Total Processing Time Of Jobs Research Articles

Effective upper and lower bounds for a two-stage reentrant flexible flow shop scheduling problem

Flow shop scheduling is important in modern industrial manufacturing to improve production efficiency. This paper studies a realistic two-stage reentrant flexible flow shop scheduling problem (TSRFFS) with broad applications in aircraft scheduling, manufacturing, and the medical industry, etc. Given a flow shop with a single machine in Stage 1, a set of parallel machines in Stage 2, and a set of jobs to be processed, the TSRFFS aims to determine the completion time of jobs in Stage 1 and then that in Stage 2, and finally returns to Stage 1, as well as determine the job-to-machine assignment in Stage 2 such that all jobs are served and the total processing time of jobs (makespan) is minimized. The optimal solution properties are investigated, based on which a mixed integer programming mathematical model and a greedy random constructive heuristic for near optimal solutions are proposed. By solving series of a revised parallel machine scheduling problem (Pm||Cmax), a lower bound method is developed. Extensive numerical experiments on 1560 random instances with up to 1000 jobs and 50 realistic airport simulation instances were conducted to demonstrate the effectiveness of the proposed algorithms. The average gap between the proposed upper bound and the best lower bounds is approximately 1.78%, and the average gap between the proposed lower bound and the best upper bounds is 0.91%, which far outperforms state-of-the-art approaches in terms of solution quality and computational time.

Penjadwalan Produksi Job shop Mesin Majemuk Menggunakan Algoritma Non Delay untuk Meminimalkan Makespan

Scheduling is an important factor in both manufacturing and service industry environments. Scheduling is a resource allocation arrangement for completing tasks that involve work, resources and time. With the scheduling, all work can be completed according to priority and can minimize processing time, so that makespan is minimal. In addition, it can reduce idle machines and reduce the inventory of semi-finished goods. Maryati Small Micro and Medium Enterprises (IKM) is a business that is engaged in the manufacture of clothing that produces various types of products such as baby clothes, teenage clothes to adults. So far, IKM Maryati is in the process of machine scheduling by determining the order of Job execution based on the longest to shortest total Job processing time. Scheduling with this method creates problems for the company, as evidenced by the accumulation of semi-finished goods at several work-stations. Another problem is when orders arrive at a certain period with a large variety and number of products, causing Job completion that exceeds the target time (due-date). The size of the makespan causes the production time to increase, so the company is late to start production of orders in the following month. In this study, the Non-delay algorithm is used to solve the problems that arise in IKM Maryati. The result obtained is the scheduling using the existing method by IKM Maryati which produces 44 days makespan value. Meanwhile, by applying the Non-delay compound engine algorithm, it produces a makespan of 42 days. This shows that the compound machine Non-delay Algorithm method can minimize the makespan value in IKM Maryati. There is an efficiency of 4.55% in both time and cost variables.

Two-agent scheduling on mixed batch machines to minimise the total weighted makespan

This paper studies a two-agent scheduling problem on mixed batch machines in parallel. A mixed batch machine can process several jobs simultaneously as a batch, as long as the number of jobs in the batch does not exceed the machine capacity. The processing time of a mixed batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimise the weighted sum of two agents' makespans. We present four approximation algorithms based on two strategies: the machine-centric strategy and the agent-centric strategy. For each strategy, a full batch longest processing time (FBLPT) rule and a longest processing time greedy (LPTG) rule are used. We conduct theoretical analyses based on the worst-case performance ratio to provide the provable guarantees on the performances of the algorithms, and simulation analyses based on randomly generated instances to evaluate the average performances of the algorithms. Furthermore, we verify the consistency between the theoretical and simulation results. The algorithms using agent-centric strategy perform better than ones using machine-centric strategy. Finally, we provide managerial insights for the problem by analysing the technological parameters of batches, importance of agents, and demand seasonality.

Mixed batch scheduling on identical machines

This paper studies a new mixed batch scheduling problem that arises in vacuum heat treatment. A mixed batch machine can process at most a given number of jobs simultaneously. The processing time of a batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimize the makespan. We first prove that the problem on a single machine can be solved in polynomial time, while the problem on multiple identical machines is NP-hard. Then, we develop a pseudopolynomial time exact algorithm when the number of machines is fixed. Further, we analyze the worst-case performance ratio of a full batch longest processing time algorithm and design Algorithm LPT-Greedy with improved worst-case performance.

