Longest Processing Time Rule Research Articles

A Heuristic Based on LPT rule and a restricted B&B Method to Minimizing the Expected Makespan on a Single Machine

Considering the production and maintenance schedule simultaneously has a great attention for more than two decades. At the beginning, most of these researches treated maintenance activities as a fixed hole in the study period. Later, in the majority of them, the maintenance periods starting time were fixed but their intervals may variate. In the non-preemptive case, only few of articles that deals with the maintenance activities starting time as a decision variable. In this article, the time to starting the planed maintenance activities (PM) is a decision variable and the expected repair time is estimated according to nonhomogeneous Poisson process (NHPP). The failure function is Weibully distributed and the repair due to failure is minimal while the PM repair is perfect. Two cases were considered for the model which is aiming to minimizing the expected makespan (EMS), first, the preemptive case which was solved optimally. Secondly, a heuristic based on longest processing time rule (LPT) and a restricted branch and bound method (B&B) are provided to solve the problem for the non-preemptive case. Each of the proposed procedures uses the optimal solution properties of the preemptive case. The optimal solution for the non-preemptive model can be reached using LPT in case of . Finally, the results showed the robustness for B&B which their lower bound obtained by the optimal solution of the preemptive case and the upper bound is the first solution obtained by LPT.

Bounding schemes for the parallel machine scheduling problem with DeJong's learning effect

In this paper, the parallel machine scheduling problem with DeJong's learning effect, is addressed. The objective function to be minimized is the makespan. This problem is proofed to be NP-Hard in the strong sense. This is the challenging theoretical side of the studied problem. Furthermore, several real-life situations in manufacturing and computer science are modeled using the current problem. Several algorithms intended to solve the studied problem within a reasonable computing time are proposed in literature. Among these algorithms the exact methods, which failed to solve the studied problem to optimality even for small size instances. In this paper several new heuristics and meta-heuristics are proposed. These heuristics are classified into three types. The first type is based on Longest Processing Time (LPT) rule. The innovation is the modification of the LPT rule in a way to cope efficiently with the learning effect concept, by randomizing the selection of the next scheduled job. The second type of heuristics, is taking advantage of an exact Branch and Bound algorithm, developed originally for the classical parallel machine scheduling problem. The contribution for this kind of heuristics is lying in the modification of the processing time values, according to a prefixed selected functions. The third type of methods is based in an adaptation of the Genetic Algorithm to the learning effect concept. This adaptation consists in enlarging the area of selection of the parameters values. To assess the performance and the efficiency of the proposed heuristics, a newly developed lower bound is proposed. This lower bound is based on a relaxation of the studied problem, which allows to obtain a minimum cost flow problem.Finally, an extensive experimental study is conducted over a benchmark test problems. The obtained results provide strong evidence that the proposed procedures outperform the earlier existing ones.

A parallel-machine scheduling problem with periodic maintenance under uncertainty

A parallel-machine scheduling problem with preventive maintenance is studied in the paper. Because of the existence of indeterminacy phenomenon, the processing and maintenance time are assume to be uncertain variables. To address these uncertain parameters, two pessimistic value mathematical programming models are developed and the equivalence is proved. The worst-case bound of longest processing time (LPT) rule for the problem under an uncertain environment is obtained. To solve this problem effectively, an improved LPT rule is proposed according to the result of the theoretical analysis. Finally, numerical experiments show that the improved LPT outperforms the LPT in improving the quality of the optimal value and has a less relative error than that of the LPT.

Job shop scheduling considering material handling process

This paper discussed job shop scheduling considering material handling process. This process is a very important aspect on a flexible manufacturing system, where raw material or semi-finished goods are delivered from one processing point unto another by utilizing automated material handling equipment, functioned as shared resources. The starting time of each process is affected by the ability of the material handling equipment to conduct timely delivery from one point to another, therefore considering this process unto scheduling is important to enable planner to get precise estimation of the process makespan. We take the case where the flexible manufacturing system is consisted of four identical machines; each has the capability of processing various jobs due to the various cutting tools installed on their tools magazine. Jobs are dispatched based on longest processing time rule and then allocated to machine which has minimum load. Being a shared resource, material handling equipment has pick-up and delivery priority rule when handling multiple requests. The two most common rules are longest waiting and closest entity. This paper will analyzed the impact of each rule to the process makespan and material handling equipment utilization. Simulation model were built using Promodel to give decision maker better visualization of the system under consideration.

Reglas de despacho en la programación de procedimientos quirúrgicos electivos: impacto en los indicadores de ocupación y oportunidad

Introduction: The performance of a surgery service is highly impacted by its schedule. This study measured the impact of the artificial variability caused by a manual scheduling of surgeries at “Hospital Universitario Mayor - Mederi (HUM)” (Colombia). The hypotheses were that the proposed algorithm is able to (i) reduce daily service variation, (ii) increase the availability of service resources, and (iii) improve the opportunity time for each surgery. Materials and methods: The studied surgical service performs around 35,000 annual surgeries and its scheduling process is presently manually made. Actual scheduling records of a regular month were compared to schedules generated by a Bin Packing (BP) algorithm hybridized with the Longest Processing Time (LPT) and Shortest Processing Time (SPT) dispatching rules. Results: It was found that the BP algorithm with LPT rule could improve service performance, reducing the variation coefficients of patients’ flow and daily service occupation by 25.09 % and 36.71 %, respectively. The programmed surgeries were also moved ahead 6.2 days, and the overall occupation rate increased by 26.72 %. Results were not better when a SPT rule was used, boosting the variability on patient flow by 22.7 % and reducing the occupation by 2.28 %. Conclusions: Semiautomatic scheduling of the surgical service at the HUM, a BP algorithm with LPT rule, may substantially increase service performance in terms of service occupation and opportunity.

