the assignment method of job sequencing

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Rules of Job Sequencing in Production

1/13/21 12:00 AM

By PlanetTogether

One of the ultimate goals in manufacturing is to ensure that all customer demands are produced on time for the lowest cost possible . As most resources in a production facility have limited capacity, it is common to have multiple jobs in the queue, waiting to be worked on by those resources.

Deciding on the order of jobs can be a real challenge for schedulers as you must coordinate variables such as material availability, resource capacity, upstream and downstream operations, and the need date - to name a few examples.

When a sub-optimal schedule is created, you may inadvertently create a ‘waiting line’ in front of slower machines, thereby increasing the number of WIP items and inventory holding costs.

Job Sequencing Rules have been created to help manufacturers and schedulers create optimized production schedules. Your production schedule sets the course for your business performance. An optimized production schedule will ensure that jobs and orders are completed within the timeframe they are given.

Job Sequencing Rules

There are many Job Sequencing Rules that can be used. Here are some of them:

Earliest Due Date - A common job sequencing technique is to prioritize jobs that have the earliest need date. This can also be referred to as ‘Due Date Assignment’ and it places a high priority on processing jobs with early dues dates in an effort to complete all jobs on time. This technique allows you to measure job shop quality performance through the number of late jobs, average tardiness across late jobs, and average tardiness among all jobs. Although the goal of this technique is to ensure that all jobs are completed before their due date, there can be some inefficiencies in the schedule due to frequent changeovers.
Longest Processing Time - The longest processing time methods assigns highest priority to jobs with the longest processing time. When scheduling longer jobs at the beginning of the schedule, the schedulers can reduce a large amount of much more time consuming jobs at the end of the job schedule. This form of job sequencing is extremely beneficial to manufacturers as it ensures that long jobs have time to complete before they are needed. This job sequencing technique relies on knowing the processing length for each operation to determine which jobs actually take the longest.
Shortest Processing Time - Another common method of job sequencing that is based on completion time is the shortest processing time method. This method assigns highest priority to jobs with the shortest processing time. Similar to the longest processing time job sequencing method, this requires a time estimation for each operation of the job. The shortest processing time can effectively reduce the average flow time and minimize the mean waiting time for jobs.
First-Come, First Serve - The first-come, first-served sequencing method processes orders in the order of their arrival at their production facility or resource. The arrival time is a key component and factor within the job sequencing rule, which is what separates it from methods such as longest processing time and shortest processing time. This method is commonly used in production facilities as it is extremely easy to implement and there is no estimation required for the processing time length.
Least Setup Hours - This rule is often used in cases where setup or changeover time is incurred when changing from one type of material, dye, or other attribute to another. This is also referred to as ‘sequence-dependent setup time’. This rule will create a schedule where there is the least amount of setup hours required, which is usually achieved by grouping jobs with like attributes together.

The above examples represent only a few of the many job sequencing rules that can be used. Applying these different rules to your production schedule will give you different outputs in which some may be more effective in meeting your business’s goals than others.

Although these rules may seem simple in isolation, scheduling hundreds of jobs simultaneously requires a lot of information such as the job’s due date, routing, standard setup, processing, whether alternative machines can be used to do the work, the current status of the job, and much more.

We feed it the facts we know, and it automatically proposes an optimized schedule that allows us to meet those dates. It’s something we tried, but never could do manually. DICK MARX, MATERIALS MANAGER, KNAPHEIDE TRUCK EQUIPMENT

Manual scheduling using spreadsheets can be extremely time-consuming and prone to error. This is why softwares such as PlanetTogether’s Advanced Planning and Scheduling (APS) system are becoming prevalent among manufacturing operations. PlanetTogether allows you to automatically create an optimized schedule based on the job sequencing rules you prefer.

In PlanetTogether, Optimize Rules are used in conjunction with Release Rules to define scheduling preferences and determine the best sequence of operations. This software also provides users with the flexibility of creating the schedule by using weighted factors and key performance indicators of interest.

