Open Shop Scheduling Research Articles

Exact solution approaches for order acceptance and scheduling decisions in m-machine open shops

This paper considers an order acceptance and scheduling (OAS) problem in open shops with m-machines and the objective of maximizing the total net revenue, which is defined as the difference between the sum of revenues and the total weighted tardiness. Open shop scheduling problems occur in many different industries, like the production or the service industry, which show a great potential for the use of integrated OAS methods. However, these mostly NP-hard problems are computationally challenging. With this work, we are the first to consider the problem of OAS in an m-machine open shop and propose several exact solution approaches. We first develop two basic mixed integer linear programming (MIP) formulations. Second, we present several enhancements to allow more problem instances to be solved to optimality with a standard solver compared to the basic MIP formulations. Third, we propose a model-based branch-and-bound (B&B) approach. In an extensive numerical study, we compare the performance of a standard solver with all developed MIP formulations as well as the B&B approach. The results demonstrate the superior performance of the enhanced MIP formulations as well as the B&B approach in terms of CPU time and the number of verified optimal solutions found.

A new two-stage constraint programming approach for open shop scheduling problem with machine blocking

In this paper, a variant of the open shop scheduling problem is considered in which the intermediate storage is forbidden among two adjacent production stages (zero buffer or machine blocking constraint). The performance measure is to minimise the maximal completion time of the jobs (makespan). Since this is an NP-hard problem, a two-stage constraint programming approach is proposed as a new exact method. Computational experiments were carried out on 222 literature problem instances in order to test the performance of the proposed algorithm. The relative deviation is adopted as the performance criteria. Computational results point to the ability of the proposed method to solve large-sized instances in comparison with the developed mixed-integer linear programming model and a simple constraint programming model, both with user cuts. In all set of instances, the proposed two-stage method performed better than benchmarking methods and integer programming models, with average relative deviation regarding objective values as lower as 12%. In addition, the results point to a competitive efficiency in computational times of the proposed method with less than 200 s in the most instances to obtain the optimal solution, in comparison to competitive metaheuristics from literature of the problem, for the tested test instances.

On the complexity of open shop scheduling with time lags

The minimization of makespan in open shop with time lags has been to be shown NP-hard in the strong sense even for the case of two machines and unit-time operations. The minimization of total completion time, however, has remained open for that case though it has been it be shown NP-hard in the strong sense for weighted total completion time or for jobs with release dates. This note shows that the minimization of total completion time for two machines and unit-time operations is NP-hard in the strong sense which answers the long standing open question.

A String of Disjoint Job Block with Processing Time Associated with Probability in Two-Stage Weighted Open Shop Model

Open-shop scheduling problem (OSSP) is a well-known topic with wide industrial applications which belongs to one of the vital issues in the field of engineering. This paper deals with a two-stage open shop scheduling problem in which the processing time of jobs is allied with probabilities. The concept of a string of two job blocks which are disjoint in nature is considered so that the first block covers the jobs with a fixed route and the second block covers the jobs with an arbitrary path. Further, the weights of jobs are also introduced due to their applicability and relative importance in the real world. The objective of this study is to propose a heuristic which on execution, provides an optimal or near-optimal schedule to diminish the makespan. Several numerical illustrations are produced in MATLAB 2018a to demonstrate the effectiveness of the proposed approach, and to confirm the performance, the results are compared with the existing methods developed by Johnson and Palmer.

Energy-efficient open-shop scheduling with multiple automated guided vehicles and deteriorating jobs

There is growing interest in energy-efficient production scheduling research because of the increasing energy shortage. However, most existing studies along this line of research have not considered the energy consumed by automated guided vehicles (AGVs) used in modern smart factories for production scheduling purposes. In this paper, we study an energy-efficient open-shop scheduling problem with multiple AGVs and deteriorating jobs. A multi-objective model with four objectives is formulated, aiming to simultaneously minimise the maximum ending time of all AGVs, the total idle time of machines and AGVs, the total tardiness of jobs, and the total energy consumption of machines and AGVs. An improved population-based multi-objective differential evolution (IMODE) algorithm is developed to solve the problem. The IMODE makes use of a problem feature-based heuristic and a mean entropy method to enhance the diversity of its initial population. A novel grey entropy parallel analysis-based fitness evaluation mechanism with reference points is adopted to evaluate the candidate solutions. To improve the local search ability of IMODE, a multi-level local search strategy is used. In the experimental study, Taguchi analysis is employed to obtain the best parameter combination. The effects of the main components of IMODE are validated via comprehensive comparison experiments. Extensive experimental results show that the IMODE is preferable to other well-known multi-objective algorithms at solving the problem being considered.

