A coordinated algorithm for integrated production scheduling and vehicle routing problem

In this paper, the integrated production scheduling and vehicle routing problem is considered for a Make-to-Order manufacturer, who has a single machine for production and limited vehicles with capacity constraints for transportation. The objective is to determine production scheduling and vehicle routing, which are two interacted decisions, to minimise the maximum order delivery time. A property on optimal production sequence is proposed first, based on which backward and forward batching methods are developed and are embedded into a proposed genetic algorithm. The proposed genetic algorithm is capable of providing high-quality solutions by determining the two decisions simultaneously. For comparison purpose, a two-stage algorithm is developed, which decomposes the overall problem into two successively solved sub-problems. The experiments show that the proposed genetic algorithm can provide higher quality solutions than the proposed two-stage algorithm and two published algorithms studying related problems.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

A memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.     

Bi-objective mathematical model and improved algorithm for optimisation of welding shop scheduling problem

This paper addresses a bi-objective welding shop scheduling problem (BWSSP) aiming to minimise the total tardiness and the machine interaction effect. The BWSSP is a special flow-shop scheduling problem (FSP) which is characterised by the fact that more than one machine can process on one job at a certain stage. This study analyses the operation of a structural metal manufacturing plant, and includes various aspects such as job sequence, machine-number-dependent processing time, lifting up time, lifting down time and different delivery time. A novel mixed-integer programming model (MIPM) is established, which can be used to minimise the delayed delivery time and the total machine interaction effect. One machine interaction effect formula is given in this paper. In order to solve this BWSSP, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII), embedded with a restarted strategy (RNSGAIII), is proposed. The restarted strategy, which can increase the diversity of the solutions, will be triggered with a restart probability. Following the iterative process, an effective strategy is applied to reduce the interaction effect penalty, on the premise that the makespan will remain unchanged. Total five algorithms, namely NSGAII, NSGAIII, harmony search algorithm (HSA), strength Pareto evolutionary algorithm (SPEA2), and RNSGAIII are utilised to solve this engineering problem. Numerical simulations show that the improved RNSGAIII outperforms the other methods, and the Pareto solution distribution and diversity, in particular, are significantly improved.     

A hybrid artificial bee colony algorithm for flexible job shop scheduling with worker flexibility

The traditional flexible job shop scheduling problem (FJSP) considers machine flexibility but not worker flexibility. Given the influence and potential of human factors in improving production efficiency and decreasing the cost in practical production systems, we propose a mathematical model of an extended FJSP with worker flexibility (FJSPW). A hybrid artificial bee colony algorithm (HABCA) is presented to solve the proposed FJSPW. For the HABCA, effective encoding, decoding, crossover and mutation operators are designed, and a new effective local search method is developed to improve the speed and exploitation ability of the algorithm. The Taguchi method of Design of Experiments is used to obtain the best combination of key parameters of the HABCA. Extensive computational experiments carried out to compare the HABCA with some well-performing algorithms from the literature confirm that the proposed HABCA is more effective than these algorithms, especially on large-scale FJSPW instances.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

Mathematical models and a hunting search algorithm for the no-wait flowshop scheduling with parallel machines

Majority of researches in no-wait flowshop scheduling assume that there is only one machine at each stage. But, factories commonly duplicate machines in parallel for each operation. In this case, they balance the speed of the stages, increase the throughput of the shop floor and reduce the impact of bottleneck stages. Despite their importance, there is no paper to study the general no-wait flowshop with parallel machines. This paper studies this problem where the objective is to minimise makespan. Since there is no mathematical model for the problem, we first mathematically formulate it in form of two mixed integer linear programming models. By the models, the small instances are optimally solved. We then propose a novel hunting search metaheuristic algorithm (HSA) to solve large instances of the problem. HSA is derived based on a model of group hunting of animals when searching for food. A set of experimental instances are carried out to evaluate the algorithm. The algorithm is carefully evaluated for its performance against an available algorithm by means of statistical tools. The related results show that the proposed HSA provides sound performance comparing with other algorithms.     

Estimation of distribution algorithm with path relinking for the blocking flow-shop scheduling problem

This article presents an effective estimation of distribution algorithm, named P-EDA, to solve the blocking flow-shop scheduling problem (BFSP) with the makespan criterion. In the P-EDA, a Nawaz–Enscore–Ham (NEH)-based heuristic and the random method are combined to generate the initial population. Based on several superior individuals provided by a modified linear rank selection, a probabilistic model is constructed to describe the probabilistic distribution of the promising solution space. The path relinking technique is incorporated into EDA to avoid blindness of the search and improve the convergence property. A modified referenced local search is designed to enhance the local exploitation. Moreover, a diversity-maintaining scheme is introduced into EDA to avoid deterioration of the population. Finally, the parameters of the proposed P-EDA are calibrated using a design of experiments approach. Simulation results and comparisons with some well-performing algorithms demonstrate the effectiveness of the P-EDA for solving BFSP.     

A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

An improved exact algorithm for single-machine scheduling to minimise the number of tardy jobs with periodic maintenance

In this paper, we investigate a single-machine scheduling problem with periodic maintenance, which is motivated by various industrial applications (e.g. tool changes). The pursued objective is to minimise the number of tardy jobs, because it is one of the important criteria for the manufacturers to avoid the loss of customers. The strong NP-hardness of the problem is shown. To improve the state-of-the-art exact algorithm, we devise a new branch-and-bound algorithm based on an efficient lower bounding procedure and several new dominance properties. Numerical experiments are conducted to demonstrate the efficiency of our exact algorithm.     

