Hybrid genetic algorithm for bi-objective resource-constrained project scheduling

In this study, we considered a bi-objective, multi-project, multi-mode resource-constrained project scheduling problem. We adopted three objective pairs as combinations of the net present value (NPV) as a financial performance measure with one of the time-based performance measures, namely, makespan (C_max), mean completion time (MCT), and mean flow time (MFT) (i.e., minC_max/maxNPV, minMCT/maxNPV, and minMFT/maxNPV). We developed a hybrid non-dominated sorting genetic algorithm II (hybrid-NSGA-II) as a solution method by introducing a backward–forward pass (BFP) procedure and an injection procedure into NSGA-II. The BFP was proposed for new population generation and post-processing. Then, an injection procedure was introduced to increase diversity. The BFP and injection procedures led to improved objective functional values. The injection procedure generated a significantly high number of non-dominated solutions, thereby resulting in great diversity. An extensive computational study was performed. Results showed that hybrid-NSGA-II surpassed NSGA-II in terms of the performance metrics hypervolume, maximum spread, and the number of non-dominated solutions. Solutions were obtained for the objective pairs using hybrid-NSGA-II and three different test problem sets with specific properties. Further analysis was performed by employing cash balance, which was another financial performance measure of practical importance. Several managerial insights and extensions for further research were presented.     

A novel branch-and-bound algorithm for the chance-constrained resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introduced to deal with uncertainty in the RCPSP. In this paper, we propose a branch-and-bound (B&B) algorithm and a mixed integer linear programming (MILP) formulation that solve a sample average approximation of the CC-RCPSP. We introduce two different branching schemes and eight different priority rules for the proposed B&B algorithm. The computational results suggest that the proposed B&B procedure clearly outperforms both a proposed MILP formulation and a branch-and-cut algorithm from the literature.     

A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

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. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

Multi-objective optimization for the multi-mode finance-based project scheduling problem

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.     

An adaptive memory programming framework for the resource-constrained project scheduling problem

The Resource-Constrained Project Scheduling Problem (RCPSP) is one of the most intractable combinatorial optimisation problems that combines a set of constraints and objectives met in a vast variety of applications and industries. Its solution raises major theoretical challenges due to its complexity, yet presenting numerous practical dimensions. Adaptive memory programming (AMP) is one of the most successful frameworks for solving hard combinatorial optimisation problems (e.g. vehicle routing and scheduling). Its success stems from the use of learning mechanisms that capture favourable solution elements found in high-quality solutions. This paper challenges the efficiency of AMP for solving the RCPSP, to our knowledge, for the first time in the literature. Computational experiments on well-known benchmark RCPSP instances show that the proposed AMP consistently produces high-quality solutions in reasonable computational times.     

An iterated-local-search heuristic for the resource-constrained weighted earliness-tardiness project scheduling problem

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.     

Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem

This paper introduces an evolutionary algorithm as a procedure to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot-sizing and scheduling of raw materials in tanks and soft drinks in bottling lines, where setup costs and times depend on the previous items stored and bottled. A multi-population genetic algorithm approach with a novel representation of solutions for individuals and a hierarchical ternary tree structure for populations is proposed. Computational tests include comparisons with an exact approach for small-to-moderate-sized instances and with real-world production plans provided by a manufacturer.     

An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

This article proposes an extended continuous estimation of distribution algorithm (ECEDA) to solve the permutation flow-shop scheduling problem (PFSP). In ECEDA, to make a continuous estimation of distribution algorithm (EDA) suitable for the PFSP, the largest order value rule is applied to convert continuous vectors to discrete job permutations. A probabilistic model based on a mixed Gaussian and Cauchy distribution is built to maintain the exploration ability of the EDA. Two effective local search methods, i.e. revolver-based variable neighbourhood search and Hénon chaotic-based local search, are designed and incorporated into the EDA to enhance the local exploitation. The parameters of the proposed ECEDA are calibrated by means of a design of experiments approach. Simulation results and comparisons based on some benchmark instances show the efficiency of the proposed algorithm for solving the PFSP.     