A new hybridization of adaptive large neighborhood search with constraint programming for open shop scheduling with sequence-dependent setup times

In recent years, researchers have been paying special attention to scheduling problems with setup times and costs, aiming to adopt more realistic assumptions. This paper aims at presenting a new hybridization of an adaptive large neighborhood search (ALNS) with constraint programming (CP) as a local search phase for open shop scheduling with non-anticipatory sequence-dependent setup time. An integer linear programming model is presented based on the classic open shop model, and a new CP model is proposed with non-anticipatory setup times. The proposed CP model has not been addressed in the revised literature and outperforms all other exact methods. The objective function adopted is makespan minimization, and we use the relative deviation as performance criteria. Since the problem under study is NP-hard, we test many approximations and exact algorithms to obtain high-quality solutions in acceptable computational times. The extensive computational experience shows that the proposed hybridization of metaheuristic and constraint programming is promising for solving large-sized instances.

Improving patient satisfaction and outpatient diagnostic center efficiency using novel online real-time scheduling

We develop a novel online real-time scheduling algorithm with applications for healthcare diagnostic centers to deal with walk-in patients based on a set of constraints on the sequence of tests and resources. The problem is especially significant at healthcare centers in developing and emerging nations, such as India, where appointment schedules do not work. Within this realistic context, our objective is to improve patient satisfaction by reducing waiting time and improve diagnostic center performance through better utilization of the constrained resources. We propose a Mixed Integer Linear Programming (MILP) formulation to represent diagnostic centers as a Flow and Open Shop, to capture the system dynamics of the Flexible Hybrid Shop Scheduling Problem. We then develop a novel Online Genetic Algorithm (OGA) capable of solving real life large scale problems, as Open Shop scheduling problems are NP-hard. The developed OGA is first validated for small instances against a theoretical lower bound and the MILP model using CPLEX solver for flow time and makespan. The OGA is then empirically validated with data collected from two diagnostic centers of different sizes and configurations. For both centers, the developed OGA shows significant improvement compared to the simulation model. This research offers an important contribution to both literature and practice as it is one of the first to model the patient scheduling problem as an online real-time process. Implementing the developed OGA would help diagnostic centers significantly improve time estimates, thus reducing actual patient time and improving the efficiency of the system. Most importantly, the OGA is generalizable beyond healthcare to a broad range of environments that share Hybrid Shop characteristics.

New efficient heuristics for scheduling open shops with makespan minimization

This paper deals with the so-called Open Shop Scheduling Problem (OSSP) with makespan objective, which consists of scheduling a set of jobs that must visit a set of machines in no established order so the maximum completion time among the jobs is minimized. This problem is known to be NP-hard, and the absence of specific routes for the processing of the jobs makes its solution space extremely large. In this work we propose several efficient constructive heuristics that exploit some specific properties of the OSSP. We carry out an extensive computational experience using problem instances taken from the related literature to assess the performance of the proposed algorithms as compared to existing ones with respect to the quality of the solutions and the CPU time required. The extensive computational tests show the excellent performance of the heuristics proposed, resulting in the best-so-far heuristics for the problem.

Ant colony optimization with a new exploratory heuristic information approach for open shop scheduling problem

This work proposes a new metaheuristic algorithm (ACONEH) for open shop scheduling problem (OSSP) with makespan minimization. The aim is to improve the exploration capability of ant colony optimization (ACO) and also solve OSSP more effectively. This is achieved by introducing a new heuristic information approach that utilizes three exploratory characteristics. The first is randomness: the heuristic information should be generated randomly. The second is diversity: each ant acquires different information. The third is improvability: each ant improves its information periodically. ACONEH is tested on three well-known benchmark problem sets that include 175 instances. The proposed heuristic approach is compared with a traditional one. The results show that the proposed approach produces considerable improvements. These improvements are 91% in the average relative deviation of the best solution and 63% in the average relative deviation of the average solution. ACONEH is compared with other six recent and best-so-far metaheuristic algorithms. The results show that it produces better solutions than all of them in a reasonable computational time. Moreover, the improvements in the average relative deviation of the best solution achieved on the best-so-far ACO and the best-so-far metaheuristic algorithm are 75% and 46%, respectively. Therefore, ACONEH can be considered as the best-so-far metaheuristic algorithm for OSSP.