Extended open shop scheduling with resource constraints: Appointment scheduling for integrated practice units

An Integrated Practice Unit (IPU) is a new approach to outpatient care in which a co-located multidisciplinary team of clinicians, technicians, and staff provide treatment in a single patient visit. This article presents a new integer programming model for an extended open shop problem with application to clinic appointment scheduling for IPUs. The advantages of the new model are discussed and several valid inequalities are introduced to tighten the linear programming relaxation. The objective of the problem is to minimize a combination of makespan and total job processing time, or in terms of an IPU, to minimize a combination of closing time and total patient waiting time. Feasible solutions are obtained with a two-step heuristic, which also provides a lower bound that is used to judge solution quality. Next, a two-stage stochastic optimization model is presented for a joint pain IPU. The expected value solution is used to generate two different patient arrival templates. Extensive computations are performed to evaluate the solutions obtained with these templates and several others found in the literature. Comparisons with the expected value solution and the wait-and-see solution are also included. For the templates derived from the expected value solution, the results show that the average gap between the feasible solution and lower bound provided by the two-step heuristic is 2% for 14 patients. They also show that either of the two templates derived from the expected value solution is a good candidate for assigning appointment times when either the clinic closing time or the patient waiting time is the more important consideration. Sensitivity analysis confirmed that the optimality gap and clinic statistics are stable for marginal changes in key resources.

Minimizing the Number of Tardy Jobs on Identical Parallel Machines Subject to Periodic Maintenance

This paper considers the problem of scheduling n independent jobs on m identical parallel machines in order to minimize the number of tardy jobs (ηT) considering the periodic preventive maintenance to avoid machine breakdowns. It assumes that there are several maintenance periods during the scheduling process and that each maintenance time is scheduled after a working time interval. Job preemption is not allowed. In this regard, a heuristic procedure and a mathematical model are proposed to minimize ηT. The S-B-C 1 heuristic is used to tackle the identical parallel machine scheduling problem. The suggested heuristic follows several steps to solve the problem. It depends on scheduling jobs with several batches based on the working time interval, where the total processing time of jobs for each batch should not exceed the working time interval. The first step uses the S-B-C 1 heuristic to determine the initial schedule for minimizing ηT. The second step calculates the slack time for each working time interval for each machine, which equals to the unscheduled time in the batch. Then, the tardy jobs are rescheduled in the system to minimize ηT considering scheduling jobs during the slack time for each batch. The results obtained show the effectiveness of the proposed heuristic to minimize ηT subject to periodic maintenance requirements. The heuristic procedure results show that the heuristic is able to find the optimal solution in 19 out of 54 instances. In the remaining cases, the ηT increases on the average 8.43%.

A note on unbounded parallel-batch scheduling

This paper revisits the scheduling problem on an unbounded parallel batch machine for minimizing a maximum cost fmax. It was reported in the literature that the decision version of the problem is solvable in O(n2+nlog⁡P) time, where n is the number of jobs and P is the total processing time of jobs. This implies that the optimization version for minimizing fmax can be solved in weakly polynomial time. But a strongly polynomial-time algorithm has not been provided for this problem. In this paper, we present an O(n4)-time algorithm for the Pareto optimization problem for minimizing Cmax and fmax, where Cmax is the maximum completion time of jobs. Consequently, the problem for minimizing fmax can also be solved in O(n4) time.

A2HA—automatic and adaptive host allocation in utility computing for bag-of-tasks

AbstractThere are increasingly more computing problems requiring lengthy parallel computations. For those without access to current cluster or grid infrastructures, a recent and proven viable solution can be found with on-demand utility computing infrastructures, such as Amazon Elastic Compute Cloud (EC2). A relevant class of such problems, Bag-of-Tasks (BoT), can be easily deployed over such infrastructures (to run on pools of virtual computers), if provided with suitable software for host allocation. BoT problems are found in several and relevant scenarios such as image rendering and software testing.In BoT jobs, tasks are mostly independent; thus, they can run in parallel with no communication among them. The number of allocated hosts is relevant as it impacts both the speedup and the cost: if too many hosts are used, the speedup is high but this may not be cost-effective; if too few are used, the cost is low but speedup falls below expectations. For each BoT job, given that there is no prior knowledge of neither the total job processing time nor the time each task takes to complete, it is hard to determine the number of hosts to allocate. Current solutions (e.g., bin-packing algorithms) are not adequate as they require knowing in advance either the time that the next task will take to execute or, for higher efficiency, the time taken by each one of the tasks in each job considered.Thus, we present an algorithm and heuristics that adaptively predicts the number of hosts to be allocated, so that the maximum speedup can be obtained while respecting a given predefined budget. The algorithm and heuristics were simulated against real and theoretical workloads. With the proposed solution, it is possible to obtain speedups in line with the number of allocated hosts, while being charged less than the predefined budget.

