Parallel Machine Scheduling Problem Research Articles

Energy-awareness scheduling of unrelated parallel machine scheduling problems with multiple resource constraints

Energy-awareness scheduling of unrelated parallel machine scheduling problems with multiple resource constraints

Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes

We consider a time-indexed formulation for the unrelated parallel machine scheduling problem. We show that all polyhedral knowledge known from the single machine problem (in particular, valid inequalities) is applicable to this formulation. We present new facet-inducing valid inequalities and a preprocessing technique involving fixing variables based on reduced costs. We combine both techniques in a basic cutting-plane algorithm and test the performance of the resulting algorithm by running it on randomly generated instances.

Matheuristics for a parallel machine scheduling problem with non-anticipatory family setup times: Application in the offshore oil and gas industry

In this paper, we address a variant of a batch scheduling problem with identical parallel machines and non-anticipatory family setup times to minimize the total weighted completion time. We developed an ILS and a GRASP matheuristics to solve the problem using a constructive heuristic and two MIP-based neighborhood searches, considering two batch scheduling mathematical formulations. The problem derives from a ship scheduling problem related to offshore oil & gas logistics, the Pipe Laying Support Vessel Scheduling Problem (PLSVSP). The developed methods overcome the current solution approaches in the PLSVSP literature, according to experiments carried out on a benchmark of 72 instances, with different sizes and characteristics, in terms of computational time and solution quality. New best solutions are provided for all medium and large-sized instances, achieving a reduction of more than 10% in the objective function of the best case.

A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators

We examine a parallel machine scheduling problem with a job splitting property, sequence-dependent setup times, and limited setup operators, for minimizing makespan. Jobs are split into arbitrary (job) sections that can be processed on different machines simultaneously. When a job starts to be processed on a machine, a setup that requires an operator is performed, and the setup time is sequence-dependent. The number of setup operators is limited, and hence not all of the machines can be set up at the same time. For this problem, we propose a mathematical programming model and analyze a lower bound. We then develop a simple but efficient heuristic algorithm so that it can be used in practice, and analytically derive a worst-case bound of the algorithm. We finally evaluate the performance of the proposed algorithm numerically with various scenarios.

A new memetic global and local search algorithm for solving hybrid flow shop with multiprocessor task scheduling problem

Hybrid flow shop (HFS) scheduling problem is combining of the flow shop and parallel machine scheduling problem. Hybrid flow shop with multiprocessor task (HFSMT) scheduling problem is a special structure of the hybrid flow shop scheduling problem. The HFSMT scheduling is a well-known NP-hard problem. In this study, a new memetic algorithm which combined the global and local search methods is proposed to solve the HFSMT scheduling problems. The developed new memetic global and local search (MGLS) algorithm consists of four operators. These are natural selection, crossover, mutation and local search methods. A preliminary test is performed to set the best values of these developed new MGLS algorithm operators for solving HFSMT scheduling problem. The best values of the MGLS algorithm operators are determined by a full factorial experimental design. The proposed new MGLS algorithm is applied the 240 HFSMT scheduling instances from the literature. The performance of the generated new MGLS algorithm is compared with the genetic algorithm (GA), parallel greedy algorithm (PGA) and efficient genetic algorithm (EGA) which are used in the previous studies to solve the same set of HFSMT scheduling benchmark instances from the literature. The results show that the proposed new MGLS algorithm provides better makespan than the other algorithms for HFSMT scheduling instances. The developed new MGLS algorithm could be applicable to practical production environment.

Scheduling pipe laying support vessels with non-anticipatory family setup times and intersections between sets of operations

In this paper, we deal with a problem that arises from the oil industry with the need to schedule a pipe laying support vessel fleet responsible for connecting oil wells to production platforms. We model it as an identical parallel machine scheduling problem, considering a particular case where jobs are composed of intersecting sets of operations and with operations partitioned into families. A non-anticipatory family setup time is incurred on three occasions: when a machine changes the execution of operations from one family to another, when the machine reaches its capacity, and before the first operation on each machine. These considerations, along with other scheduling features, make the problem more challenging and attractive to the scheduling literature. We propose three mathematical formulations to solve 72 generated instances, based on actual data, with up to 50 operations to schedule. Among the formulations, the Batch Scheduling presents better results with the smallest gaps, when compared to the best lower bounds obtained. This formulation considers a dispatching rule to sequence operations within batches, generating better solutions in 22 of the 24 largest instances, dominating the other formulations. A Brazilian oil company currently uses this approach in a production system for its tactical planning.

