Penjadwalan Mesin dengan Metode Integer Linear Programming pada PT. XYZ

Author(s):  
Fransiskus Lauson Matondang ◽  
Rosnani Ginting

PT XYZ sering mengalami keterlambatan waktu karena dalam setiap keterlambatan yang dilakukan selalu ada penalty yang diberikan kepada perusahaan dan hal ini mengakibatkan tambahan biaya , oleh karena itu hal ini harus dihindari dengan membuat penjadwalan yang efisien, dalam hal ini dilakukanlah perbaikan dengan meminimisasi waktu penyelesaian maksimum Cmax pada mesin paralel yang berpola aliran flowshop (dan tidak boleh dilakukan interupsi yang dilakukan pada pekerjaan yang sedang diproses, untuk melakukan pekerjaan lainnya, satu lintasan hanya memproduksi satu produk dan hanya satu produk juga yang dikerjakan secara langsung. Waktu penyelesaian yang berbeda dari setiap mesin dengan pengerjaannya juga adalah masalah yang dihadapi untuk menjadikan mesin mesin ini sesuai menjadi satu penjadwalan yang terintegrasi dengan metode integer programming yang membuat penjadwalan dengan konsep riset operasi dengan metode pendekatan 0-1 utuk menjadi lebih efisien lagi , dihasilkan minimisasi keterlambatan total penyelesaian order dengan 42,28 menit lebih baik dari sebelumnya.   PT XYZ often experiences time delays because in every delay made there is always a penalty given to the company and this results in additional costs, therefore this must be avoided by making efficient scheduling, in this case repairs are carried out by minimizing the maximum completion time of Cmax on parallel machines that are patterned with flowshop flow (and no interruptions should be carried out on the work being processed, to do other work, one track only produces one product and only one product is directly worked. Different completion times of each machine with the workmanship is also the problem faced to make this machine suitable to be one scheduling integrated with integer programming methods that makes scheduling with the operational research concept with the 0-1 approach method to be more efficient, resulting in minimization of the delay in the total settlement of orders with 42.28 minutes was better than before.

2021 ◽  
Vol 11 (8) ◽  
pp. 3677
Author(s):  
Yassine Ouazene ◽  
Nhan-Quy Nguyen ◽  
Farouk Yalaoui

This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.


Algorithmica ◽  
2021 ◽  
Author(s):  
Matthias Englert ◽  
David Mezlaf ◽  
Matthias Westermann

AbstractIn the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and $$\approx 1.4659$$ ≈ 1.4659 . They show that $$k = O(m)$$ k = O ( m ) is sufficient to achieve this bound and no $$k = o(n)$$ k = o ( n ) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a $$\delta = \varTheta (1)$$ δ = Θ ( 1 ) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than $$1.4659 + \delta $$ 1.4659 + δ with $$k = o(n)$$ k = o ( n ) . We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and $$\approx 1.7992$$ ≈ 1.7992 with $$k = O(m)$$ k = O ( m ) . We also show that $$k = \varOmega (m)$$ k = Ω ( m ) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.


2013 ◽  
Vol 441 ◽  
pp. 602-606
Author(s):  
Wei Jun Pan ◽  
Wen Bin Qiu ◽  
Rui Kang

A nonlinear integer programming model (NIPM) with constraints is proposed to solve the allocation of approach flight flow where ends with terminal airspace, an example of an airport terminal airspace is given, where the flow is accurately forecasted.Analysising flight delays, theres a conclusion: the results solved by NIPM is far better than the average allocation method, for the second-level airspace, NIPM can reduce two flight delays, and the allocation in each flight route tends to be equilibrium, NIPM can also provide air traffic controllers with accurate and reasonable allocation schedule.


2013 ◽  
Vol 437 ◽  
pp. 748-751
Author(s):  
Chi Yang Tsai ◽  
Yi Chen Wang

This research considers the problem of scheduling jobs on unrelated parallel machines with inserted idle times to minimize the earliness and tardiness. The aims at investigating how particular objective value can be improved by allowing machine idle time and how quality solutions can be more effectively obtained. Two mixed-integer programming formulations combining with three dispatching rules are developed to solve such scheduling problems. They can easy provide the optimal solution to problem involving about nine jobs and four machines. From the results of experiments, it is found that: (1) the inserted idle times decreases objective values more effectively; (2) three dispatching rules are very competitive in terms of efficiency and quality of solutions.