A differential evolution algorithm for the no-idle flowshop scheduling problem with total tardiness criterion

In this paper, we investigate the use of a continuous algorithm for the no-idle permutation flowshop scheduling (NIPFS) problem with tardiness criterion. For this purpose, a differential evolution algorithm with variable parameter search (vpsDE) is developed to be compared to a well-known random key genetic algorithm (RKGA) from the literature. The motivation is due to the fact that a continuous DE can be very competitive for the problems where RKGAs are well suited. As an application area, we choose the NIPFS problem with the total tardiness criterion in which there is no literature on it to the best of our knowledge. The NIPFS problem is a variant of the well-known permutation flowshop (PFSP) scheduling problem where idle time is not allowed on machines. In other words, the start time of processing the first job on a given machine must be delayed in order to satisfy the no-idle constraint. The paper presents the following contributions. First of all, a continuous optimisation algorithm is used to solve a combinatorial optimisation problem where some efficient methods of converting a continuous vector to a discrete job permutation and vice versa are presented. These methods are not problem specific and can be employed in any continuous algorithm to tackle the permutation type of optimisation problems. Secondly, a variable parameter search is introduced for the differential evolution algorithm which significantly accelerates the search process for global optimisation and enhances the solution quality. Thirdly, some novel ways of calculating the total tardiness from makespan are introduced for the NIPFS problem. The performance of vpsDE is evaluated against a well-known RKGA from the literature. The computational results show its highly competitive performance when compared to RKGA. It is shown in this paper that the vpsDE performs better than the RKGA, thus providing an alternative solution approach to the literature that the RKGA can be well suited.     

A genetic algorithm for solving the economic lot scheduling problem in flow shops

In this study, we propose a hybrid genetic algorithm (HGA) to solve the economic lot scheduling problem in flow shops. The proposed HGA utilizes a so-called Proc PLM heuristic that tests feasibility for the candidate solutions obtained in the evolutionary process of genetic algorithm. When a candidate solution is infeasible, we propose to use a binary search heuristic to ‘fix’ the candidate solution so as to obtain a feasible solution with the minimal objective value. To evaluate the performance of the proposed HGA, we randomly generate a total of 2100 instances from seven levels of utilization rate ranged from 0.45 to 0.80. We solve each of those 2100 instances by the proposed HGA and the other solution approaches in the literature. Our experiments show that the proposed HGA outperforms traditional methods for solving the economic lot scheduling problem in flow shops.     

Open shop scheduling problem with a multi-skills resource constraint: a genetic algorithm and an ant colony optimisation approach

The continuous evolution of manufacturing environments leads to a more efficient production process that controls an increasing number of parameters. Production resources usually represent an important constraint in a manufacturing activity, specially talking about the management of human resources and their skills. In order to study the impact of this subject, this paper considers an open shop scheduling problem based on a mechanical production workshop to minimise the total flow time including a multi-skill resource constraint. Then, we count with a number of workers that have a versatility to carry out different tasks, and according to their assignment a schedule is generated. In that way, we have formulated the problem as a linear as and a non-linear mathematical model which applies the classic scheduling constraints, adding some different resources constraints related to personnel staff competences and their availability to execute one task. In addition, we introduce a genetic algorithm and an ant colony optimisation (ACO) method to solve large size problems. Finally, the best method (ACO) has been used to solve a real industrial case that is presented at the end.     

A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem

An optimization algorithm based on the ‘divide-and-conquer’ methodology is proposed for solving large job shop scheduling problems with the objective of minimizing total weighted tardiness. The algorithm adopts a non-iterative framework. It first searches for a promising decomposition policy for the operation set by using a simulated annealing procedure in which the solutions are evaluated with reference to the upper bound and the lower bound of the final objective value. Subproblems are then constructed according to the output decomposition policy and each subproblem is related to a subset of operations from the original operation set. Subsequently, all these subproblems are sequentially solved by a particle swarm optimization algorithm, which leads directly to a feasible solution to the original large-scale scheduling problem. Numerical computational experiments are carried out for both randomly generated test problems and the real-world production data from a large speed-reducer factory in China. Results show that the proposed algorithm can achieve satisfactory solution quality within reasonable computational time for large-scale job shop scheduling problems.     