Bi-objective parallel machine scheduling with additional resources during setups

We present a bi-objective parallel machine scheduling problem with machine and job sequence dependent setup times, with the additional consideration of resources needed during setups. The availability of such resources is limited. This models many practical situations where setup times imply, for example, cleaning and/or the reconfiguration of productive equipment. These setups are performed by personnel, who are of course limited in number. The objectives considered are the minimization of the makespan and the minimization of the number of resources. Fewer available resources reduce production costs but inevitably increase the makespan. On the contrary, a greater number of resources increase costs but allow for more setups to be done in parallel and a reduced makespan. An algorithm based on iterated greedy approaches is proposed to search for the Pareto front of the problem. This algorithm is compared with state-of-the art methods adapted to the problem. Computational experiments, supported by statistical analyses, indicate that the proposed approach outperforms all other tested procedures.

A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection

In this paper, we focus on a semi-online scheduling problem with rejection on identical parallel machines, where “semi-online” means that the ratio of the longest processing time among all jobs to the shortest one is no more than γ with γ ≥ 1. In particular, in this setting, there are a coupling of independent jobs arriving online over time with the flexibility of rejection, which implies that each job will be either accepted and scheduled on one of identical machines or rejected at the cost of penalty cost. Our objective is minimizing the total completion time of the accepted jobs plus the total penalty cost of the rejected jobs. For this problem, we design a deterministic polynomial time semi-online algorithm entitled as α Delayed Shortest Processing Time with Rejection (ADSPTR). In competitive analysis, by adopting the approach “Improved Instance Reduction”, we obtain the competitive ratio of ADSPTR is at most 1+1+γ(γ−1)−1γ.

Parallel machine scheduling with the total weighted delivery time performance measure in distributed manufacturing

In this paper, we address a parallel machine scheduling problem that is motivated by distributed manufacturing settings. Our objective is to minimize the total weighted delivery time (TWD) after including delivery durations for the jobs. We first analyse several special cases which can be solved to optimality in polynomial time. Based on the gained insights of the analysis, constructive algorithms are proposed for the general problem setting. A greedy randomized adaptive search (GRASP) framework is proposed to guide the subordinate heuristics to further improve algorithm performance for large-sized problem instances. Computational experiments based on randomly generated problem instances are carried out. They demonstrate that the GRASP computes competitive schedules for the special cases. For small problem instances, the GRASP is able to compute optimal solutions. Moreover, it outperforms two genetic algorithms (GAs) that differ in the way how structural properties of optimal solutions are included in terms of both solution quality and computing time.

Scheduling uniform parallel dedicated machines with job splitting, sequence-dependent setup times, and multiple servers

We address a uniform parallel machine scheduling problem with machine eligibility, job splitting, sequence-dependent setup times, and limited setup servers, which has been defined from a real application of piston manufacturing in Korea. The objective is to minimize the makespan. We first propose a mathematical programming model and derive four lower bounds. We then develop an efficient heuristic algorithm that assigns jobs to machines by considering processing times, setup times, and machine eligibility constraints, and then balances machine workloads by splitting jobs. We analyze a worst-case bound of the algorithm and perform extensive experiments with various scenarios. The gap from a lower bound is not significant for practical cases.

Computational Experiments on Workflow Balancing of Parallel Machine Scheduling with Precedence Constraints and Sequence Independent Setup Time

The workflow balancing of parallel machines scheduling (PMS) with precedence constraints and sequence independent setup time is considered for study. The setup time consideration produces alternate schedule along with lesser relative percentage of imbalance (RPI) value for PMS problem is demonstrated with an example. The lesser RPI indicates better workflow balancing among machines. The computational experiments are conducted on large instances of randomly generated PMS problems with precedent constraints and setup time. The various combinations of heuristics are used to solve the problems. The results show that genetic algorithm (GA) performs well against the other heuristics with lesser RPI values

