Resource-constrained Scheduling Problem Research Articles

A Comparative Study of Optimization Models for Condition-Based Maintenance Scheduling of an Aircraft Fleet

Condition-based maintenance (CBM) scheduling of an aircraft fleet in a disruptive environment while considering health prognostics for a set of systems is a very complex combinatorial problem, which is becoming more challenging in light of the uncertainty included in health prognostics. This type of problem falls under the broad category of resource-constrained scheduling problems under uncertainty and is often solved using a mixed integer linear programming (MILP) formulation. While a MILP framework is very promising, the problem size can scale exponentially with the number of considered aircraft and considered tasks, leading to significantly high computational costs. The most recent advances in artificial intelligence have demonstrated the capability of deep reinforcement learning (DRL) algorithms to alleviate this curse of dimensionality, as once the DRL agent is trained, it can achieve real-time optimization of the maintenance schedule. However, there is no guarantee of optimality. These comparative merits of a MILP and a DRL formulation for the aircraft fleet maintenance scheduling problem have not been discussed in the literature. This study is a response to this research gap. We conduct a comparison of a MILP and a DRL scheduling model, which are used to derive the optimal maintenance schedule for various maintenance scenarios for aircraft fleets of different sizes in a disruptive environment, while considering health prognostics and the available resources for the execution of each task. The quality of solutions is evaluated on the basis of four planning objectives, defined according to real airline practice. The results show that the DRL approach achieves better results with respect to scheduling of prognostics-driven tasks and requires less computational time, whereas the MILP model produces more stable maintenance schedules and induces less maintenance ground time. Overall, the comparison provides valuable insights for the integration of health prognostics in airline maintenance practice.

An Effective 4–Phased Framework for Scheduling Job-Shop Manufacturing Systems Using Weighted NSGA-II

Improving the performance of manufacturing systems is a vital issue in today’s rival market. For this purpose, during the last decade, scientists have considered more than one objective function while scheduling a production line. This paper develops a 4-phased fuzzy framework to identify effective factors, determine their weights on multi-objective functions, and, accordingly, schedule manufacturing systems in a fuzzy environment. The aim is to optimize product completion time and operational and product defect costs in a job-shop-based multi-objective fuzzy scheduling problem. In the first and second phases of the proposed framework, it was shown that the existing uncertainty of the internal factors for the studied cases causes the weights of factors to change up to 44.5%. Then, a fuzzy-weighted NSGA-II is proposed (FW-NSGA-II) to address the developed Non-linear Fuzzy Multi-objective Dual resource-constrained scheduling problem. Comparing the outcomes of the proposed method with other solving algorithms, such as the Sine Cosine Algorithm, Simulated Annealing, Tabu Search, and TLBO heuristic, using seven series of comprehensive computational experiments, indicates the superiority of the proposed framework in scheduling manufacturing systems. The outcomes indicated that using the proposed method for the studied cases saved up to 5% in the objective function for small-scale, 11.2% for medium-scale, and 3.8% for large-scale manufacturing systems. The outcomes of this study can help production planning managers to provide more realistic schedules by considering fuzzy factors in their manufacturing systems. Further investigating the proposed method for dynamic product conditions is another direction for future research.

Minimizing the total weighted completion time in relocation scheduling

This study investigates a resource-constrained scheduling problem to minimize the total weighted completion time. A set of jobs is to be processed on a single machine subject to the limited availability of a single-type resource. An initial level of the resource is provided to support the processing of the jobs. Each job requires an amount of the resource to commence its processing, and returns an amount of the resource back to the resource pool when its processing is finished. The amount of the resource consumed and that returned by each job may not be identical. Minimizing the total weighted completion time under this resource-constraint setting is known to be strongly NP-hard. In this study, we propose several optimality dominance properties, a lower bound and two approximate bounds for developments of branch-and-bound-based approximation algorithms. Heuristic algorithms and subsequent improvement procedures are deployed to produce initial upper bounds for the branch-and-bound-based approximation algorithms. We conduct computational experiments to appraise the performance of the proposed properties and algorithms.