Optimisation of the reverse scheduling problem by a modified genetic algorithm

Traditional scheduling methods can only arrange the operations on corresponding machines with appropriate sequences under pre-defined environments. This means that traditional scheduling methods require that all parameters to be determined before scheduling. However, real manufacturing systems often encounter many uncertain events. These will change the status of manufacturing systems. These may cause the original schedule to no longer be optimal or even to be infeasible. Traditional scheduling methods, however, cannot cope with these cases. New scheduling methods are needed. Among these new methods, one method ‘reverse scheduling’ has attracted more and more attentions. This paper focuses on the single-machine reverse scheduling problem and designs a modified genetic algorithm with a local search (MLGA) to solve it. To improve the performance of MLGA, efficient encoding, offspring update mechanism and a local search have been employed and developed. To verify the feasibility and effectiveness of the proposed MLGA, 27 instances have been conducted and results have been compared with existing methods. The results show that the MLGA has achieved satisfactory improvement. This approach also has been applied to solve a real-world scheduling problem from one shipbuilding industry. The results show that the MLGA can bring some benefits.     

An effective shuffled frog-leaping algorithm for solving the hybrid flow-shop scheduling problem with identical parallel machines

In this article, an effective shuffled frog-leaping algorithm (SFLA) is proposed to solve the hybrid flow-shop scheduling problem with identical parallel machines (HFSP-IPM). First, some novel heuristic decoding rules for both job order decision and machine assignment are proposed. Then, three hybrid decoding schemes are designed to decode job order sequences to schedules. A special bi-level crossover and multiple local search operators are incorporated in the searching framework of the SFLA to enrich the memetic searching behaviour and to balance the exploration and exploitation capabilities. Meanwhile, some theoretical analysis for the local search operators is provided for guiding the local search. The parameter setting of the algorithm is also investigated based on the Taguchi method of design of experiments. Finally, numerical testing based on well-known benchmarks and comparisons with some existing algorithms are carried out to demonstrate the effectiveness of the proposed algorithm.     

A hybrid genetic algorithm and tabu search for a multi-objective dynamic job shop scheduling problem

In most real manufacturing environments, schedules are usually inevitable with the presence of various unexpected disruptions. In this paper, a rescheduling method based on the hybrid genetic algorithm and tabu search is introduced to address the dynamic job shop scheduling problem with random job arrivals and machine breakdowns. Because the real-time events are difficult to express and take into account in the mathematical model, a simulator is proposed to tackle the complexity of the problem. A hybrid policy is selected to deal with the dynamic feature of the problem. Two objectives, which are the schedule efficiency and the schedule stability, are considered simultaneously to improve the robustness and the performance of the schedule system. Numerical experiments have been designed to test and evaluate the performance of the proposed method. This proposed method has been compared with some common dispatching rules and meta-heuristic algorithms that have been widely used in the literature. The experimental results illustrate that the proposed method is very effective in various shop-floor conditions.     

An effective hybrid immune algorithm for solving the distributed permutation flow-shop scheduling problem

In this article, an effective hybrid immune algorithm (HIA) is presented to solve the distributed permutation flow-shop scheduling problem (DPFSP). First, a decoding method is proposed to transfer a job permutation sequence to a feasible schedule considering both factory dispatching and job sequencing. Secondly, a local search with four search operators is presented based on the characteristics of the problem. Thirdly, a special crossover operator is designed for the DPFSP, and mutation and vaccination operators are also applied within the framework of the HIA to perform an immune search. The influence of parameter setting on the HIA is investigated based on the Taguchi method of design of experiment. Extensive numerical testing results based on 420 small-sized instances and 720 large-sized instances are provided. The effectiveness of the HIA is demonstrated by comparison with some existing heuristic algorithms and the variable neighbourhood descent methods. New best known solutions are obtained by the HIA for 17 out of 420 small-sized instances and 585 out of 720 large-sized instances.     