A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions

This paper addresses a parallel machine scheduling problem with restrictions on employees’ working-times and break times. Tasks must be processed by employees nonpreemptively on unrelated parallel machines with different thresholds that specify for each employee the maximum total and consecutive working-time, and the minimum break time. The objective is to minimize the weighted sum of the makespan, the machine depreciation costs, and the labor costs. To solve this problem, a mixed integer linear programming model is formulated, and two different decomposition-based exact algorithms are implemented as well as a list scheduling (LS)-based heuristic method. Extensive computational experiments are performed on randomly generated instances, and the results demonstrate the efficiency of our proposed combinatorial Benders decomposition approach.

Scheduling on a Single Machine and Parallel Machines with Batch Deliveries and Potential Disruption

In this paper, we study several coordinated production-delivery scheduling problems with potential disruption motivated by a supply chain in the manufacturing industry. Both single-machine environment and identical parallel-machine environment are considered in the production part. The jobs finished on the machines are delivered to the same customer in batches. Each delivery batch has a capacity and incurs a delivery cost. There is a situation that a possible disruption in the production part may occur at some particular time and will last for a period of time with a probability. We consider both resumable case and nonresumable case where a job does not need (needs) to restart if it is disrupted for a resumable (nonresumable) case. The objective is to find a coordinated schedule of production and delivery that minimizes the expected total flow times plus the delivery costs. We first present some properties and analyze the NP-hard complexity for four various problems. For the corresponding single-machine and parallel-machine scheduling problems, pseudo-polynomial-time algorithms and fully polynomial-time approximation schemes (FPTASs) are presented in this paper, respectively.

A robust bi-objective mathematical model for disaster rescue units allocation and scheduling with learning effect

This paper proposes a novel bi-objective mixed-integer linear programming (MILP) model for allocating and scheduling disaster rescue units considering the learning effect. When a natural phenomenon (e.g., earthquake or flood) occurs, the presented decision support model is expected to help decision-makers of emergency relief centers to provide efficient planning for rescue units to minimize the total weighted completion time of rescue operations, as well as the total delay in rescue operations. The problem has some features in common with unrelated parallel machine scheduling (UPMS) problem and traveling salesman problem (TSP). To deal with the inherent uncertainty and bi-objective nature of the problem, an uncertainty-set based robust optimization technique and multi-choice goal programming (MCGP) with utility functions are applied. To demonstrate the applicability of the proposed model, a real case study in Mazandaran province in Iran is presented. The computational results confirm the high complexity of the problem and the significant impacts of the uncertainty on the solution. Moreover, the analytical results provide useful insights to decision-makers for disastrous situations.

Parallel machine scheduling with position-based deterioration and learning effects in an uncertain manufacturing system

This research investigates a parallel machine scheduling problem with position-dependent deteriorating jobs and DeJong’s learning effects in an uncertain manufacturing system. We utilize the fuzzy set theory to handle such an uncertain system. The objective is to minimize the fuzzy makespan. To tackle such an NP-hard scheduling problem, we design a fuzzy simplified swarm optimization algorithm with local search, which is appraised by comparing it with other state-of-the-art meta-heuristics. Given that the parameter values of meta-heuristic algorithms have a remarkable impact on performance, we first apply the Taguchi method to select proper values for the control factors. Afterward, extensive numerical comparisons are conducted. Finally, to further analyze the performance of meta-heuristic algorithms from a statistical viewpoint, Friedman’s test and the Wilcoxon signed-rank test are carried out. Results imply that the designed algorithm can find satisfactory solutions in a reasonable time and performs better than the compared algorithms.

