Resource–constrained project scheduling: a heuristic for the multi–mode case

Resource levelling for projects with schedule-dependent time windows

An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes

Multi-mode resource leveling in projects with mode-dependent generalized precedence relations

This paper deals with the weighted earliness-tardiness resource-constrained project scheduling problem with minimum and maximum time lags (WET-RCPSP/max). The problem consists of scheduling the activities of a project subject to prescribed resource and temporal constraints such that the total weighted deviation of the activities' completion times from prescribed due dates is minimized. Key applications are planning of just-in-time production and reactive scheduling. For the (approximative) solution of the WET-RCPSP/max, we present a population-based iterated-local-search heuristic. We also report the results of an experimental performance analysis where this heuristic outperformed state-of-the-art methods.

Resource-constrained project scheduling (RCPS) aims to minimize project duration under limited resource availabilities. The heuristic methods that are often used to solve the RCPS problem make use of different priority rules. The comparative merits of different priority rules have not been discussed in the literature in sufficient detail. This study is a response to this research gap. It compares 17 heuristic priority rules and seeks the best performing heuristic priority rule. This is the first study ever that compares heuristic priority rules by considering combinations of variations in (1) resource allocation procedures, (2) number of activities, (3) number of resource constraints, and (4) resource supply levels. The objective is to understand the relative merits of heuristic rules used in solving the RCPS problem. The findings indicate that the “minimum late finish time” rule generates the shortest predicted project duration when used in parallel resource allocation, whereas the “minimum late start time”, “minimum late finish time”, and the “highest rank of positional weight 2” rules perform best in serial resource allocation. It was also found that parallel resource allocation is slightly superior to serial resource allocation in most instances.

In this study, a new heuristic approach to the resource constrained project scheduling problem is introduced. This approach, which is called local constraint based analysis (LCBA), is more robust than the dispatching rules found in the literature, since it does not depend on an a priori insight as do the dispatching rules. LCBA consists of the application of local essential conditions which respect the current temporal and resource constraints to generate a necessary sequence of activities at a scheduling decision time point in a single-pass parallel scheduling algorithm. LCBA is a time efficient procedure due to the localized aspect with which the activities are handled. Only the activities which are schedulable at the current scheduling time are considered for the application of the essential conditions. LCBA is tested against well-known rules from the literature and some recently developed rules. This testing is done using a set of problems of a special design and also a set of optimally solved problems from a recent benchmark in the literature. It is observed that near optimal time efficient solutions are obtained by LCBA and the procedure's performance is considerably better than that of the dispatching rules.

As an archipelagic country, Indonesia has high needs for its aviation development. About 270 million people are predicted to fly from and within Indonesia in 2034, which is three times larger than current market conditions. Due to the complexity of aircraft development projects, management of a well-designed Indonesian aircraft design project needs to be implemented. This research aims to analyze the scheduling of aircraft wing structure design project made in Indonesia. Critical Path Method (CPM) and Resource-Constrained Project Scheduling (RCPS) are used to get better scheduling with a shorter duration to complete the project. Results from resource allocation using RCPS can yield a shorter project duration (730 working days) compared to the company’s normal resource allocation (950 working days).

In this study, a cluster-based heuristic algorithm to solve multi-mode resource constrained project scheduling problem (MMRCPSP) is presented. The MMRCPSPs are usually challenging to schedule because each activity has multiple execution modes with renewable and non-renewable resources that are categorized as an NP-hard problem. In this paper, we propose and apply three ideas to solve an MMRCPSP. Firstly, an MMRCPSP with two objectives namely, makespan and executive cost is converted into a single mode resource-constrained project scheduling problem (RCPSP) with three objectives by relaxing the non-renewable resource constraints and then defining a corresponding penalty value. In the second phase, in the light of precedence and renewable resource constraints, the new RCPSP are scheduled by calling the multi-directional scheduling schemes (multi-dss). In the end, on the basis of three objectives’ value (namely makespan, cost, and penalty value), we defined a density-based fitness function for an evolutionary approach regarding the clustering methods on the new solution space. Our numerical results showed that the multi-dss with higher dimension regarding the automatic cluster-based fitness functions affected the performance of the evolutionary approach. Furthermore, the evolutionary approach based on multi-directional scheduling schemes prevents to trap into the local optimums by increasing the solutions’ diversity.