Network-based dynamic dispatching rule generation mechanism for real-time production scheduling problems with dynamic job arrivals

Although the concept of Industrial 4.0 has been well accepted, only few studies have dealt with real-time production scheduling of smart factories. Due to the advantages of simplicity, efficiency and quick response, heuristic rules have become the most promising technology to solve such problems. However, they suffer some drawbacks, such as high development and maintenance costs, low solution quality, and excessive emphasis on local information. To design heuristics from the perspective of system optimization and ensure the performance of heuristics in real-time production scheduling environments, this study develops a network-based dynamic dispatching rule generation mechanism. The complex network theory is introduced to extract a series of low-level heuristics from the perspective of system optimization, while the automatic heuristic generation problem is formulated as a multiple attribute decision making problem. Given that the dispersity of local features indicates their value for decision-making, the entropy weighting method is employed to automatically produce an adequate combination of the provided easy-to-implement low-level heuristics. Finally, the open shop scheduling problem with dynamic job arrivals is taken as an example to evaluate the effectiveness of the proposed algorithm. Numerical results demonstrate the excellent performance of the proposed algorithm in terms of algorithm effectiveness and computational time.

Optimization of energy-efficient open shop scheduling with an adaptive multi-objective differential evolution algorithm

There have been growing interests in the energy-efficient production scheduling recently because of the growing shortage of energy. Open shop scheduling problem (OSSP) is a kind of common but seldom concerned production scheduling problem. This paper focuses on energy-efficient OSSP (EOSSP), where the effect of setup operation on production efficiency and energy consumption is considered. A multi-objective energy-efficient model based on machine speed scaling mechanism is proposed. To handle this multi-objective problem, we propose an effective adaptive multi-objective differential evolution (AMODE) algorithm. The AMODE uses a new fitness evaluation mechanism (FEM) based on dynamic reference point and fuzzy correlation entropy analysis to assess the solutions in evolution population. It also uses an adaptive opposition-based learning (AOBL) to improve its local search ability. Taguchi method is utilized to obtain the best combination of critical parameters of the AMODE. The proposed mathematical model is validated with CPLEX, and a lexicographic method is used to determine the preferable solution. Experimental results show that both our proposed FEM and AOBL can improve the performance of AMODE. Extensive experiments reveal that the performance of AMODE is superior to the other three well-known algorithms in addressing the EOSSP.

Multiobjective Parallel Algorithms for Solving Biobjective Open Shop Scheduling Problem

Open Shop Scheduling Problem (OSSP) is one of the most important scheduling problems in the field of engineering and industry. This kind of problem includes m machines and n jobs, each job contains a certain number of operations, and each operation has a predetermined processing time on its corresponding machine. The order of processing of these operations affects the completion times of all jobs. Therefore, the purpose of OSSP is to achieve a proper order of processing of jobs using specified machines, so that the completion time of all jobs is minimized. In this paper, the strengths and limitations of three methods are evaluated by comparing the results of solving the OSSP in large‐scale and small‐scale benchmarks. In this case, the minimized completion time and total tardiness are considered the objective functions of the adapted methods. To solve small‐scale problems, we adapt a mathematical model called Multiobjective Mixed Linear Programming (MOMILP). To solve large‐scale problems, two metaheuristic algorithms including Multiobjective Parallel Genetic Algorithm (MOPGA) and Multiobjective Parallel Simulated Annealing (MOPSA) are adapted. In experimental results, we randomly generated small‐scale problems to compare MOMILP with the Genetic Algorithm (GA) and Simulate Annealing (SA). To compare MOPSA and MOPGA with the state of the art and show their strengths and limitations, we use a standard large‐scale benchmark. The simulation results of the proposed algorithms show that although the MOPSA algorithm is faster, the MOPGA algorithm is more efficient in achieving optimal solutions for large‐scale problems compared with other methods.

Minimising the tardiness in open shop scheduling problems using variants of the firefly algorithm and genetic algorithm

Minimising the tardiness in open shop scheduling problems using variants of the firefly algorithm and genetic algorithm

A Matheuristic Approach to the Open Shop Scheduling Problem with Sequence-Dependent Setup Times*

This paper deals with an open shop scheduling problem in which sequence-dependent setup times are present. In open shops there are no restrictions on the processing route of each job, so the decision regards not only the sequencing of jobs on each machine, but also the sequencing of operations (machines) for each job. These type of problems typically arise in application contexts where the order in which the operations are executed is irrelevant. In this work a novel heuristic approach based on mathematical programming, i.e., a matheuristic, is developed and its performance is assessed through a computational study on open shop benchmark instances.