Workers-constrained shutdown maintenance scheduling with skills flexibility: Models and solution algorithms

Shutdown maintenance (SM) projects are typically of a complex nature, have a predetermined time window, and require large number of limited resources such as multi-skill workers among many others. This paper devises two mixed-integer mathematical models along with efficient solution algorithms for the flexible multi-skill resource-constrained scheduling problem. Given the limited availability of multi-skill maintenance crew and the pressing need toward minimizing SM completion time, the proposed optimization models allow for the possibility of having a higher skilled worker perform a task requiring lower skill levels, if needed. Given the NP-hard nature of this problem, two constructive heuristics are developed, with the second adopting a multi-start approach for an improved exploration of the feasible solution space. The quality of the two heuristics is assessed using 60 randomly generated test instances of various sizes and complexities. The practical relevance of the problem is also illustrated via an industrial case study drawn from the cement industry. Numerical results suggest an average reduction of 16.52% in shutdown completion time when flexible workers are better utilized. The results also demonstrate the efficiency of the heuristics as they quickly yield solutions that are within average deviations of 1.24% and 2.71%, respectively, from the optimally solved instances. Upon developing efficient lower bounds, Heuristic-2 yields solutions that are on average 0.22% and 4.1% away from the lower bound for large instances involving 100 and 200 tasks, respectively, where optimal solutions for such instances are not attainable within reasonable computational time.

Hybrid differential evolution particle swarm optimization (DEA-DCWPSO) for resource-constrained multi-project scheduling problem

In this paper, we studied the resource constrained project scheduling problem, and the research object is extended to the multi-project environment. On the basis of multi-project priority evaluation, with the goal of minimizing the weighted duration of multi-project, a multi-project schedule planning model is constructed. Through reasonable scheduling of multiple parallel projects sharing resources under resource constraints, it provides a decision-making basis for project managers to allocate resources reasonably under resource constraints to meet the duration requirements of each project and to shorten the weighted total duration of multiple projects as much as possible. A two-stage hybrid differential evolution particle swarm optimization algorithm is used to solve the model. In the first stage, differential evolution algorithm is used to produce new individuals, and in the second stage, particle swarm optimization algorithm uses a new speed update formula. In the first stage, in order to ensure that the optimal individual will not be destroyed by crossover and mutation, and to maintain the convergence of differential evolution algorithm, we try to introduce Elitist Retention (ER) strategy into differential evolution algorithm. In the second stage, we use a kind of particle swarm optimization algorithm with dynamically changing inertia weight. Through the dynamic changing inertia weight, the global search and local search ability of the algorithm can be adjusted flexibly. The case verification shows that the hybrid differential evolution particle swarm optimization algorithm can be used to solve the RCMPSP model more effectively.

Optimising resource-constrained project probabilistic scheduling problem through a combination of simulation and meta-heuristic algorithm (case study: Govah Sanat Company)

Optimising resource-constrained project probabilistic scheduling problem through a combination of simulation and meta-heuristic algorithm (case study: Govah Sanat Company)

Optimizing resource-constrained project probabilistic scheduling problem through a combination of simulation and meta-heuristic algorithm (Case study: Govah Sanat Company)

Optimizing resource-constrained project probabilistic scheduling problem through a combination of simulation and meta-heuristic algorithm (Case study: Govah Sanat Company)

Dynamic Auto Reconfiguration of Operator Placement in Wireless Distributed Stream Processing Systems

The data is generated at significant speed and volume by devices in real-time. The data generation and the growth of fog and edge computing infrastructure have led to the noteworthy development of the corresponding distributed stream processing systems (DSPS). A DSPS application has Quality of Service (QoS) restrictions in terms of resource cost and time. The physical resources are distributed and heterogeneous. The resource-constrained scheduling problem has considerable implications on the performance of the system and QoS violations. The static deployment of applications in fog or edge scenario has to be monitored continuously for runtime issues, and actions have to be taken accordingly. In this paper, we propose an adaptation capability with reinforcement learning techniques to an existing stream processing framework scheduler. This functionality enables the scheduler to make decisions on its own when the system model or knowledge of the environment is not known upfront. The reinforcement learning methods adapt to the system when the system model for different states is not available. We consider applications whose workload cannot be characterized or predicted. In such applications, predictions of input load are not helpful for online scheduling. The Q-Learning based online scheduler learns to make dynamic scaling decisions at runtime when there is performance degradation. We validated the proposed approach with real-time and benchmark applications on a DSPS cluster. We obtained an average of 6% reduction in the response time and a 15% increase in the throughput when the Q Learning module is employed in the scheduler.