Comparison of genetic and binary particle swarm optimization algorithms on system maintenance scheduling using prognostics information

Recent technical advances in condition-based maintenance technology have made it possible to not only diagnose existing failures, but also forecast future failures, which is called prognostics. A common method of maintenance scheduling in condition-based maintenance is to apply thresholds to prognostics information, which is not appropriate for systems consisting of multiple serially connected machinery. Maintenance scheduling is defined as a binary optimization problem and has been solved with a genetic algorithm. In this article, various binary particle swarm optimization methods are analysed and compared with each other and a genetic algorithm on a maintenance-scheduling problem for condition-based maintenance systems using prognostics information. The trade-off between maintenance and failure is quantified as the risk to be minimized. The forecasted failure probability of serially connected machinery is utilized in the analysis of the whole system. In addition to the comparison of a genetic algorithm and binary particle swarm optimization methods, a new binary particle swarm optimization that combines the good sides of two binary particle swarm optimizations is presented.     

A workload balancing genetic algorithm for the quay crane scheduling problem

This paper proposes a novel genetic algorithm to deal with the quay crane scheduling problem (QCSP), which is known to be one of the most critical tasks in terminal operations because its efficiency and the quality of the schedule directly influence the productivity of the terminal. QCSP has been studied intensively in recent years. Algorithms in this field are concerned in the solution quality obtained and the required computational time. As QCSP is known to be NP-hard, heuristic approaches are widely adopted. The genetic algorithm proposed is constructed with a novel workload balancing heuristics, which is capable of considering the loading conditions of different quay cranes (QCs) during the reassignment of task-to-QC. The idea is modelled as a fuzzy logic controller to guide the mutation rate and mutation mechanism of the genetic algorithm. As a result, the proposed algorithm does not require any predefined mutation rate. Meanwhile, the genetic algorithm can more adequately reassign tasks to QCs according to the QCs’ loading condition throughout the evolution. The proposed algorithm has been tested with the well-known benchmark problem sets in this field and produces some new best solutions in a much shorter computational time.     

Simultaneous planning of the project scheduling and material procurement problem under the presence of multiple suppliers

Simultaneous planning of project scheduling and material procurement can improve the project execution costs. Hence, the issue has been addressed here by a mixed-integer programming model. The proposed model facilitates the procurement decisions by accounting for a number of suppliers offering a distinctive discount formula from which to purchase the required materials. It is aimed at developing schedules with the best net present value regarding the obtained benefit and costs of the project execution. A genetic algorithm is applied to deal with the problem, in addition to a modified version equipped with a variable neighbourhood search. The underlying factors of the solution methods are calibrated by the Taguchi method to obtain robust solutions. The performance of the aforementioned methods is compared for different problem sizes, in which the utilized local search proved efficient. Finally, a sensitivity analysis is carried out to check the effect of inflation on the objective function value.     

The integration of resource allocation and time buffering for bi-objective robust project scheduling

In the recent decades, the recognition that uncertainty lies at the heart of modern project management has induced considerable research efforts on robust project scheduling for dealing with uncertainty in a scheduling environment. The literature generally provides two main strategies for the development of a robust predictive project schedule, namely robust resource allocation and time buffering. Yet, the previous studies seem to have neglected the potential benefits of an integration between the two. Besides, few efforts have been made to protect simultaneously the project due date and the activity start times against disruptions during execution, which is desperately demanded in practice. In this paper, we aim at constructing a proactive schedule that is not only short in time but also less vulnerable to disruptions. Firstly, a bi-objective optimisation model with a proper normalisation of the two components is proposed in the presence of activity duration variability. Then a two-stage heuristic algorithm is developed which deals with a robust resource allocation problem in the first stage and optimally determines the position and the size of time buffers using a simulated annealing algorithm in the second stage. Finally, an extensive computational experiment on the PSPLIB network instances demonstrates the superiority of the combination between resource allocation and time buffering as well as the effectiveness of the proposed two-stage algorithm for generating proactive project schedules with composite robustness.