ONLINE AND SEMI-ONLINE SCHEDULING ON CAPACITATED TWO-PARALLEL MACHINES

In this paper, we investigate the capacitated two-parallel machines scheduling problem, where one machine is only available for a special period of time after which it can no longer process any job while the other machine is continuously available. Our objective is to minimize the completion time of the machine which is continuously available. The offline version of the problem is equivalent to the minimization version of the Subset-Sum problem. We first show the lower bound of the online version is infinite. We also consider the semi-online version with known the total job processing time in advance, for which both lower bound and semi-online algorithms are given.

Online scheduling on two uniform machines to minimize the makespan

We consider two problems of online scheduling on two uniform machines: online scheduling under a grade of service (GoS) and online scheduling with reassignment. These problems are online in the sense that when a job presents, we have to irrevocably assign it to one of the machines before the next job is seen. The objective is to minimize the makespan. In the first problem, GoS means that some jobs have to be processed by some machine so that they can be guaranteed a higher quality. Assume that the speed of the higher GoS machine is normalized to 1, while the speed of the other one is s . We show that a lower bound of competitive ratio is 1 + 2 s s + 2 in the case 0 < s ≤ 1 and 1 + s + 1 s ( 2 s + 1 ) in the case s > 1 . Then we propose and analyze two online algorithms: HSF algorithm and EX-ONLINE algorithm. HSF is optimal in the case where s > 1 and Σ 1 ≥ Σ 2 s , where Σ 1 and Σ 2 denote the total processing time of jobs which request higher GoS machine and the total processing time of jobs which request the normal one, respectively. EX-ONLINE is optimal in the case 2 ( 2 − 1 ) ≤ s ≤ 1 . In the second problem, we study two subproblems P L and P A proposed in [Z. Tan, S. Yu, Online scheduling with reassignment, Operations Research Letters 36 (2008) 250–254]. Assume that the speeds of 2 uniform machines are 1 and s ≥ 1 , respectively. For P L where we can reassign the last k jobs of the sequence, we show a lower bound of competitive ratio 1 + 1 1 + s . For P A where we can reassign arbitrary k jobs, we show a lower bound of competitive ratio ( s + 1 ) 2 s 2 + s + 1 . We propose a s + 1 s -competitive algorithm HSF-1 for both P L and P A . For P A , we propose a ( s + 1 ) 2 s + 2 -competitive algorithm EX-RA, which is superior to HSF-1 when 1 ≤ s ≤ 2 .

Task time estimation in a multi-product manually operated workstation

Many manual workstations are designed so that a specific set of tasks to be completed on jobs are performed at the workstation. The subset of individual tasks executed on each job may vary, and a jobs total processing time at the workstation is the sum of those individual task times. Since estimates of the mean and variance of the individual task times are used to make operational and planning decisions, data should be collected on a regular basis to ensure accurate estimates. In this research, we apply a least-squares method and maximum likelihood estimation to estimate the mean and variance of individual task times at a manual workstation from total job-processing time data. Both methods assume that the time to execute individual tasks at a workstation can be treated as independent random variables whose distributions are the same regardless of what other tasks are executed on a job. The maximum likelihood method also assumes that these times are normally distributed. Efficient computational formulas developed for the least-squares method are ideal for use with an automatic data collection system, and both methods provide good estimates of mean task times that are adequate for planning and operational decisions.

Semi on-line scheduling problem for maximizing the minimum machine completion time on m identical machines

In this paper, a semi cm-line version on m identical machines M1, M2, …, Mm (m≥3) was considered, where the processing time of the largest job is known in advance. Our goal is to maximize the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m−1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2m−1)pmax where pmax is the largest job’s processing time, then the worst-case ratio is 2−1/m.