A quantitative approach for the long-term assessment of Railway Rapid Transit network construction or expansion projects

One of the main issues to address in the analysis of a public railway rapid transit network construction project is the assessment of expected revenue and cost. On a network topology already defined, the problem considered in this paper consists on finding the construction schedule that maximizes the project long-term net profit, not only deciding on the construction schedule and the network operation but also determining the subsidy to compensate the service operator along the considered long-term planning horizon. Aiming at early attending the demand of citizens, partial pieces of the constructed lines are put into service as soon as they were finished. Hence, in order to determine a subsidy to compensate service operators from a possible non-profitable network operation, it is necessary to measure the variable operation costs that emerge along with the progressive enlargement of a connected network. Further, the problem can be viewed as a particular case of a multiple resource-constrained scheduling problem, where both, the budget and the construction equipment availability act as limiting resources. We propose a non-linear mixed integer programming model which is fully linearized and solved by using a two-phase branch-and-cut procedure. We illustrate the proposed methodology within a real case, the Metro network project of the city of Seville.

Metaheuristics for the multi-task simultaneous supervision dual resource-constrained scheduling problem

This comprehensive study develops advantageous optimization methods to solve a nascent problem, namely multi-task simultaneous supervision dual resource-constrained (MTSSDRC) scheduling. MTSSDRC is a complex problem that deals with machine assignment, job sequencing, operator allocation, and task sequencing. Setup and unloading must be scheduled to operators, and they are allowed to leave machines while processing jobs. Earlier research on MTSSDRC developed a permutation-based genetic algorithm (PGA) with a specific decoding scheme, namely DSE, to solve the problem. Many previous studies succeed in solving scheduling problems by modifying well-known metaheuristic techniques. Therefore, we are inspired by this to explore further modifications to particular metaheuristics. The first contribution of the present study lies in the development of new decoding schemes that can perform better than the existing option. Five new decoding schemes are considered. Two of those schemes, namely DS2 and DS4, perform significantly better than DSE, reaching 6% relative deviation. DS4 is superior in terms of solution quality, but DS2 can run eight times faster. Another contribution is the development of six modified metaheuristics that are implemented for the MTSSDRC problem: tabu search, simulated annealing, particle swarm optimization, bees algorithm (BA), artificial bee colony, and grey wolf optimization. The performance of these metaheuristics is compared with that of the PGA. The results show that the PGA and BA are consistently superior for medium- and large-sized problems. The BA is more promising in terms of solution quality, but the PGA is faster.

Discrete imperialist competitive algorithm for the resource-constrained hybrid flowshop problem

ABSTRACT The resource constrained scheduling problem has been investigated widely in recent years, and many heuristic algorithms have been applied to solve this problem. In this study, we propose a discrete imperialist competitive algorithm (DICA) to solve a variety of resource-constrained hybrid flowshop scheduling problems with the objective of minimizing the completion time. In the proposed algorithm, we employ a two-phase-based coding mechanism, where a local search method is applied. Then, we combine DICA and simulated annealing algorithm (SA) to improve the performance of the algorithm. In addition, we consider the dynamic allocation of resources in the decoding process. We tested the proposed algorithm based on a randomly generated set of real shop scheduling system instances, as well as numerically analyzing and comparing the proposed algorithm with existing heuristic algorithms to verify its effectiveness.

NSGA-II variants for solving a social-conscious dual resource-constrained scheduling problem

This present study compares various non-dominated sorting genetic algorithm II (NSGA-II) variants to deal with multi-task simultaneous supervision dual resource-constrained (MTSSDRC) scheduling to minimize the makespan and workload unbalance among operators. MTSSDRC is a complex problem that needs to integrate two types of scheduling, i.e., job sequencing on the machines and task sequencing, which includes setup, unloading, and moving, by the operators. Since there are two resources, one may be busier than the other. Task sequencing should be prioritized if the operator is very busy, otherwise, we should accentuate the job sequencing. The existing NSGA-II variant prioritizes the machine assignment over the operator. Therefore, its performance is not so well when the operator-to-machine ratio is small. Thus, this proposed research develops two new NSGA-II variants identified by their modified decoding schemes. They posit the operator more important or at least equal to the machine. To the best of our knowledge, this research is the first to analyze MTSDDRC based on the operator-to-machine ratio. The essential finding insists that each variant fits the specific ratio. The new ones are promising for cases with a ratio ⩽0.5. Otherwise, the existing variant is still recommended. Besides, one of the new decoding schemes performs well for all ratio, but not the best.

