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In this paper, first a fuzzy random resource-constrained project scheduling problem is presented. The object of the problem is to find the optimal scheduling of project activities. In this model, duration of project activities is a fuzzy random variable. Then, the proposed model is formulated by using the expected value of fuzzy random variables as an IP model. An illustrative example is also provided to clarify the concept. © 2010 World Academic Press, UK. All rights reserved  

In this paper, we propose a new mathematical programming model to tackle the multi-skilled project scheduling problem. Considering the effect of learning and forgetting on the human skills, an exponential learning function has been developed by assuming the efficiency of employees performing activities to be dynamic. Taking the nonlinearity of the function into account, we use separable programming to acquire an appropriate linear approximation for it. Moreover, the proposed model allows us to relax some of the binary variables linearly without any modifications. At the end, the final model is tested with some instances and is solved by CPLEX in order to confirm the implemented... 

In this paper, we study a resource-constrained project scheduling problem in which a set of project activities have due dates. If the finish time of each one of these activities is not equal to its due date, an earliness or a tardiness cost exists for each tardy or early period. The objective is to minimize the sum of discounted weighted earliness-tardiness penalty costs of these activities. Scatter Search algorithm is used to deal with this extended form of resource-constrained project scheduling problem. Our implementation of Scatter Search integrates the advanced methods such as dynamic updating of the reference set and the use of frequency-based memory within the diversification... 

Time, cost and quality are among the major objectives of any project. In recent years, the demands of project stakeholders regarding reductions in the total cost and time of a project along with achieving the desirable quality of the project have risen significantly. This leads researchers to developing models that incorporate the quality factor to previously existing time-cost trade-off models. This study presents a model for the discrete time-cost-quality trade-off problem. In this model there are a number of execution modes to select for each activity, and the best execution mode (t, c, q) of the activities should be determined to optimize total cost and time objectives, subjected to... 

Correct scheduling of the project is the necessary condition for the project success. In traditional models, the activities duration times are deterministic and known. In real world however, accurate calculation of time for performing each activity is not possible and is always faced with uncertainty. In this paper, the duration of each activity is estimated by the experts as linguistic variables and the said variables are represented in fuzzy numbers form using the fuzzy theory. Estimating the project accomplishment duration and determining the project critical path will be possible through resolving a fuzzy linear programming model. For solving model, Fuzzy Critical Path Method Algorithm... 

One subcategory of project scheduling is the resource constrained project scheduling problem (RCPSP). The present study proposes a differential evolution algorithm for solving the RCPSP making a small change in the method to comply with the model. The RCPSP is intended to program a group of activities of minimal duration while considering precedence and resource constraints. The present study introduces a differential evolution algorithm and local search was added to improve the performance of the algorithm. The problems were then solved to evaluate the performance of the algorithm and the results are compared with genetic algorithm. Computational results confirm that the differential... 

The present paper introduces a novel two-part self-adaptive technique in designing the genetic algorithm for project scheduling problems. One part of the algorithm includes a self-adaptive mechanism for genetic operators like crossover and mutation. The second part contains another self-adaptive mechanism for genetic parameters such as crossover probability. The parts come in turn repeatedly within a loop feeding each other with the information regarding the performance of operators or parameters. The capability of the method is tested and confirmed in comparison to metaheuristic and exact algorithms based on well-known benchmarks  

Satisfying the clients' uncompromising priorities is a challenge for decision makers of organizations that face multiple projects. This paper considers an organization with a multi-skilled workforce working on several predetermined projects under time-of-use energy tariffs where distributed load energy usage is the primary concern of energy suppliers. This paper also considers different time-of-use energy tariffs, which are among the most common strategies to reach a more balanced energy utilization. The problem is stated as a bi-objective mixed-integer programming model containing two conflicting objectives; to minimize the total cost of the multi-skilled workforce and obtain a sustainable... 

Most of the research works conducted on Project Scheduling Problem (PSP) especially Resource Constrain Project Scheduling Problem (RCPSP) either ignore equipment planning or schedule the activities first, and then plan for the required equipment. Moreover, little works that consider simultaneous PSP and Equipment Planning (EP) are based on the assumption that the equipment is continuously available. However, in reality, equipment is subject to either random breakdowns or deterministic maintenance programs that make it not being available all the time. In this paper, the PSP and EP problems are simultaneously considered in closer to reality situations in which the equipment is not always... 

