the most general modes of scheduling problems under the title of multi-mode project scheduling with limited resources, which solves many real problems and can be modeled for application.

Oil, gas and petrochemical industry managers are nowadays preoccupied with finding ways of punctually completing projects while maintaining the highest implementational standards and minimizing financial costs and environmental threats. Reaching a balance among time, cost, quality and environmental effects is a paramount goal for these managers since these goals are contradictory and focus on any of them can lead to changes in the others. The purpose of this applied mathematical research was hence to design an authentic simulated multi-purpose mathematical model that can review and resolve the issue of project scheduling and balancing time, cost, quality and environmental effects in multi-mode projects. Using the GAMS software and CPLEX solver, the Model was validated through Expanded Epsilon Limitation Method and the analytical results of various sensitivities are reported.

One of the popular problems in operations research and project management is resource-constrained project scheduling problem. In the present study, this problem is modeled considering important goals consisted of minimization of the project completion time, as well as minimization of the maximum cost of the project in one day. In this regard, all the possible prerequisite relations between the activities of a project are considered. The proposed model has been implemented for three real projects in different sizes and by using metaheuristic algorithms including genetic algorithm, particle swarm optimization and differential evolution. The results showed that differential evolution and particle swarm optimization algorithms have efficient performances compared to the genetic algorithms for large- and medium-scale projects respectively. The use of metaheuristic algorithms for solving small-scale projects is not recommended.

In the present research, Time-Cost-Quality trade off problem is formulated and solved, from a new point of view. To this end, quality is defined as a function of time and cost, then by defining the project’s quality as minimum value of quality of activities and regarding predecessor relations between activities, a tri-objective programming model is formulated to trade off the time, cost and quality. In order to solve the problem, objective functions of time and cost described as fuzzy goals and a fuzzy decision-making methodology has been used to reformulate the proposed tri-objective model to a single-objective model. Producing a final solution, instead of a set of Pareto efficient solutions, is one of the advantages of proposed method, which prevents decision maker from confusion. In order to describe performance and show the potential applicability of proposed methodology, a time-cost-quality trade-off problem for a project with real data from Organization for Renovating, Developing and Equipping Schools of Kerman province is solved. Finally, in order to validate the proposed model and method, a parametric analysis, which systematically varies the main parameters of model, is employed.

In this paper, we address the multi-skilled RCPSP with time-dependent resource capacities and generalized precedence relations between activities. In this problem, a set of multi-skilled workforces are required to execute project activities. Each worker is able to perform several skills. The availability of workforces is time-dependent due to holidays, weekends, sicknesses, etc. Therefore, in this study, a mathematical formulation is proposed for the multi-skilled RCPSP with time-dependent resource availabilities. The objective function of the model is minimization of project completion time. The proposed model in this study is an NP-Hard problem in the strong sense. Hence, we develop a new meta-heuristic algorithm based on harmony search algorithm to solve the proposed model. New crossover and mutation operators have been designed for the proposed method to produce diverse solutions and to prevent the proposed algorithm from converging to a local optima. Hence, the proposed method not only uses the common procedure in harmony search algorithm, but also it employs the proposed crossover and mutation operators to explore solution space more accurately. The generated solutions are all combined and the harmony memory is updated. The effectiveness of this method has been compared to particle swarm optimization (PSO) and genetic algorithm (GA) in solving 30 test problems. The results show that the proposed method has been superior in terms of multiple performance measures.

In the single-mode resource-constrained project scheduling problem, it is assumed that each activity has a specified known execution time and resource consumption can be done only in one way. In practice, there are many cases in which the make span can be reduced by providing additional resources activities. In this case, each activity can be done in one of the procedures, which is called the multi-mode resource-constrained project scheduling. In this paper, the problem includes determination of the basic schedule for the project activities which may be done in several models and the precedence relations are met, While the project make-span, cost and resource fluctuations are minimal. In this research project scheduling problem network will model using ED simulation software and the results of the simulation and a meta-heuristic algorithm has been compared. Finally, management strategies to optimize the scheduling, i.e such minimize total time, cost and resource leveling, will be offered.

Frog leaping algorithm combination (SFLA) is an algorithm based on memetic Meta-heuristic. Created in recent years by Eusuff and Lansey, SFLA algorithm works in a way that the frog groups search for food. The development of memetic algorithms for local search method is similar to the activities of a frog among subgroups. SFLA uses a combination of strategy and provides the ability to exchange messages in local search. Frog leaping algorithm combines the advantages of particle swarm optimization algorithm and memetic development (PSO). Since the resource-constrained project scheduling problem is the timing issue, scheduling issues in the construction sites and plants is highly considered. One of the main duties of the project scheduling and project management is to reduce the completion time. Because of the resource constraints and precedence relationships between activities, project scheduling problem is difficult. In this paper, the algorithm performance LeapFrog (SFLA) is applied to reduce the project scheduling problems with resource constraints. The findings prove the robust performance of the new meta-heuristic algorithm.

One of the issues considered by the projects responsible especially project managers is the execution of project activities according to time schedule. The very difficult nature of that issue is also another reason for the researchers to take much note of it. Therefore, there are especial techniques and methods to solve those issues. Also, project managers pay much attention to the stability of the time schedule as it is important for them. This paper is provided with a real project time schedule for a refinery by using stable time schedule. Particle swarm optimization algorithm is suggested to resolve the problem since the project time schedule has resources limitation including NP- Hard. In order to accesses the validation of the model, 4 issues with small scales has been selected and the results from the suggested algorithm was compared with the accurate result obtained from lingo software. These results indicate that the suggested algorithm is effective and convergent with the optimized result.

