Total Completion Time Objective Research Articles

Online algorithms to schedule a proportionate flexible flow shop of batching machines

This paper is the first to consider online algorithms to schedule a proportionate flexible flow shop of batching machines (PFFB). The scheduling model is motivated by manufacturing processes of individualized medicaments, which are used in modern medicine to treat some serious illnesses. We provide two different online algorithms, proving also lower bounds for the offline problem to compute their competitive ratios. The first algorithm is an easy-to-implement, general local scheduling heuristic. It is 2-competitive for PFFBs with an arbitrary number of stages and for several natural scheduling objectives. We also show that for total/average flow time, no deterministic algorithm with better competitive ratio exists. For the special case with two stages and the makespan or total completion time objective, we describe an improved algorithm that achieves the best possible competitive ratio varphi =frac{1+sqrt{5}}{2}, the golden ratio. All our results also hold for proportionate (non-flexible) flow shops of batching machines (PFB) for which this is also the first paper to study online algorithms.

Propose a Polynomial Time Algorithm for Total Completion Time Objective

In this study, we integrate deteriorate jobs with repair&maintenance activity on a single machine scheduling subject to total completion time. This work has more than one motivation. First, jobs are assigned to machines in an automated production line. Later, to schedule the maintenance activities, if needed, to prevent machinery from breaking down later. There are some important mathematical models to solve this combination. However, due to the complexity of the problem which is Np-hard, a polynomial algorithm should be needed for solving large problems. Therefore, this article introduces several polnomial algorithms to determine the order of things best. With using these algorithms, it will be possible to determine where to assign to the schedule, taking into account the number of maintenance activities required and their optimum total completion time.

Distributed permutation flowshop scheduling problem with total completion time objective

This paper considers the distributed permutation flowshop scheduling problem (DPFSP) which is an extension of permutation flowshop scheduling problem (PFSP). In DPFSP, there are multiple parallel factories instead of one factory as in PFSP. Each factory consists of same number of machines, and jobs can be processed in either of the factories to perform all necessary operations. This paper considers DPFSP for minimizing the total completion time objective. An MILP formulation is developed to find the optimal solution. To solve the problem, a metaheuristic, tabu search (TS) is proposed. Numerical experiments are performed on benchmark problem instances from the literature, and results of the proposed method are compared with current metaheuristics in the literature for this problem. The tabu search outperforms all existing metaheuristics in terms of solution quality.

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.

Flexible flow line scheduling considering machine eligibility in a digital dental laboratory

Introduction of digital solutions has made dentistry more efficient and effective in response to patients’ demands. Moreover, digital solution helps participants to manage daily workflow simpler than traditional practices. Scanners, CAD/CAM software, CNC machines and 3D printers are components of digital solutions in current dentistry. Responding to patients as quickly as possible is essential in medical fields and dentistry has similar situations. On the other hand, demands in dentistry are highly customized that it makes managing orders more difficult because each order needs special design and production. Thus, this paper assesses orders in digital dentistry and develops a mathematical model to optimize production planning and scheduling of orders by considering different objectives and requirements that are common in dentistry. In addition, a metaheuristics algorithm was developed based on PSO to respond to NP-hard challenges of the model. The developed algorithm includes two steps that PSO metaheuristics consider in the second step to search new solutions. Finally, through case studies, performance of the developed model and proposed algorithm was investigated. Developed algorithm generates solutions with proper quality considering makespan and total completion time objectives and required time to obtain a solution with high quality depends on problem data and can increase.

The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective

We study a single-machine scheduling problem to minimize the total completion time of the given set of jobs, which have to be processed without job preemptions. The lower and upper bounds on the job duration is the only information that is available before scheduling. Exact values of the job durations remain unknown until the completion of the jobs. We use the optimality region for the job permutation as an optimality measure of the optimal schedule. We investigate properties of the optimality region and derive O ( n ) -algorithm for calculating a quasi-perimeter of the optimality set (i.e., the sum of lengths of the optimality segments for n given jobs). We develop a fast algorithm for finding a job permutation having the largest quasi-perimeter of the optimality set. The computational results in constructing such permutations show that they are close to the optimal ones, which can be constructed for the factual durations of all given jobs.

Robust single machine scheduling with a flexible maintenance activity

In this paper, we address a problem arising in a manufacturing environment concerning the joint scheduling of multiple jobs and a maintenance activity on a single machine. Such activity must be processed within a given time window and its non-deterministic duration takes values in a given interval.We seek job schedules which are robust to any possible changes in the maintenance activity duration. We consider makespan and total completion time objectives under four different robustness criteria. We discuss a few properties and the complexity of finding robust schedules for the resulting eight problem scenarios.For the case of total completion time objective and maximum absolute regret criterion, we design and test exact and heuristic algorithms. The results of an extensive computational campaign, performed for assessing the performance of the proposed solution approaches, are reported.