Scheduling of the maintenance activities is considered, in which the duration of activities is uncertain, delivery date of the maintenance shutdown is predefined, and activities are multi-mode. The problem is a multi-mode time-constrained project scheduling problem (MTCPSP). The glycol regeneration unit in a gas refinery is as the case study. Based on the effect of equipment or sub-equipment on the system reliability, the importance value of equipment and sub-equipment within the system is determined, and these values are used in a heuristic algorithm as a priority rule for choosing activities in the schedule. Outcomes demonstrate the performance of the algorithm in early or on time delivery... 

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered.... 

A lot of projects in real life are subject to some kinds of nonrenewable resources that are not exactly similar to the type defined in the project scheduling literature. The difference stems from the fact that, in those projects, contrary to the common assumption in the project scheduling literature, nonrenewable resources are not available in full amount at the beginning of the project, but they are procured along the project horizon. In this paper, we study this different type of nonrenewable resources. To that end, we extend the resource constrained project scheduling problem (RCPSP) by this resource type (RCPSP-NR) and customize four basic branch and bound algorithms of RCPSP for it,... 

This research considers a project scheduling problem with the object of minimizing weighted earliness-tardiness penalty costs, taking into account a deadline for the project and precedence relations among the activities. An exact recursive method has been proposed for solving the basic form of this problem. We present a new depth-first branch and bound algorithm for extended form of the problem, which time value of money is taken into account by discounting the cash flows. The algorithm is extended with two bounding rules in order to reduce the size of the branch and bound tree. Finally, some test problems are solved and computational results are reported. © 2008 Asian Network for Scientific... 

The growing importance of energy consumption has become an integral part of many decision-making processes in various organizations. In this paper, a framework is proposed for an organization where the undertaken project is implemented by multi-skilled workforce and energy tariffs depending on the time-of-use. This is a real-life situation where energy tariffs are significantly high during the peak demand compared to the one in off peak demand in order to control overloaded consumption of energy. A formulation is developed for the problem to minimize the total cost of consuming required energy. The proposed formulation is validated using several small-scale instances solved by GAMS software.... 

In the project scheduling literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is very common that these resources are procured along the project horizon according to some pre-scheduled plan. In this paper, we study an extended form of the resource-constrained project scheduling problem that is subject to this type of nonrenewable resources in addition to the renewable resources. In order to solve this problem, we propose a branch and cut algorithm. We incorporate with the algorithm some technics and fathoming rules to shorten the solving process. The algorithm is capable of specifying lower bounds for the... 

Scheduling under nonrenewable resources is one of the challenging issues in project scheduling problems. There are many cases where the projects are subject to some nonrenewable resources. In most of the literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is prevalent that these resources are procured along the project horizon. This paper studies the generalized resource-constrained project scheduling problem (RCPSP) where, in addition to renewable resources, nonrenewable resources are considered, such as budget or consuming materials by the project activities. As the problem is NP-hard, some sub-algorithm... 

This paper considers a project scheduling problem with the objective of minimizing resource availability costs required to execute the activities in a project by a given project deadline. The project contains activities interrelated by finish-start-type precedence relations with a time lag of zero, which require a set of renewable resources. Two metaheuristics, path relinking and genetic algorithm, are developed to tackle this problem in which a schedule is created with a precedence feasible priority list given to the schedule generation scheme. In these procedures, each new generation of solutions are created using the combination of current solutions. Comparative computational results... 

A resource investment problem with discounted cash flows is a project scheduling problem in which the availability levels of the resources are considered decision variables and the goal is to find a schedule and resource requirement levels such that the net present value of the project cash flows optimizes. In this paper, we present a genetic algorithm to solve this problem. We explain the elements of the algorithm such as chromosome structure, fitness function, crossover, mutation, and local improvement operations and solve more than 220 problems with known optimal solutions to evaluate the performance of the proposed algorithm. The results of the experimentation are quite satisfactory. ©... 

Traditionally, the model of a resource-constrained project-scheduling problem (RCPSP) contains a single objective function of either minimizing project makespan or maximizing project net present value (NPV). In order to be more realistic, in this paper, two multi-objective meta-heuristic algorithms of multi-population and two-phase sub-population genetic algorithms are proposed to find Pareto front solutions that minimize the project makespan and maximize the project NPV of a RCPSP, simultaneously. Based on standard test problems constructed by the RanGen project generator, a comprehensive computational experiment is performed, where response surface methodology is employed to tune the...