Spatial and temporal optimization for smart warehouses with fast turnover

With the rapid development of e-commerce and the new retail, the same-day or even same-half day delivery service is provided to compete for market share. Recently, an increased number of e-commerce companies implement the unmanned smart warehouses to improve the logistics efficiency. In order to further reduce the demand response time, a novel picking strategy is designed to firstly split the orders, and then assign the partial orders to different pickers. After all the order segments have been collected, it is shipped to the customer. Due to the inherent complexity of the problem, a two stage optimization model is introduced. In the first stage, an order splitting and batching strategy based on spatial measure is proposed. And a MIP model is constructed to minimize the total picking distance, which is then solved via a column generation based algorithm. In the second stage, the newly formed batches are considered as a priori inputs, which are then assigned to automatic pickers. The picking process is modeled as a special parallel machine scheduling problem with multiple due dates for a single item, which could reduce to a customer order scheduling problem on parallel machines, and it is unary NP-complete. A heuristic method is proposed to obtain an approximate solution. Although the order splitting technique is not new in the logistics industry, the split orders are picked according to a vehicle routing problem, which fails to address the kitting issue for fast turnovers. In the numerical analysis section, the proposed algorithm is validated through extensive testing on various scales of instances. It is observed that the optimality gap for our algorithm is within 9%, and the computation time is around 5 min. Also, the average turnover rate increases by approximately 50% in comparison with the no-splitting policy. In most cases, the average order tardiness decreases by 90% compared with order splitting and no-kitting policy.

HEART: Unrelated parallel machines problem with precedence constraints for task scheduling in cloud computing using heuristic and meta‐heuristic algorithms

SummaryCloud computing is becoming a profitable technology because of it offers cost‐effective IT solutions globally. A well‐designed task scheduling algorithm ensures the optimal utilization of clouds resources and reducing execution time dynamically. This research article deals with the task scheduling of inter‐dependent subtasks on unrelated parallel computing machines in a cloud computing environment. This article considers two variants of the problem‐based on two different objective function values. The first variant considers the minimization of the total completion time objective function while the second variant considers the minimization of the makespan objective function. Heuristic and meta‐heuristic (HEART) based algorithms are proposed to solve the task scheduling problems. These algorithms utilize the property of list scheduling algorithm of unrelated parallel machine scheduling problem. A mixed integer linear programming (MILP) formulation has been provided for the two variants of the problem. The optimal solution is obtained by solving MILP formulation using A Mathematical Programming Language (AMPL) software. Extensive numerical experiments have been performed to evaluate the performance of proposed algorithms. The solutions obtained by the proposed algorithms are found to out‐perform the existing algorithms. The proposed algorithms can be used by cloud computing service providers (CCSPs) for enhancing their resources utilization to reduce their operating cost.

Parallel machine scheduling with stochastic release times and processing times

Stochastic scheduling has received much attention from both industry and academia. Existing works usually focus on random job processing times. However, the uncertainty existing in job release times may largely impact the performance as well. This work investigates a stochastic parallel machine scheduling problem, where job release times and processing times are uncertain. The problem consists of a two-stage decision-making process: (i) assigning jobs to machines on the first stage before the realisation of uncertain parameters (job release times and processing times) and (ii) scheduling jobs on the second stage given the job-to-machine assignment and the realisation of uncertain parameters. The objective is to minimise the total cost, including the setup cost on machines (induced by job-to-machine assignment) and the expected penalty cost of jobs' earliness and tardiness. A two-stage stochastic program is proposed, and the sample average approximation (SAA) method is applied. A scenario-reduction-based decomposition approach is further developed to improve the computational efficiency. Numerical results show that the scenario-reduction-based decomposition approach performs better than the SAA, in terms of solution quality and computation time.

Modified Harris Hawks Optimizer for Solving Machine Scheduling Problems

Scheduling can be described as a decision-making process. It is applied in various applications, such as manufacturing, airports, and information processing systems. More so, the presence of symmetry is common in certain types of scheduling problems. There are three types of parallel machine scheduling problems (PMSP): uniform, identical, and unrelated parallel machine scheduling problems (UPMSPs). Recently, UPMSPs with setup time had attracted more attention due to its applications in different industries and services. In this study, we present an efficient method to address the UPMSPs while using a modified harris hawks optimizer (HHO). The new method, called MHHO, uses the salp swarm algorithm (SSA) as a local search for HHO in order to enhance its performance and to decrease its computation time. To test the performance of MHHO, several experiments are implemented using small and large problem instances. Moreover, the proposed method is compared to several state-of-art approaches used for UPMSPs. The MHHO shows better performance in both small and large problem cases.

A Multi-objective Optimization Approach to Solve a Parallel Machines Scheduling Problem

A Multi-objective Optimization Approach to Solve a Parallel Machines Scheduling Problem