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

In recent years, the resource-constrained project scheduling problem RCPSP with multiple execution modes is becoming more and more popular. In this paper, a new cooperative coevolutionary algorithm based on the concept of organizations, namely Organizational Cooperative Coevolutionary Algorithm for MRCPSPs OCCA-MRCPSPs, is proposed for solving this problem. The objective is to find a schedule of activities together with their execution modes so that the makespan is minimized. In the OCCA-MRCPSPs, the population is divided into two subpopulations, for activities execution modes, respectively. The two subpopulations evolve independently, and each subpopulation is composed of organizations. During the evolutionary process, the global searching and the local searching are combined efficiently by conducting different operators. At first, each subpopulation searches the whole space of its domain through the splitting operator, the annexing operator, and the cooperation operator. Afterwards, the two subpopulations are combined to form complete solutions, and a local search operator is performed. In the experiments, the performance of OCCA-MRCPSPs is validated on benchmark problem sets J10, J12, J14, and J16 from the PLPSIB, and the experimental results show that the OCCA-MRCPSPs obtains a good performance not only in terms of the optimal solutions found but also in terms of the average deviations from optimal solutions.

Optimizing the operation of cooperative multi-agent systems that can deal with large and realistic problems has become an important focal area of research in the multi-agent community. In this paper, we first present a new model, the OC-DEC-MDP (Opportunity Cost Decentralized Markov Decision Process), that allows us to represent large multi-agent decision problems with temporal and precedence constraints. Then, we propose polynomial algorithms to efficiently solve problems formalized by OC-DEC-MDPs. The problems we deal with consist of a set of agents that have to execute a set of tasks in a cooperative way. The agents cannot communicate during task execution and they must respect resource and temporal constraints. Our approach is based on Decentralized Markov Decision Processes (DEC-MDPs) and uses the concept of opportunity cost borrowed from economics to obtain approximate control policies. Experimental results show that our approach produces good quality solutions for complex problems which are out of reach of existing approaches.

The Resource-Constrained Project Scheduling Problem (RCPSP) is a general problem class of scheduling problems. It even contains the well-known job shop scheduling problem as a special case. In these problems, jobs demand different amounts from multiple resources at once. The goal is to minimize completion time while satisfying resource capacity constraints throughout the schedule. The RCPSP has several variations and generalizations, one of which is the multi-mode problem. Multiple operation modes are given for jobs, differing in resource usages and execution times. Another generalization is where resources have time-varying capacities instead of a constant limit. The S-graph framework was developed for batch process scheduling and used successfully in various applications. The advantages of this approach motivate research to extend its capabilities to more general problem classes and apply it in various specialized case studies. The authors have previously presented an extension of the S-graph framework for RCPSP and its multi-mode generalization. In this work, a further extension is proposed for handling time-varying capacities. The method relies on a model transformation technique and recent algorithmic developments of the framework.

A production scheduling and control system for CAR T cell manufacturing

This paper introduces methods for formulating and solving a general class of nonpreemptive resource-constrained project scheduling problems in which the duration of each job is a function of the resources committed to it. The approach is broad enough to permit the evaluation of numerous time or resource-based objective functions, while simultaneously taking into account a variety of constraint types. Typical of the objective functions permitted are minimize project duration, minimize project cost given performance payments and penalties, and minimize the consumption of a critical resource. Resources which may be considered include those which are limited on a period-to-period basis such as skilled labor, as well as those such as money, which are consumed and constrained over the life of the project. At the planning stage the user of this approach is permitted to identify several alternative ways, or modes, of accomplishing each job in the project. Each mode may have a different duration, reflecting the magnitude and mix of the resources allocated to it. At the scheduling phase, the procedure derives a solution which specifies how each job should be performed, that is, which mode should be selected, and when each mode should be scheduled. In order to make the presentation concrete, this paper focuses on two problems: given multiple resource restrictions, minimize project completion time, and minimize project cost. The latter problem is also known as the resource-constrained time-cost tradeoff problem. Computational results indicate that the procedures provide cost-effective optimal solutions for small problems and good heuristic solutions for larger problems. The programmed solution algorithms are relatively simple and require only modest computing facilities, which permits them to be potentially useful scheduling tools for organizations having small computer systems.

The authors consider the problem of minimizing the duration of a project under fixed resource constraints. For the case that there are only minimal time lags between the start of successive activities and that therefore the project can be described by an acyclic network, a large number of exact and heuristic algorithms can be found in the literature. In this paper, the authors permit both minimal and maximal time lags between activities. The project can then be modelled by an activityon-node network containing cycles. Efficient priority-rule heuristics are presented for solving the resource-constrained project-scheduling problem. Computational results are discussed for projects containing up to 1000 activities and several resources.