Operating Room Planning under Surgery Type and Priority Constraints

Operating room (OR) planning is critical in healthcare systems to reduce cost and improve the efficiency of OR scheduling. The OR planning problem is complicated, involving many conflicting factors, such as overtime and idle time, both of which affect OR utilization and consequently affect cost to a hospital. Allocating different types of surgeries into OR blocks affects the setup cost, whereas priorities of surgeries affect OR block scheduling. Surgery durations affect both OR utilization and OR block scheduling. Traditionally, one important method for OR block scheduling is the bin packing model, and the longest processing time (LPT) rule is the most commonly used method to generate the initial sequence for bin packing. In this study. We propose a multistep approach and a priority-type-duration (PTD) rule to generate the initial sequence for bin packing. The results of our case studies show that our PTD rule outperforms the LPT rule based on the cost to OR scheduling.

Improving the Performance of Aeronautical Machine Shop with Functional Layout by Simulation Method

The manufacture of aeronautical parts has the characteristics of short preparation time and small batch with varied types. To satisfy these requirements, the manufacturer must select efficient machine layout and proper dispatching rule, so they can fabricate the expected products and quantity under the least cost. This research used the machine shop of the biggest domestic aeronautical company as the research object and focused on the manufacturing procedures of 7 parts of the landing gear. The research rearranged the production layout and conducted the production simulation to evaluate the performance by comparing current machine layout with modified functional machine layout. Historical order schedules are applied to be the releasing policy of the simulation. Furthermore, the simulation also compared the performance with different dispatching rules, SPT (Shortest Processing Time) and LPT (Longest Processing Time) rule separately. This research found out that the modified functional machine layout adopting SPT rule is the best for machine efficiency. The results of the simulation would provide the machine shop for a reference for improvements.

Non-identical parallel machine scheduling with fuzzy processing times using genetic algorithm and simulation

This paper addresses non-identical parallel machine scheduling problem with fuzzy processing times (FPMSP). A genetic algorithm (GA) approach embedded in a simulation model to minimize maximum completion time (makespan) is proposed. The results are compared with those obtained by using longest processing time rule, known as the most appropriate dispatching rule for such problems. This application illustrates the need for efficient and effective heuristics to solve FPMSPs. The proposed GA approach yields good results and reaches them fast and several times in one run. Moreover, due to its advantage of being a search algorithm, it can explore alternative schedules providing the same results.

Workflow balancing strategies in parallel machine scheduling

Workflow balancing on a shop floor helps to remove bottlenecks present in the manufacturing system. Workflow refers to the total time during which the work centres are busy. Idle time is not taken into account when calculating workflow. Earlier researchers have not specified the method for jobs to be executed in parallel in order to balance the workflow to each machine. In many manufacturing environments, multiple processing stations are used in parallel to obtain adequate capacity. In parallel machine scheduling there are m machines to which n jobs are to be assigned based on different priority strategies. The procedure is based on the idea of workload balancing and on balancing the workload among machines. In this paper, workflow and workload are assumed to have the same meaning. A machine with the lowest workflow is selected for assignment of a new job from the list of unfinished jobs. Different priority strategies are followed for the selection of jobs. Three different strategies are considered, namely random (RANDOM), shortest processing time (SPT) and longest processing time (LPT) for the selection of jobs for workflow balancing. The relative percentage of imbalance (RPI) is adopted among the parallel machines to evaluate the performance of these strategies in a standard manufacturing environment. The LPT rule shows better performance for the combination of larger job sizes and higher number of work centres or machines. A computer program was coded for validation in a standard manufacturing environment on an IBM/PC compatible system in the C++ language.

Scheduling jobs with proportionate early/tardy penalties

We address the problem of scheduling jobs subject to proportionate early/tardy penalties. The problem is known to be NP-complete. We identify interesting special cases, and develop polynomial time procedures for solving them optimally. It is shown that the shortest processing time rule is optimal when due dates are set using the widely known total work content rule or the equal slack rule. If jobs have a common due date, many alternative optimal solutions exist, and the longest processing time rule yields an optimal sequence. Also, a simple formula is provided for determining the optimal start times forjobs in the common due date problem. Our results for the common due date problem generalize and extend earlier research. Further extensions are discussed.

AN EXCHANGE HEURISTIC FOR GENERALIZED JOB SHOP SCHEDULING

Abstract An efficient heuristic for the generalized job shop scheduling problem, with or without multiple parallel machines, is herein presented. This heuristic, in a somewhat more general form, was explained in some detail in our earlier work in project scheduling; and we now suggest that, through this approach, problems in the areas of job shop scheduling and project scheduling may be viewed as elements of the same class. Given an initial feasible solution, the algorithm seeks to improve on this schedule through reduction of makespan by effectively identifying rearrangement opportunities. The quality of the final schedule appears to be, in general, directly correlated to the quality of the starting solution. However, it is recommended that the process be initiated with a reasonably good randomly-generated schedule, rather than a better one produced through rule-based scheduling (such as the Longest Processing Time rule), owing to the fact that such better schedules actually tend to offer less opportunit...

The Asymptotic Optimality of the LPT Rule

For the problem of minimizing makespan on parallel machines of different speed, the behaviour of list scheduling rules is subjected to a probabilistic analysis under the assumption that the processing requirements of the jobs are independent, identically distributed nonnegative random variables. Under mild conditions on the probability distribution, we obtain strong asymptotic optimality results for the LPT (Longest Processing Time) rule, in which the jobs are assigned to the machines in order of nonincreasing processing requirements.