The construction supply chain encounters with a lot of challenges that one of the most significant can refer to the higher sources wasting in project site and also the high pollution on amount of this type of supply chains. On the other hand, the most managers of supply chains need to the integration of supply chain such as project sources and time specifics, determining the production and inventory level, and also determining numbers and type of vehicles that are included, in order to its cost is calculated in an optimal form. For this purpose, in this article an integrated model has been proposed which first objective function is maximizing the profit, and the second objective amount is minimizing the emission of the carbon dioxide gas, whereas a solution way for the prevention of sources waste in project site is presented.  With assumption of determining project network and also the durations and daily demand of each activity, this supply chain model pans the different periods of time. To consider this bi-objective and nonlinear model, the model has been first linearized, and by using the epsilon-constraint method and also coding in GSMS software has been solved and its results have been finally analyzed with two numerical examples. 

In this paper, a mathematical model is proposed for project portfolio selection and resource availability cost problem to scheduling activities in order to maximize net present value of the selected projects preserving precedence and resource constraints. Since the developed model belongs to NP-hard problems list, so a genetic based meta-heuristic algorithm is proposed to tackle the developed model. In the proposed algorithm beside common operators of genetic algorithms such as crossover & mutation, some intelligent operators are utilized for local search in computed resources and shifting the activities with negative cash flows. The key parameters of the algorithm are calibrated using Taguchi method to accelerate convergence of the proposed algorithm. Then, the algorithm is used to solve 90 test problems consisting 30 small-scale, 30 middle-scale and 30 large scale problems to examine the algorithm’s performance. It is observed that, in small problems, the obtained solutions from the proposed genetic algorithm have been comparably better than the local optimum solutions stemmed from Lingo software. On the other hand, for the middle and large size problems which there is no local optimum available within the limited CPU time, robustness of the proposed algorithm is appropriate.

In this article, with the aim of maximizing net present value and considering various ways of the payment, the problem of selecting and scheduling several projects using mathematical programming and constraint programming have been investigated, in a way that the project feasibility with regards to the level of available resources is guaranteed and all of the prerequisite relationships are observed. Activities with the different modes of resources can be done. They uses renewable (human resources, equipment) and non-renewable (raw materials, budgets) resources. In calculating the costs, the overtime cost of renewable resources, late penalties or rewards of delivery before the project due date is considered. Created Models are tested by a number of projects from the PSPLIB libraries.

Resource Constrained Project Scheduling Problem (RCPSP) is the most general scheduling problem. Job shop scheduling, flow shop scheduling and other scheduling problems are the subsets of RCPSP. The present paper examines the multimode multi-objective resource constrained project scheduling problem (RCPSP) with partial precedence relations. To enhance the practical aspects of this prominent problem, important practical purposes including minimizing the completion time of the project, maximizing the quality of project activities and minimizing the total cost of the project were considered. After validation of the model using the Bees Algorithm, the proposed multi-objective model was solved. The results obtained from the proposed model were compared with those obtained from NSGA-II. The results demonstrated the good performance of the proposed algorithm in solving RCPSPs.

Accurate scheduling of project is one of the main fundamentals and essential success factors of the project management and also accordance of planning and implementation is considered as the main subject of project management. In this paper, it is tried to propose a practical and suitable system in order to schedule various projects more accurately. Currently Program Evaluation and Review Technique (PERT) is used extensively for management of large- scaled projects. In traditional methods of PERT technique, implementation time of each activity is obtained in the form of definite figures or through Beta Distribution but in the real world; it is very hard to estimate the practical implementation time of each activity in an accurate way. By using fuzzy logic in order to overcome the problems related to uncertainty, fuzzy expert system is designed which many limitations and factors affecting the project completion time have been considered in this article. In this regard, output and input parameters of the system have been acquired by questionnaire and validation of the results has been analyzed. The obtained results indicate high power of the system in controlling different situations affecting the project completion time.

Selecting the best way to perform the project constituting activities is one of the most important issues in the project scheduling, so time and cost be proportionate with contractor or the employer's perspective to implement the project. The other hand considering that many activities in the majority of project and consequently many Choice options for activity implementation, So this choice does not possess a unique solution, But also includes a set of solutions, are not preferred None of which On the other and is called the Pareto solutions this set. Therefore, in this paper, is presented a mathematical model for project scheduling with multiple objectives based cost payment patterns and resource constraints Since this problem, is considered as combinational optimization in NP-hard problems. metaheuristic algorithm is used to solve the proposed model in project scheduling and has been evaluated for finding optimal solution by using comparable indicators algorithms performance. and ultimately for validation, obtained Solutions by the proposed algorithm were compared with the obtained exact solutions form the GAMS software. show that the obtained results the proposed algorithm are efficient and converges to the optimal solutions.

This research studies resource constrained project scheduling problem in a part of a refinery construction project in real world. In real world، most of the activities are new and we have problems such as activity duration uncertainty. This problem causes a change in a project makespan. The RCPSP is NP-hard. Hence، we proposed an optimization method based on simulated annealing to solve the RCPS Problem. In this paper، Fuzzy sets theory is used to represent this activity duration uncertainty. Used schedule generation scheme، in the proposed simulated annealing algorithm، is a fuzzy parallel scheduling generation method. Proposed algorithm generates the minimum project makespan while considers renewable resource-constrained and activity precedence and also has ability to perform with fuzzy numbers for presenting project details such as start and final time of activities and project whole time with fuzzy numbers. Finally، the results of the algorithm will be evaluated and it will be represented that the proposed algorithm is very efficient and can be used by managers and scheduling programmers in real projects.