A new heuristic for the flowshop scheduling problem to minimize makespan and maximum tardiness

This paper presents a new heuristic for solving the flowshop scheduling problem that aims to minimize makespan and maximize tardiness. The algorithm is able to take into account the aforementioned performance measures, finding a set of non-dominated solutions representing the Pareto front. This method is based on the integration of two different techniques: a multi-criteria decision-making method and a constructive heuristic procedure developed for makespan minimization in flowshop scheduling problems. In particular, the technique for order preference by similarity of ideal solution (TOPSIS) algorithm is integrated with the Nawaz–Enscore–Ham (NEH) heuristic to generate a set of potential scheduling solutions. To assess the proposed heuristic's performance, comparison with the best performing multi-objective genetic local search (MOGLS) algorithm proposed in literature is carried out. The test is executed on a large number of random problems characterized by different numbers of machines and jobs. The results show that the new heuristic frequently exceeds the MOGLS results in terms of both non-dominated solutions, set quality and computational time. In particular, the improvement becomes more and more significant as the number of jobs in the problem increases.     

Minimizing total tardiness of orders with reentrant lots in a hybrid flowshop

This study focuses on a hybrid flowshop scheduling problem, in which there are serial stages, each with identical parallel machines. In the hybrid flowshop, each order is composed of multiple lots with the same due date, and each lot can be processed on any one of parallel machines at each stage. In addition, there are reentrant flows since lots of certain orders have to visit the stages twice. Heuristic algorithms are suggested for the scheduling problem with the objective of minimizing total tardiness of a given set of orders. In these algorithms, the list-scheduling method is employed, and lots are scheduled with priorities determined with a construction method. Computational experiments are performed on randomly generated test problems. Results show that the suggested algorithms perform better than well-known dispatching rules for various scheduling problems and an algorithm that is used in a real system.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

A hybrid flowshop scheduling problem for a cold treating process in seamless steel tube production

Seamless steel tubes often have various categories and specifications, which further require complicated operations in production, especially in the cold treating process (CTP). This paper investigates the scheduling problem using the seamless tube plant of Baoshan Iron and Steel Complex as a study background. By considering the practical production constraints such as sequence-dependent setup times, maintenance schedule, intermediate material buffers, job-machine matches, we formulate the hybrid flowshop scheduling problem with a non-linear mixed integer programming model (NMIP). In addition, our model provides a flexibility to remove the permutation assumption, which is often a limitation in early studies. In order to obtain the solution of the above NMIP problem, a two-stage heuristic algorithm is proposed and it combines a modified genetic algorithm and a local search method. With real production instances, our computation experiments indicate that the proposed algorithm is efficient and it outperforms several other approaches. Industrial implementation also shows that such a scheduling tool brings a cost saving of more than 10% and it substantially reduces the computation time. Our study also illustrates the need of relaxing permutation assumption in such a scheduling problem with complicated operation sequences.     

Single-machine scheduling for minimizing total cost with identical,asymmetrical earliness and tardiness penalties

Costs of flowtime, earliness and tardiness should be incorporated in real production scheduling. This paper constructs a single-machine scheduling model with a common due date to minimize the total cost including an identical, asymmetric earliness-tardiness cost. Several dominance conditions necessary for an optimal schedule are derived. A branch and bound algorithm exploiting the conditions is proposed to find an optimal schedule for an unconstrained version of the scheduling problem. Numerical experiments are demonstrated to show the effectiveness of the proposed method.     

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.     

Sequencing a hybrid two-stage flowshop with dedicated machines

We treat the n -job, two-stage hybrid flowshop problem with one machine in the first stage and two different machines in parallel in the second stage. The objective is to minimize the makespan. We demonstrate that the problem is NP-complete. We formulate a dynamic program, which is beyond our grasp for problems of more than 15 jobs. Our search for heuristic approaches led to the adoption of the Johnson sequence, which motivated two of the three approaches: dynamic programming and sequence-and-merge. The third approach, the greedy heuristic, was included as example of an elementary heuristic.     

Minimisation of total tardiness for identical parallel machine scheduling using genetic algorithm

In recent years research on parallel machine scheduling has received an increased attention. This paper considers minimisation of total tardiness for scheduling of n jobs on a set of m parallel machines. A spread-sheet-based genetic algorithm (GA) approach is proposed for the problem. The proposed approach is a domain-independent general purpose approach, which has been effectively used to solve this class of problem. The performance of GA is compared with branch and bound and particle swarm optimisation approaches. Two set of problems having 20 and 25 jobs with number of parallel machines equal to 2, 4, 6, 8 and 10 are solved with the proposed approach. Each combination of number of jobs and machines consists of 125 benchmark problems; thus a total for 2250 problems are solved. The results obtained by the proposed approach are comparable with two earlier approaches. It is also demonstrated that a simple GA can be used to produce results that are comparable with problem-specific approach. The proposed approach can also be used to optimise any objective function without changing the basic GA routine.     