2013 ◽  
Vol 330 ◽  
pp. 843-847 ◽  
Author(s):  
Fuh Der Chou ◽  
Hui Mei Wang

This paper considers the scheduling problem of the four-stage open shop with parallel machines per stage observed in the chip sorting operation of light emitting diode (LED) testing. In this operation, each job (epiwafer) should be processed by the four working stages without predetermined processing route in order to separate specific LED grades. The considered problem is one of hard combinatorial optimization problems which have not been received much attention in the literature. Due to its computational complexity, in this study, two simulated annealing (SA) algorithms with different initial solutions are proposed to minimize total weighted completion times of jobs. A set of twenty benchmark solutions from a five-job problem is used to evaluate the performances of two SAs. Computational results reveal that the algorithms perform efficient and effective whatever the dimensions of problems are small or large.


Author(s):  
Hanane Krim ◽  
Nicolas Zufferey ◽  
Jean-Yves Potvin ◽  
Rachid Benmansour ◽  
David Duvivier

AbstractWe consider in this work a bicriteria scheduling problem on two different parallel machines with a periodic preventive maintenance policy. The two objectives considered involve minimization of job rejection costs and weighted sum of completion times. They are handled through a lexicographic approach, due to a natural hierarchy among the two objectives in the applications considered. The main contributions of this paper are first to present a new problem relevant to practice, second, to develop a mixed-integer-linear-program model for the problem, and third, to introduce two generalizable tabu-search metaheuristics relying on different neighborhood structures and solution spaces. Computational results for 120 instances (generated from a real case) are reported to empirically demonstrate the effectiveness of the proposed metaheuristics.


2019 ◽  
Vol 34 (6) ◽  
pp. 856-856
Author(s):  
K Indorewalla ◽  
M Lanca ◽  
J Osher ◽  
R Kartik ◽  
N Vaidya ◽  
...  

Abstract Objective The Color Trails Test (CTT) is a neuropsychological measure tapping into frontal and executive functioning, while at the same time minimizing the cultural and language barriers inherent in similar neurocognitive measures such as the Trail Making Test (TMT). This study generates culturally-appropriate normative data for the CTT in an adult Indian population. Method Six-hundred and sixty-nine cognitively healthy, community dwelling Indian individuals between ages 18 and 69 participated in the study. Eligible participants were stratified on the basis of age, gender, and educational attainment. Participant performance on the CTT and TMT were correlated to establish concurrent validity. Results Significant correlations were found between TMT-part A and CTT-part 1 (r = .61) and between TMT-part B and CTT-part 2 (r = .66). In addition to generating culturally-appropriate normative data, the current study found that age and educational attainment significantly impacted participant performance on CTT-Part 1 [F(4, 649) = 4.395, p = .002], whereas gender, along with age, and educational attainment significantly impacted performance on CTT-Part 2 [F(4,649) = 2.446, p = .045]. In general, younger participants with more educational attainment performed better on both parts of the CTT. Interestingly, older female participants with lower educational attainment performed better than their younger counterparts on CTT-Part 2, whereas no such findings were noted for male participants. Conclusions Age, gender, and educational attainment are important factors to consider when interpreting CTT completion times in the Indian population. Normative data generated from this study has important clinical implications and contributes to the growing body of culturally-appropriate normative data available for the Indian population.


Author(s):  
Michael Racer ◽  
Robin Lovgren

The quality of a solution to an integer programming problem is a function of a number of elements. Lightly constrained problems are easier to solve than those with tighter constraints. Local search methods generally perform better than greedy methods. In the companion paper to this one, the authors investigated how peripheral information could be gathered and utilized to improve solving subsequent problems of the same type. In the current paper, they extend this to the dynamic environment – that is, utilizing such “peripheral” information as the solver is in progress, in order to determine how best to proceed.


2018 ◽  
Vol 35 (04) ◽  
pp. 1850024
Author(s):  
Wenjie Li ◽  
Hailing Liu ◽  
Shisheng Li

This paper studies online scheduling on [Formula: see text] identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When [Formula: see text], we prove that WSPT is an optimal online algorithm. When [Formula: see text], we first present a lower bound [Formula: see text], and then show that WSPT is a 2-competitive online algorithm for the case [Formula: see text]. For the case in which [Formula: see text] and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of [Formula: see text].


Sign in / Sign up

Export Citation Format

Share Document