An intelligent hybridized distributed feedback control approach for the JIT open-shop scheduling problem

An intelligent hybridized distributed feedback control approach for the JIT open-shop scheduling problem

Bi-objective dynamic multiprocessor open shop scheduling for maintenance and healthcare diagnostics

This paper addresses a bi-objective dynamic multiprocessor open shop scheduling problem in which the simultaneous objectives of minimizing both the mean weighted flow time and the makespan are considered. This problem is commonly encountered in maintenance and healthcare diagnostic systems. Since it is NP-hard for both objectives, efficient heuristics are needed to quickly generate a set of non-dominated solutions that a decision maker would choose from. For this sake, two metaheuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective grey wolf optimizer (MOGWO) are developed in this paper. Both metaheuristics are hybridized with simulated annealing (SA) local search. Parameter tuning computational experiments are conducted first on a set of 30 small instances from the literature for which Pareto optimal solutions are known. Then, computational experiments on large randomly generated instances are conducted. Computational results for small instances show that the NSGA-II is capable of generating non-dominated solutions that are very close to the optimal Pareto front. Results also reveal that the performance of the NSGA-II is better in most of the cases compared to the MOGWO under different settings of the studied problem for both small and large instances. However, for large instances with large number of workstations and jobs, low loading level and high percentage of busy machines at the beginning of the schedule, the difference in performance between both metaheuristics is minor.

A new variable neighbourhood search with a constraint programming search strategy for the open shop scheduling problem with operation repetitions

This article presents a new variant for the open shop scheduling problem, the open shop scheduling problem with repetitions (OSSPR), where the jobs can be processed on any machine more than once (operation by operation). Thereby, all the jobs can be scheduled in an unconstrained way, substantially increasing the number of feasible solutions in comparison with the classical open shop. The OSSPR has many applications in automotive and maintenance actives. To solve the problem, a mixed-integer linear programming model is presented and a new constraint programming model is proposed. Since the problem under study is NP-hard, a new efficient variable neighbourhood search is proposed using variable search strategies through the proposed constraint programming model. The objective function is makespan minimization, and it uses the lower bound deviation as performance criterion. Computational results show very good performance of the proposed metaheuristic on the instances tested.

A new efficient biased random key genetic algorithm for open shop scheduling with routing by capacitated single vehicle and makespan minimization

Over the last years, researchers have been paying particular attention to scheduling problems integrating production environments and distribution systems to adopt more realistic assumptions. This paper aims to present a new biased random key genetic algorithm with an iterated greedy local search procedure (BRKGA-IG) for open shop scheduling with routing by capacitated vehicles. We propose approximation and exact algorithms to obtain high-quality solutions in acceptable computational times. This paper presents a new integer linear programming model. The proposed integer model has not been addressed in the revised literature. The objective function adopted is makespan minimization, and we use the relative deviation as performance criteria. BRKGA-IG has a new decoding scheme for OSSP-VRP solutions, an intensive exploitation mechanism with an iterated greedy local search procedure, and a restart mechanism to reduce premature population convergence. With these new mechanisms, the extensive computational experience carried out shows that the proposed metaheuristic BRKGA-IG is promising in solving large-sized instances for the new proposed problem, outperforming all other tested methods.

A PTAS for non-resumable open shop scheduling with an availability constraint

A PTAS for non-resumable open shop scheduling with an availability constraint

A scatter search algorithm with a novel solution representation for flexible open shop scheduling: a multi-objective optimization

The flexible open shop scheduling problem is the combination of two classical open shop and a parallel machine scheduling problems. Due to the computational complexity of solving the open shop scheduling problem, so far, limited research has considered the assumption of flexibility in this problem. In this study, a bi-objective flexible open shop scheduling with independent setup time is considered. The considered objective functions are to minimize the maximum completion time of jobs and total tardiness. Using the first objective function, an attempt is made to balance the amount of workloads on the machines so that the completion time of the last job is minimized, while using the second one, from the customers' point of view, an attempt is made to reduce the amount of tardiness in delivery of jobs to the customers. Here, firstly, a mixed-integer nonlinear programming model is proposed. Then, to deal with the multi-objective problem, the weighted Lp-metric method is used. Since, this problem is a non-deterministic polynomial-time hard problem (NP-hard), a scatter search algorithm is developed to obtain near-optimal solutions in a reasonable time. In this regard, for the first time, a novel solution representation method is also presented. To ensure the efficiency of the proposed algorithm, the results were compared with NSGA-II using several instances. After analyzing the results using four evaluation metrics, it is observed that the scatter search algorithm performs better than the NSGA-II.