Single Machine Scheduling Problem with Interval Processing Times and Total Completion Time Objective

We consider a single machine scheduling problem with uncertain durations of the given jobs. The objective function is minimizing the sum of the job completion times. We apply the stability approach to the considered uncertain scheduling problem using a relative perimeter of the optimality box as a stability measure of the optimal job permutation. We investigated properties of the optimality box and developed algorithms for constructing job permutations that have the largest relative perimeters of the optimality box. Computational results for constructing such permutations showed that they provided the average error less than 0 . 74 % for the solved uncertain problems.

The 2-stage assembly flowshop scheduling problem with total completion time: Efficient constructive heuristic and metaheuristic

In this paper, we address the 2-stage assembly scheduling problem where there are m machines in the first stage to manufacture the components of a product and one assembly station (machine) in the second stage. The objective considered is the minimisation of the total completion time. Since the NP-hard nature of this problem is well-established, most previous research has focused on finding approximate solutions in reasonable computation time. In our paper, we first review and derive a number of problem properties and, based on these ideas, we develop a constructive heuristic that outperforms the existing constructive heuristics for the problem, providing solutions almost in real-time. Finally, for the cases where extremely high-quality solutions are required, a variable local search algorithm is proposed. The computational experience carried out shows that the algorithm outperforms the best existing metaheuristic for the problem. As a summary, the heuristics presented in the paper substantially modify the state-of-the-art of the approximate methods for the 2-stage assembly scheduling problem with total completion time objective.

New approximate algorithms for the customer order scheduling problem with total completion time objective

In this paper, we study a customer order scheduling problem where a number of orders, composed of several product types, have to be scheduled on a set of parallel machines, each one capable to process a single product type. The objective is to minimise the sum of the completion times of the orders, which is related to the lead time perceived by the customer, and also to the minimisation of the work-in-process. This problem has been previously studied in the literature, and it is known to be NP-hard even for two product types. As a consequence, the interest lies on devising approximate procedures to obtain fast, good performing schedules. Among the different heuristics proposed for the problem, the ECT (Earliest Completion Time) heuristic by Leung et al. [6] has turned to be the most efficient constructive heuristic, yielding excellent results in a wide variety of settings. These authors also propose a tabu search procedure that constitutes the state-of-the-art metaheuristic for the problem. We propose a new constructive heuristic based on a look-ahead mechanism. The computational experience conducted shows that it clearly outperforms ECT, while having both heuristics the same computational complexity. Furthermore, we propose a greedy search algorithm using a specific neighbourhood that outperforms the existing tabu search procedure for different stopping criteria, both in terms of quality of solutions and of required CPU effort.

Open Shop Scheduling with Synchronization

In this paper, we study open shop scheduling problems with synchronization. This model has the same features as the classical open shop model, where each of the n jobs has to be processed by each of the m machines in an arbitrary order. Unlike the classical model, jobs are processed in synchronous cycles, which means that the m operations of the same cycle start at the same time. Within one cycle, machines which process operations with smaller processing times have to wait until the longest operation of the cycle is finished before the next cycle can start. Thus, the length of a cycle is equal to the maximum processing time of its operations. In this paper, we continue the line of research started by Weiß et al. (Discrete Appl Math 211:183–203, 2016). We establish new structural results for the two-machine problem with the makespan objective and use them to formulate an easier solution algorithm. Other versions of the problem, with the total completion time objective and those which involve due dates or deadlines, turn out to be NP-hard in the strong sense, even for m=2 machines. We also show that relaxed models, in which cycles are allowed to contain less than m jobs, have the same complexity status.

Robust single machine scheduling with external-party jobs

In this paper we address a problem arising in a manufacturing environment in which the owner of a machining resource, besides its own jobs, must process also jobs belonging to an external party. Due to contract commitments, the jobs of the external party must be processed within a certain due date, that can be considered as a deadline. Moreover, these jobs have a given release date corresponding to their actual availability in the manufacturing system. The external party jobs arrive with an estimate of their durations and the owner of the machining resource, when planning the schedule of its jobs, must take into account possible deviations from the nominal values of the external processing times. It is therefore important to determine a schedule which is robust to any possible changes in the durations of the external jobs.We consider the total completion time objective for the owner of the machining resource. However, due to the uncertainty on the external jobs processing times, we seek for a solution minimizing the maximum absolute deviation from an optimal schedule. We derive some properties of such robust schedules and evaluate the performance two mixed integer linear programming formulations.