A branch-and-bound algorithm for the cell formation problem

The Cell Formation Problem (CFP) is an important optimisation problem in manufacturing. It has been introduced in the Group Technology (GT) and its goal is to group machines and parts processed on them into production cells minimising the movement of parts to other cells for processing and maximising for each cell the loading of its machines with operations on its parts. We consider one of the computationally hardest formulations of this problem – the CFP with a variable number of cells and the grouping efficacy objective, which is a fractional function. The CFP literature contains many heuristic algorithms, but only a small number of exact approaches especially for this formulation. In the current paper, we present an exact branch-and-bound algorithm for the same hard CFP formulation. To linearise the fractional objective function, we apply the Dinkelbach approach. We have been able to solve 24 of the 35 instances from the well known GT benchmark. For the remaining 11 instances, the difference in the grouping efficacy with the best known solutions is less than 2.6%.     

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.     

Bi-objective reentrant hybrid flowshop scheduling: an iterated Pareto greedy algorithm

The multi-objective reentrant hybrid flowshop scheduling problem (RHFSP) exhibits significance in many industrial applications, but appears under-studied in the literature. In this study, an iterated Pareto greedy (IPG) algorithm is proposed to solve a RHFSP with the bi-objective of minimising makespan and total tardiness. The performance of the proposed IPG algorithm is evaluated by comparing its solutions to existing meta-heuristic algorithms on the same benchmark problem set. Experimental results show that the proposed IPG algorithm significantly outperforms the best available algorithms in terms of the convergence to optimal solutions, the diversity of solutions and the dominance of solutions. The statistical analysis manifestly shows that the proposed IPG algorithm can serve as a new benchmark approach for future research on this extremely challenging scheduling problem.     

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.     

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.     

A branch-and-bound algorithm for the single-row equidistant facility layout problem

In this paper, we deal with the single-row equidistant facility layout problem (SREFLP), which asks to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a branch-and-bound algorithm for solving this problem. The lower bound is computed first by performing transformation of the flow matrix and then applying the well-known Gilmore–Lawler bounding technique. The algorithm also incorporates a dominance test which allows to drastically reduce redundancy in the search process. The test is based on the use of a tabu search procedure designed to solve the SREFLP. We provide computational results for problem instances of size up to 35 facilities. For a number of instances, the optimal value of the objective function appeared to be smaller than the best value reported in the literature.     

A flowshop scheduling problem with two operations per job

This paper considers a special case of the flowshop scheduling problem where each job requires only two operations on specified machines and shows that this problem is NP-hard in the strong sense even if the first operation of all jobs is processed on the same machine and the number of machines performing the second operation equals two. For the case when the first operation of all jobs is performed on the same machine, it is sufficient to consider only permutation schedules for minimizing any regular measure of performance. Five polynomially bounded heuristic algorithms are described for minimizing makespan for this case and their performance in finding a minimum makespan schedule is theoretically and empirically evaluated.     

Schedules for a two-stage hybrid flowshop with parallel machines at the second stage

Approximate solution algorithms are developed to find a minimum makespan schedule in a two-stage hybrid flowshop when the second stage consists of multiple identical machines. Computational experience comparing the ‘approximate’ makespans with their respective global lower bounds for large problems indicates that proposed polynomially bounded approximate algorithms are quite effective. It is shown that the proposed heuristic algorithms can be used to improve the efficiency of an existing branch and bound 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.     

A study on open shop scheduling to minimise total tardiness

This paper deals with open shop scheduling to minimise total tardiness. Contrary to other scheduling problems (i.e., flow and job shops), the formulation of the open shop is given far less attention in the literature. Therefore, we intend to fulfil this gap by the presentation of four different mixed integer linear programming models. We compare the models on the basis of their complexity sizes. Furthermore, we propose two metaheuristics based on genetic algorithm and variable neighbourhood search. We exhaustively explore the effect of different operators and parameters on the performance of genetic algorithm by means of Taguchi method. Two computational experiments are conducted to evaluate the models and algorithms for performance. The first one includes small-sized instances by which the models and general performance of the algorithms are examined. The second one consists of three well-known benchmarks by which we further evaluate the algorithms. The results show the effectiveness of the proposed models and algorithms.