Genetic algorithm with local search for the unrelated parallel machine scheduling problem with sequence-dependent set-up times

In this paper, a genetic algorithm (GA) with local search is proposed for the unrelated parallel machine scheduling problem with the objective of minimising the maximum completion time (makespan). We propose a simple chromosome structure consisting of random key numbers in a hybrid genetic-local search algorithm. Random key numbers are frequently used in GAs but create additional difficulties when hybrid factors are implemented in a local search. The best chromosome of each generation is improved using a local search during the algorithm, but the better job sequence (which might appear during the local search operation) must be adapted to the chromosome that will be used in each successive generation. Determining the genes (and the data in the genes) that would be exchanged is the challenge of using random numbers. We have developed an algorithm that satisfies the adaptation of local search results into the GAs with a minimum relocation operation of the genes’ random key numbers – this is the main contribution of the paper. A new hybrid approach is tested on a set of problems taken from the literature, and the computational results validate the effectiveness of the proposed algorithm.     

An adaptive scheduling algorithm for a parallel machine problem with rework processes

The development of a scheduling methodology for a parallel machine problem with rework processes is presented in this paper. The problem is to make a schedule for parallel machines with rework probabilities, due-dates, and sequence dependent setup times. Two heuristics are developed based on a dispatching algorithm and problem-space-based search method. In order to evaluate the efficacy of the proposed algorithms, six performance indicators are considered: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of tardy jobs, and the number of reworks. This paper shows how these algorithms can adaptively capture the characteristics of manufacturing facilities for enhancing the performance under changing production environments. Extensive experimental results show that the proposed algorithms give very efficient performance in terms of computational time and each objective value.     

A modified harmony search algorithm for the multi-objective flowshop scheduling problem with due dates

This paper presents a modified harmony search optimisation algorithm (MHSO), specifically designed to solve two- and three-objective permutation flowshop scheduling problems, with due dates. To assess its capability, five sets of scheduling problems have been used to compare the MHSO with a known and highly efficient genetic algorithm (GA) chosen as the benchmark. Obtained results show that the new procedure is successful in exploring large regions of the solution space and in finding a significant number of Pareto non-dominated solutions. For those cases where the exhaustive evaluation of sequences can be applied the algorithm is able to find the whole non-dominated Pareto border, along with a considerable number of solutions that share the same optimal values for the considered optimisation parameters. To validate the algorithm, five sets of scheduling problems are investigated in-depth in comparison with the GA. Results obtained by both methods (exhaustive solutions have been provided as well for small sized problems) are fully described and discussed.     

A competitive memetic algorithm for the distributed two-stage assembly flow-shop scheduling problem

This article addresses the distributed two-stage assembly flow-shop scheduling problem (DTSAFSP) with makespan minimisation criterion. A mixed integer linear programming model is presented, and a competitive memetic algorithm (CMA) is proposed. When designing the CMA, a simple encoding scheme is proposed to represent the factory assignment and the job processing sequence; and a ring-based neighbourhood structure is designed for competition and information sharing. Moreover, some knowledge-based local search operators are developed to enhance the exploitation ability. The influence of parameter setting on the CMA is investigated using the analysis of variance method. Extensive computational tests and comparisons are carried out, which demonstrate the effectiveness of the proposed CMA in solving the DTSAFSP.     

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 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.     

An integrated model for multi-resource constrained scheduling problem considering multi-product and resource-sharing

This paper studies a multi-resource constrained scheduling problem considering multi-product and resource-sharing in the manufacturing supply chain, in which many independent production units coordinate with a truck resource manager. A mixed integer programming model is formulated to minimise the total system cost and some analytical properties are proposed to tighten the model. A Lagrangian relaxation-based heuristic with several enhancements, e.g. warm startup, approximating solve and parallel computation of subproblems, is proposed to solve the model. Finally, computational experiments are conducted to verify that (i) the proposed method has a better performance in both objective and CPU time than CPLEX, (ii) all three enhancements can help reduce the total computation time and (iii) a certain degree of resource-sharing can help reduce the total cost of the system.     

A modified generalized extremal optimization algorithm for the quay crane scheduling problem with interference constraints

The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.     

A bounded-search iterated greedy algorithm for the distributed permutation flowshop scheduling problem

As the interest of practitioners and researchers in scheduling in a multi-factory environment is growing, there is an increasing need to provide efficient algorithms for this type of decision problems, characterised by simultaneously addressing the assignment of jobs to different factories/workshops and their subsequent scheduling. Here we address the so-called distributed permutation flowshop scheduling problem, in which a set of jobs has to be scheduled over a number of identical factories, each one with its machines arranged as a flowshop. Several heuristics have been designed for this problem, although there is no direct comparison among them. In this paper, we propose a new heuristic which exploits the specific structure of the problem. The computational experience carried out on a well-known testbed shows that the proposed heuristic outperforms existing state-of-the-art heuristics, being able to obtain better upper bounds for more than one quarter of the problems in the testbed.