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.

Multi-factory parallel machine problems: Improved mathematical models and artificial bee colony algorithm

This paper considers the problem of multi factory parallel machine problems. This problem is already studied in the literature and there is a mathematical model and a genetic algorithm for the problem. We analyzed the model and algorithm, and showed that they suffer from serious shortcomings. Then, we propose three mathematical models for makespan and total completion time objectives. The proposed models are compared with the available model in both size and computational complexities. The available model is significantly outperformed. Moreover, we propose three effective metaheuristics based on artificial bee colony algorithms. The proposed metaheuristics are compared against the four available algorithms on both small and large instances. The proposed metaheuristics perform much more effectively.

The inverse parallel machine scheduling problem with minimum total completion time

In inverse scheduling problems, ajob sequence is given and the objective is to determine the minimalperturbation to parameters, such as processing times or weights ofjobs so that the given schedule becomes optimal with respect to apre-selected objective function. In this paper we study thenecessary and sufficient conditions for optimality of the totalcompletion time problem on parallel machines and inverse schedulingproblem of the total completion time objective on parallel machinesin which the processing times are minimally adjusted, so that agiven target job sequence becomes an optimal schedule.

A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine

In this paper, we consider the scheduling a set of deteriorating jobs on a single processor. We propose a model which reflects real life situations in which the processing time of jobs change depending on its initial processing time (deteriorating jobs) and activities, such as machine maintenance or a break for workers. A rate-modifying activity (rma) is a maintenance activity given to a machine to restore it to its original state. The general problem we deal with in this study is to determine the job sequence, the number of rmas, and rma positions within the work sequence. We formulate a unique integer program to solve this model for makespan and total completion time objectives. We also propose efficient heuristic algorithms for solving large size problems for both makespan and total completion time objectives.

A new heuristic for minimizing total completion time objective in permutation flow shop scheduling

A constructive heuristic for the permutation flow shop scheduling problem with the objective of minimizing total completion time is proposed in this paper. It is constructed using a population-based technique and also the insertion rule similar to that presented in the Nawaz–Enscore–Ham (Omega 11:91–95, 1983) heuristic for the makespan criterion. We show, through computational results, that the proposed heuristic performs better than the heuristic of Woo and Yim (Comput Oper Res 25:175–182, 1998) for small and large problem sizes and the heuristic of Framinan and Leisten (Omega 31:311–317, 2003) for small and medium problem sizes. However, the relative performance of the heuristic of Framinan and Leisten improves compared to the proposed method when the job size increases. The time complexity of the proposed method has been shown to be less than those required by the existing heuristics. The average CPU time of the proposed heuristic is significantly less than the heuristic of Framinan and Leisten for large jobs.

Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem

We study a scheduling problem motivated by the challenges observed in the newest semiconductor manufacturing wafer fabrication facilities. As wafers are larger and heavier in these wafer fabs, it is becoming more common to use specialized material handling containers that carry multiple orders coming from different customers and to schedule the containers as jobs in the fab. The system performance is a function of the completion times of orders, which ultimately depend on both (1) how the orders are assigned to such containers (“job formation”), and (2) how the containers are scheduled in the fab (“job scheduling”). The overall problem is to find the best way to form and schedule the jobs subject to complicating constraints, including the restrictions on the number of containers that can be used at one time and on the number of wafers the containers can carry. We focus on the single machine job formation and scheduling problem with the total completion time objective. We show that this problem is quite different from conventional parallel and serial batching scenarios and prove that the uncapacitated special case is polynomially solvable and the capacitated case is strongly NP-hard. We use a dynamic programming algorithm to solve the uncapacitated problem, which not only provides tight lower bounds for the capacitated problem, but also becomes a basis for a heuristic approach for the capacitated problem. The computational results show that this approach is very effective, leading to small optimality gaps that get even smaller as the problems become larger.

SCHEDULING TWO-MACHINE FLOW SHOPS WITH EXACT DELAYS

We consider two-machine flow shop problems with exact delays. In this model, there are two machines, the upstream machine and the downstream machine. Each job j has two operations: the first operation has to be processed on the upstream machine and the second operation has to be processed on the downstream machine, subject to the constraint that the time interval between the completion time of the first operation and the start time of the second operation is exactly [Formula: see text]. We concentrate on the objectives of makespan and total completion time. For the makespan objective, we first show that the problem is strongly NP-hard even if there are only two possible delay values. We then show that some special cases of the problem are solvable in polynomial time. Finally, we design efficient approximation algorithms for the general case and some special cases. For the total completion time objective, we give optimal polynomial-time algorithm for a special case and an efficient approximation algorithm for another one.