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.     

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.     

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.     

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.     

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 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.     

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.     

Incorporating supplier selection and order allocation into the vehicle routing and multi-cross-dock scheduling problem

In the vehicle routing problem with cross-docking (VRPCD), it is assumed that the selected suppliers and the quantity of the products purchased from each supplier are known. This paper presents an MILP model which incorporates supplier selection and order allocation into the VRPCD in a multi-cross-dock system minimising the total costs, including purchasing, transportation, cross-docking, inventory and early/tardy delivery penalty costs. The sensitivity of the model on the key parameters of the objective function is analysed and the supply decisions are evaluated when the coefficients of the distribution cost are changed. A two-stage solution algorithm (TSSA) is proposed and the results of the TSSA for small-sized instances are compared with the exact solutions. Finally, a large-sized real case of an urban freight transport is solved using the TSSA.     

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.     

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

A flow-shop scheduling problem with blocking has important applications in a variety of industrial systems but is underrepresented in the research literature. In this study, a novel discrete artificial bee colony (ABC) algorithm is presented to solve the above scheduling problem with a makespan criterion by incorporating the ABC with differential evolution (DE). The proposed algorithm (DE-ABC) contains three key operators. One is related to the employed bee operator (i.e. adopting mutation and crossover operators of discrete DE to generate solutions with good quality); the second is concerned with the onlooker bee operator, which modifies the selected solutions using insert or swap operators based on the self-adaptive strategy; and the last is for the local search, that is, the insert-neighbourhood-based local search with a small probability is adopted to improve the algorithm's capability in exploitation. The performance of the proposed DE-ABC algorithm is empirically evaluated by applying it to well-known benchmark problems. The experimental results show that the proposed algorithm is superior to the compared algorithms in minimizing the makespan criterion.     

A model, heuristic procedure and decision support system for solving the movie shoot scheduling problem

Creating a movie shoot schedule is an important part of the movie production process. Even for a small movie project already 50 activities requiring 130 resources such as different actors, director, team, special effects and locations etc. have to be scheduled respecting complex constraints which may be imposed on single resources as well as on every activity. In this paper, we present the movie shoot scheduling problem and formulate a conceptual model. We present a metaheuristic approach for generating operational schedules, outline the modules of the decision support system Schedule This which we have developed and finally we shortly report practical experiences. Our experience from using the DSS in real movie shooting projects shows significant improvements with respect to faster and better scheduling as well as ad hoc re-scheduling.     

An artificial bee colony algorithm for the economic lot scheduling problem

In this study, we present an artificial bee colony (ABC) algorithm for the economic lot scheduling problem modelled through the extended basic period (EBP) approach. We allow both power-of-two (PoT) and non-power-of-two multipliers in the solution representation. We develop mutation strategies to generate neighbouring food sources for the ABC algorithm and these strategies are also used to develop two different variable neighbourhood search algorithms to further enhance the solution quality. Our algorithm maintains both feasible and infeasible solutions in the population through the use of some sophisticated constraint handling methods. Experimental results show that the proposed algorithm succeeds to find the all the best-known EBP solutions for the high utilisation 10-item benchmark problems and improves the best known solutions for two of the six low utilisation 10-item benchmark problems. In addition, we develop a new problem instance with 50 items and run it at different utilisation levels ranging from 50 to 99% to see the effectiveness of the proposed algorithm on large instances. We show that the proposed ABC algorithm with mixed solution representation outperforms the ABC that is restricted only to PoT multipliers at almost all utilisation levels of the large instance.     

A heuristic algorithm for master production scheduling problem with controllable processing times and scenario-based demands

Master production scheduling (MPS) is widely used by manufacturing industries in order to handle the production scheduling decisions in the production planning hierarchy. The classical approach to MPS assumes infinite capacity, fixed (i.e. non-controllable) processing times and a single pre-determined scenario for the demand forecasts. However, the deterministic optimisation approaches are sometimes not suitable for addressing the real-world problems with high uncertainty and flexibility. Accordingly, in this paper, we propose a new practical model for designing an optimal MPS for the environments in which processing times may be controllable by allocating resources such as facilities, energy or manpower. Due to the NP-hardness of our model, an efficient heuristic algorithm using local search technique and theory of constraints is developed and analysed. The computational results especially for large-sized test problems show that the average optimality gap of proposed algorithm is four times lower than that of exact solution using GAMS while it consumes also significantly smaller run times. Also, the analysis of computational results confirms that considering the controllable processing times may improve the solution space and help to more efficiently utilise the available resources. According to the model structure and performance of the algorithm, it may be proposed for solving large and complex real-world problems particularly the machining and steel industries.     

Tabu search for the job-shop scheduling problem with multi-purpose machines

In this paper we study the following generalization of the job-shop scheduling problem. Each operation can be performed by one machine out of a set of machines given for this operation. The processing time does not depend on the machine which has been chosen for processing the operation. This problem arises in the area of flexible manufacturing. As a generalization of the jobshop problem it belongs to the hardest problems in combinatorial optimization. We show that an application of tabu search techniques to this problem yields excellent results for benchmark problems.Supported by Deutsche Forschungsgemeinschaft, Project JoP-TAG     

A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem

This paper deals with the two-stage assembly flowshop scheduling problem with minimisation of weighted sum of makespan and mean completion time as the objective. The problem is NP-hard, hence we proposed a meta-heuristic named imperialist competitive algorithm (ICA) to solve it. Since appropriate design of the parameters has a significant impact on the algorithm efficiency, we calibrate the parameters of this algorithm using the Taguchi method. In comparison with the best algorithm proposed previously, the ICA indicates an improvement. The results have been confirmed statistically.