Batch scheduling with controllable setup and processing times to minimize total completion time

We study a problem of scheduling n jobs on a single machine in batches. A batch is a set of jobs processed contiguously and completed together when the processing of all jobs in the batch is finished. Processing of a batch requires a machine setup time dependent on the position of this batch in the batch sequence. Setup times and job processing times are continuously controllable, that is, they are real-valued variables within their lower and upper bounds. A deviation of a setup time or job processing time from its upper bound is called a compression. The problem is to find a job sequence, its partition into batches, and the values for setup times and job processing times such that (a) total job completion time is minimized, subject to an upper bound on total weighted setup time and job processing time compression, or (b) a linear combination of total job completion time, total setup time compression, and total job processing time compression is minimized. Properties of optimal solutions are established. If the lower and upper bounds on job processing times can be similarly ordered or the job sequence is fixed, then O(n3 log n) and O(n5) time algorithms are developed to solve cases (a) and (b), respectively. If all job processing times are fixed or all setup times are fixed, then more efficient algorithms can be devised to solve the problems.

On-line scheduling with extendable working time on a small number of machines

Speranza and Tuza [Ann. Oper. Res. 86 (1999) 494–506] studied the on-line problem of scheduling jobs on m identical machines with extendable working time. In this problem, each machine is assumed to have an identical regular working time, which can be extended if necessary. The working time of a machine is the larger one between its regular working time and the total processing time of jobs assigned to it. The objective is to minimize the total working time of machines. They presented an on-line algorithm H x , with a competitive ratio at most 1.228 for any number of machines by choosing an appropriate parameter x. In this paper we consider a small number of machines. The best choices of x are given for m=2,3,4 and the tight bounds, 7/6, 11/9 and 19/16, respectively, are proved. Among them, the algorithm for m=2 is best possible. We then derive a new algorithm for m=3 with a competitive ratio 7/6.

Scheduling in a two-machine flowshop with batch processing machine(s) for earliness/tardiness measure under a common due date

This paper considers a scheduling problem for a two-machine flowshop with batch processing machine(s) (BPMs) incorporated where the earliness/tardiness (E/T) measure and a common due date are considered. It assumes that each batch has the same processing time and that the common due date is not set earlier than the total job processing time on the first machine. Under these assumptions, some solution properties are characterized for three different problem cases to derive their associated solution algorithms. For the first two cases concerned with two different machine sequences such as batch-to-discrete and batch-to-batch machine sequences, a polynomial time algorithm is derived based on some of the solution properties. For the last case concerned with discrete-to-batch machine sequence, a pseudopolynomial algorithm is exploited.

Production and maintenance integrated planning

This paper introduces an expert system for the planning and management of a multi-product and one-stage production system made up of flexible machines operating in parallel. The following characteristics of the production system were considered: production costs depending on the machine and on the job processed, setups depending on the machine and on the job-processing sequence, preventive maintenance, order portfolio defined by order quantities, release dates and due dates. The system schedules both production and maintenance at the same time. It pursues three objectives: to meet release and due dates, to minimize the total cost of the plan (sum of the expected maintenance cost, the setup cost and the production cost) and to minimize the total plant utilization time (sum of the total job processing time, the total setup time, the total machine idle time and the total maintenance time).

Scheduling and Re-Scheduling of FMS Using AGVs on the Basis of Petri Net

This paper deals with a scheduling and re-scheduling method for flexible manufacturing systems (FMS) using automatically guided vehicles (AGVs) and input-output buffers. The purpose is to solve coordination problems of AGVs transferring jobs between machines so as to minimize idle time of each machine and the total job processing time without collision of AGVs, and quick generation of another substituting effective schedule in the case of troubles of AGVs. A hierachical timed Petri net is applied to modeling and analysis of systems. Two priority functions are defined to effectively determine job processing precedence relationships among machining orders and AGV assignment. Some scheduling simulation results are also shown in this paper.

Manufacturing systems with forbidden early shipment: Implications for setting manufacturing lead times

SUMMARY The authors compare two well-known methods for setting manufacturing lead times (flow allowances) in a general job shop when early shipment of completed jobs is forbidden. One of the methods for setting a job's allowance is to make it proportional to the total processing time for the job. This method, referred to as TWK., is compared to a second method PPW. With the PPW method, a job's allowance is obtained by adding to the total job-processing time an allowance for waiting that is proportional to the number of operations that the job requires. The two allowance methods are compared using a computer simulation of an 8-machine job shop. The model is unique in that jobs are not permitted to leave the shop early. This feature of forbidding early shipment (FES) complicates the comparison between allowance methods because it draws the issue of finished-order inventory management into the analysis. Results of computer simulations over a wide range of average due-date difficulty suggest that TWK is the d...