Advanced Planning and Scheduling (APS) Software

Advanced Planning and Scheduling Softwares have become a must for modern-day manufacturing operations as customer demand for increased product assortment, fast delivery, and downward cost pressures become prevalent. These systems help planners save time while providing greater agility in updating ever-changing priorities, production schedules, and inventory plans. APS Systems can be quickly integrated with an ERP/MRP software to fill the gaps where these systems lack planning and scheduling flexibility, accuracy, and efficiency.

With PlanetTogether APS you can:

Create optimized schedules that balance production efficiency and delivery performance
Maximize throughput on bottleneck resources to increase revenue
Synchronize supply with demand to reduce inventories
Provide company-wide visibility to resource capacity
Enable scenario data-driven decision making

The implementation of an Advanced Planning and Scheduling (APS) Software will take your manufacturing operations to the next level of production efficiency by taking advantage of the operational data you already possess in your ERP system . APS is a step in the right direction of efficiency and lean manufacturing production enhancement. Try out a free trial or demo !

APS Resources

Topics: Optimize , Advanced Planning and Scheduling , operations planning , production scheduling

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Job Sequencing with Deadline

Job scheduling algorithm.

Job scheduling algorithm is applied to schedule the jobs on a single processor to maximize the profits.

The greedy approach of the job scheduling algorithm states that, “Given ‘n’ number of jobs with a starting time and ending time, they need to be scheduled in such a way that maximum profit is received within the maximum deadline”.

Set of jobs with deadlines and profits are taken as an input with the job scheduling algorithm and scheduled subset of jobs with maximum profit are obtained as the final output.

Consider the following tasks with their deadlines and profits. Schedule the tasks in such a way that they produce maximum profit after being executed −

S. No.	1	2	3	4	5
Jobs	J1	J2	J3	J4	J5
Deadlines	2	2	1	3	4
Profits	20	60	40	100	80

Find the maximum deadline value, dm, from the deadlines given.

Arrange the jobs in descending order of their profits.

S. No.	1	2	3	4	5
Jobs	J4	J5	J2	J3	J1
Deadlines	3	4	2	1	2
Profits	100	80	60	40	20

The maximum deadline, d m , is 4. Therefore, all the tasks must end before 4.

Choose the job with highest profit, J4. It takes up 3 parts of the maximum deadline.

Therefore, the next job must have the time period 1.

Total Profit = 100.

The next job with highest profit is J5. But the time taken by J5 is 4, which exceeds the deadline by 3. Therefore, it cannot be added to the output set.

The next job with highest profit is J2. The time taken by J5 is 2, which also exceeds the deadline by 1. Therefore, it cannot be added to the output set.

The next job with higher profit is J3. The time taken by J3 is 1, which does not exceed the given deadline. Therefore, J3 is added to the output set.

Since, the maximum deadline is met, the algorithm comes to an end. The output set of jobs scheduled within the deadline are {J4, J3} with the maximum profit of 140 .

Following is the final implementation of Job sequencing Algorithm using Greedy Approach −

Job Sequencing and Scheduling

First Online: 20 September 2022

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Chen, TC.T. (2023). Job Sequencing and Scheduling. In: Production Planning and Control in Semiconductor Manufacturing. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-14065-5_5

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Job Sequencing with Deadlines

Job sequencing with deadlines is a problem that involves scheduling a set of jobs to maximize profit while adhering to their respective deadlines. This approach assumes that each job can be completed in exactly one unit of time. If jobs have different durations, a more advanced scheduling algorithm might be necessary. Also, if the deadlines are represented as relative time (e.g., time units after job release), the algorithm would require adjustments accordingly.

In this article, we explain Job Sequencing with Deadlines through algorithms like the Greedy method.

What is Job Sequencing with Deadlines?

The prime objective of the Job Sequencing with Deadlines algorithm is to complete the given order of jobs within respective deadlines, resulting in the highest possible profit. To achieve this, we are given a number of jobs, each associated with a specific deadline, and completing a job before its deadline earns us a profit. The challenge is to arrange these jobs in a way that maximizes our total profit.