Identical parallel machine scheduling with discrete additional resource and an application in audit scheduling

Resource scheduling has been one of the most prominent problems due to its technical challenges and prevalence in real-life. In this paper, we focus on an extension of the parallel machine scheduling problem with additional resources, which can be classified as a static resource-constrained parallel machine scheduling problem with unspecified job-machine assignment. The novelty of the problem we tackle stems from the additional resource that consists of components with discrete levels. The allocation of this resource to machines induces general covering constraints. This distinct characteristic of the additional resource also arises in a real-life audit scheduling problem, in which local branches of a financial firm are to be audited by a set of auditors with different experience levels. The quantification of the auditor experience and the branch experience requirement enable us to model this problem as an extension of the aforementioned scheduling problem with extra constraints related to the auditing process. We propose mathematical models for these problems and two constructive heuristic algorithms. The upper bounds attained by these algorithms are improved by a tabu-search algorithm, and an efficient lower bounding technique is developed for comparative purposes. We conduct extensive computational experiments to assess the performance of the proposed algorithms.

FBI inspired meta-optimization

This study developed a novel optimization algorithm, called Forensic-Based Investigation (FBI), inspired by the suspect investigation–location–pursuit process that is used by police officers. Although numerous unwieldy optimization algorithms hamper their usability by requiring predefined operating parameters, FBI is a user-friendly algorithm that does not require predefined operating parameters. The performance of parameter-free FBI was validated using four experiments: (1) The robustness and efficiency of FBI were compared with those of 12 representations of the top leading metaphors by using 50 renowned multidimensional benchmark problems. The result indicated that FBI remarkably outperformed all other algorithms. (2) FBI was applied to solve a resource-constrained scheduling problem associated with a highway construction project. The experiment demonstrated that FBI yielded the shortest schedule with a success rate of 100%, indicating its stability and robustness. (3) FBI was utilized to solve 30 benchmark functions that were most recently presented at the IEEE Congress on Evolutionary Computation (CEC) competition on bound-constrained problems. Its performance was compared with those of the three winners in CEC to validate its effectiveness. (4) FBI solved high-dimensional problems, by increasing the number of dimensions of benchmark functions to 1000. FBI is efficient because it requires a relatively short computational time for solving problems, it reaches the optimal solution more rapidly than other algorithms, and it efficaciously solves high-dimensional problems. Given that the experiments demonstrated FBI’s robustness, efficiency, stability, and user-friendliness, FBI is promising for solving various complex problems. Finally, this study provided the scientific community with a metaheuristic optimization platform for graphically and logically manipulating optimization algorithms.

Stochastic Optimization Approaches for Elective Surgery Scheduling and Downstream Capacity Planning: Models, Challenges, and Opportunities

Elective surgery patients receive surgery in the operating room (OR) and then recover in one or more subsequent downstream recovery units for several consecutive hours or days after surgery. Indeed, upstream scheduling that focuses on OR alone or a resource-constrained scheduling approach that fails to account for the inherent uncertainty in surgery durations and postoperative downstream recovery times yield sub-optimal or infeasible schedules and, consequently, higher cost and reduced quality of care. However, modeling such uncertainties at multiple levels is challenging, especially with limited reliable data on the random parameters in the models. Moreover, sequencing of surgical and recovery activities, and the multiple conflicting objectives of all parties involved (including management, clinicians, patients), lead to a class of complex combinatorial and multi- criteria stochastic optimization problems. In this review, we focus on stochastic optimization (SO) approaches for elective surgery scheduling and downstream capacity planning. We describe the art of formulating and solving such a class of stochastic resource-constrained scheduling problems, provide an analysis of existing SO approaches and their challenges, and highlight areas of opportunity for developing tractable, implementable, and data-driven approaches that might be applicable within and outside healthcare operations, particularly where multiple entities/jobs share the same downstream limited resources.

Entropy-Directed Scheduling for FPGA High-Level Synthesis

High-level synthesis (HLS) is important for compiling an application design onto field-programmable gate array (FPGA) but still faces challenges of balancing scalability and quality of results in the scheduling process. In this article, we propose an entropy-directed scheduling (EDS) algorithm that efficiently generates high-quality schedules for FPGA HLS. This article is novel in three ways. First, we make the first attempt to adopt entropy in the scheduling of HLS, which is an intuitive and robust measurement with lots of good analytic properties. Second, we creatively leverage the maximum entropy principle to describe the scheduling process, which is proved equivalent to the optimal solution in some particular cases. Third, we make EDS automatically analyze the input graph structure and leverage a three-stage scheduling process to obtain high-quality results. As a result, EDS has the lowest time complexity among existing scheduling algorithms and is flexible to solve both latency- and resource-constrained problems while satisfying other constraints. The experimental results show that for latency-constrained scheduling problem, EDS reduces up to 68% resource usage and is $294\times $ faster than the force-directed scheduling algorithm. For resource-constrained scheduling problem, EDS obtains near-optimal solutions with an average speedup of 16 $410\times $ compared with ILP. To our best knowledge, this is the first EDS algorithm for FPGA HLS.