It is not always possible to complete all of the assigned jobs within the deadlines. For each job, denoted as Ji, we have a deadline di and a profit pi associated with completing it on time. Our objective is to find the best solution that maximizes profit while still ensuring that the jobs are completed within their deadlines.

Here’s how Job Sequencing with Deadlines algorithm works:

Problem Setup

You’re given a list of jobs, where each job has a unique identifier (job_id), a deadline (by which the job should be completed), and a profit value (the benefit you gain by completing the job).

Sort the Jobs by Profit

To ensure we consider jobs with higher profits first, sort the jobs in non-increasing order based on their profit values.

Initialize the Schedule and Available Time Slots

Set up an array to represent the schedule. Initialize all elements to -1, indicating that no job has been assigned to any time slot. Also, create a boolean array to represent the availability of time slots, with all elements set to true initially.

Assign Jobs to Time Slots

Go through the sorted jobs one by one. For each job, find the latest available time slot just before its deadline. If such a time slot is available, assign the job to that slot. If not, skip the job.

Calculate Total Profit and Scheduled Jobs

Sum up the profits of all the scheduled jobs to get the total profit. Additionally, keep track of which job is assigned to each time slot.

Output the Results

Finally, display the total profit achieved and the list of jobs that have been scheduled.

Job Sequencing with Deadlines algorithm

Given jobs J(i) with deadline D(i) and profit P(i) for 0≤i≤1, these jobs are arranged in descending order of profit p1⩾p2⩾p3⩾…⩾pn.

Job-Sequencing-With-Deadline (D, J, n, k)

D(0) := J(0) := 0

J(1) := 1 // means first job is selected

for i = 2 … n do

while D(J(r)) > D(i) and D(J(r)) ≠ r do

if D(J(r)) ≤ D(i) and D(i) > r then

for l = k … r + 1 by -1 do

J(l + 1): = J(l)

J(r + 1): = i

Job Sequencing with Deadlines using Greedy method

Job sequencing with deadlines is often solved using a Greedy algorithm approach, where jobs are selected based on their profitability and deadline constraints. The goal is to maximize the total profit by scheduling jobs in the most optimal manner.

Here’s a C code implementation of the Job Sequencing with Deadlines using Greedy method :

#include <stdio.h>

#include <stdlib.h>

struct Job {

int deadline;

int profit;

int compare_jobs(const void* a, const void* b) {

return ((struct Job*)b)->profit – ((struct Job*)a)->profit;

void job_sequencing_with_deadlines(struct Job* jobs, int n) {

qsort(jobs, n, sizeof(struct Job), compare_jobs);

int max_deadline = 0;

for (int i = 0; i < n; i++) {

if (jobs[i].deadline > max_deadline)

max_deadline = jobs[i].deadline;

int* schedule = (int*)calloc(max_deadline, sizeof(int));

int total_profit = 0;

int deadline = jobs[i].deadline;

while (deadline > 0) {

if (schedule[deadline – 1] == 0) {

schedule[deadline – 1] = 1;

total_profit += jobs[i].profit;

deadline–;

printf(“Total profit: %d\n”, total_profit);

free(schedule);

int main() {

printf(“Enter the number of jobs: “);

scanf(“%d”, &n);

struct Job* jobs = (struct Job*)malloc(n * sizeof(struct Job));

printf(“Enter job details (deadline profit) for each job:\n”);

for (int i = 0; i < n; i++)

scanf(“%d %d”, &jobs[i].deadline, &jobs[i].profit);

job_sequencing_with_deadlines(jobs, n);

free(jobs);

Examples of Job Sequencing with Deadlines

In the given job sequencing problem, we need to determine the optimal job sequence within their deadlines to achieve maximum profit. Each job is characterized by a deadline and a profit. Our goal is to find the most profitable combination of jobs that meet their respective deadlines.