A New Decision Support System for Optimal Integrated Project Scheduling and Resource Planning

Two scheduling practices are commonly used depending on the availability of resources. When resources are not expensive, activities are scheduled and then resources are allocated until the available resources are exhausted. Then, iterative adjustments are applied to the resource allocation plan and the activities sequence to reach a feasible solution. Conversely, when expensive resources are involved, a resource allocation plan based on the economics of the resource is established and then activities are scheduled accordingly. However, Resource Constrained Scheduling Problems (RCSP) are not solved efficiently with either of these approaches. To find the optimal solution, activity scheduling and resource allocation should be formulated as an integrated optimization problem. Such models become numerically cumbersome for practical size problems and difficult to solve. In this article, a novel mathematical formulation and an efficient solution algorithm are proposed for solving RCSPs. Then, this framework is used for solving a practical problem in the context of the construction industry.

Solving the resource-constrained multi-project scheduling problem with an improved critical chain method

In view of the fact that the critical chain method (CCM) is mainly used in single project scheduling, this article improves the method and applies it to multi-project scheduling. Taking into consideration the flow of the drum resource within and among sub-projects, this study proposes methods that can be used to identify the critical chain and buffer settings, based on the concepts of the task chain, sub-project drum resource flow, and multi-project drum resource flow. The improvement of the CCM includes two aspects. First, by analysing the impact of the drum buffer and capacity constrained buffer on the project buffer and feeding buffer, the calculation methods of these buffers are optimised. Second, a risk contribution index is designed for the modification of these buffers, in order to further improve their anti-interference ability. Then, combined with the improved CCM and the different hierarchical scheduling objectives, a critical chain resource-constrained multi-project scheduling model with a hierarchical strategy is proposed as a way of solving multi-project scheduling plans. Eight theoretical test cases with different scales, and a practical example under different risk levels of uncertainty are used to test this model. The results show that the stability of the scheduling plans clearly improved, and the project duration and tardiness costs were significantly reduced, thus proving the effectiveness of the model.

A hybrid multi-objective EDA for robust resource constraint project scheduling with uncertainty

This paper presents a multi-phased algorithm hybrid genetic algorithm and multi-objective Markov network based Estimation of Distribution Algorithm (robust hGMEDA), to solve the robust scheduling problem for resource constrained scheduling problem (RCSP) with time uncertainty. Firstly, for modelling, two kinds of robust measures on time-based-robust and capacity-based-robust are introduced to evaluate the robustness of scheduling solutions. Secondly, for solving methodology, within the multi stage architecture based on sequential co-evolutionary paradigm, genetic algorithm (GA) is used to find feasible solution for sequencing sub-problem, and multi-objective Markov network based Estimation of Distribution Algorithm (MMEDA) is adopted to model the interrelation for resource allocation and calculate the Pareto set with the scenario based approach. Next, the alternative solutions are checked by the chance constraints by using scenario-based simulation. Moreover, one problem-specific local search with considering both makespan and robustness is designed to improve the solution quality. The implementation results provide practical support that experiment results based on a benchmark “Project Scheduling Problems Library” (PSPLIB) and comparisons demonstrate that our approach is highly effective and tolerant of uncertainty.

A Constraint-Based Declarative Programming Framework for Scheduling and Resource Allocation Problems

Scheduling and resource allocation problems are widespread in many areas of today’s technology and management. Their different forms and structures appear in production, logistics, software engineering, computer networks, project and human resources management, services, etc. The literature (problem classification, scheduling and resource allocation models, solutions) is vast and exhaustive. In practice, however, classical scheduling problems with fixed structures and standard constraints (precedence, disjoint, etc.) are rare. Practical scheduling problems include also logical and nonlinear constraints, and they use nonstandard criteria of schedule evaluations. Indeed, in many cases, decision makers are interested in the feasibility and/or optimality of a given schedule for specified conditions formulated as general and/or specific questions. Thus, there is a need to develop a programming framework that will facilitate the modeling and solving of a variety of diverse scheduling problems. The framework should be able to (a) model any types of constraints, (b) ask questions/criteria relating to the schedule execution mode and (c) be highly effective in finding solutions (schedule development). This paper proposes such a constraint-based declarative programming framework for modeling and solving scheduling problems which satisfies the assumptions above. It was built with the Constraint Logic Programming (CLP) environment and supported with Mathematical Programming (MP). The functionality and effectiveness of this framework are presented with the use of an illustrative example for the resource-constrained scheduling problem with additional resources.