Job	Job 1	Job 2	Job 3	Job 4	Job 5
Deadline	2	1	2	1	3
Profit	100	50	75	80	90

We want to find the optimal sequence of jobs to perform, considering their deadlines, in order to maximize the total profit. So, we’ll arrange the profits in descending order:

Job	Job 1	Job 5	Job 4	Job 3	Job 2
Deadline	2	3	1	2	1
Profit	100	90	80	75	50

Job 1 (100) can be assigned to the deadline 2 (at index 1) since it’s the highest possible deadline available.

Job 5 (90) can be assigned to the deadline 3 (at index 2) since it’s the highest possible deadline available.

Job 3 (75) can be assigned to the deadline 2 (at index 1) since it’s the highest possible deadline available.

Job 4 (80) can’t be assigned as the only available slots have deadlines 2 and 3, both occupied.

Job 2 (50) can’t be assigned as all slots with deadlines 2 and 3 are occupied.

The total profit obtained by scheduling the selected jobs is 100 + 90 + 75 = 265.

The sequence of jobs that are scheduled: Job 1, Job 5, and Job 3.

The optimal sequence of jobs, considering their deadlines, that maximizes the total profit is Job 1, Job 5, and Job 3, with a total profit of 265.

Frequently Asked Questions on Job Sequencing with Deadlines

What is the job sequencing with deadlines problem.

The Job Sequencing with Deadlines problem involves scheduling a set of jobs to maximize profit while adhering to their respective deadlines. Each job has a deadline and a profit, and the goal is to find the best arrangement of jobs that yields the highest total profit within the given time constraints.

How is the Job Sequencing with Deadlines algorithm structured?

The algorithm can be broken down into the following steps:

Sort the jobs in non-increasing order based on their profits.
Initialize the schedule and available time slots.
Assign jobs to time slots based on their deadlines and availability.
Calculate the total profit and track the scheduled jobs.
Output the final results, including the total profit and the list of scheduled jobs.

What if some jobs cannot be completed within their deadlines?

The Job Sequencing with Deadlines algorithm aims to maximize profit while respecting deadlines. If some jobs cannot be completed within their deadlines, they are skipped during the scheduling process to meet the time constraints of higher-priority jobs.

How does the Greedy method apply to Job Sequencing with Deadlines?

The Greedy method is often used to solve the Job Sequencing with Deadlines problem. It involves selecting jobs based on their profitability and deadline constraints. By arranging the jobs in descending order of profit, the Greedy method can achieve an optimal sequence of jobs that maximizes the total profit while considering deadline limitations.

Can the Job Sequencing with Deadlines algorithm handle jobs with different durations?

The basic Job Sequencing with Deadlines algorithm assumes that each job requires exactly one unit of time to complete. If jobs have different durations, a more advanced scheduling algorithm would be necessary to accommodate varying processing times

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Job Sequencing Problem – Loss Minimization

We are given N jobs numbered 1 to N. For each activity, let Ti denotes the number of days required to complete the job. For each day of delay before starting to work for job i, a loss of Li is incurred. We are required to find a sequence to complete the jobs so that overall loss is minimized. We can only work on one job at a time. If multiple such solutions are possible, then we are required to give the lexicographically least permutation (i.e earliest in dictionary order). Examples:

Let us consider two extreme cases and we shall deduce the general case solution from them.

All jobs take same time to finish, i.e Ti = k for all i. Since all jobs take same time to finish we should first select jobs which have large Loss (Li). We should select jobs which have the highest losses and finish them as early as possible. Thus this is a greedy algorithm. Sort the jobs in descending order based on Li only.
All jobs have the same penalty. Since all jobs have the same penalty we will do those jobs first which will take less amount of time to finish. This will minimize the total delay, and hence also the total loss incurred. This is also a greedy algorithm. Sort the jobs in ascending order based on Ti. Or we can also sort in descending order of 1/Ti.

From the above cases, we can easily see that we should sort the jobs not on the basis of Li or Ti alone. Instead, we should sort the jobs according to the ratio Li/Ti, in descending order.

We can get the lexicographically smallest permutation of jobs if we perform a stable sort on the jobs. An example of a stable sort is merge sort .

To get most accurate result avoid dividing Li by Ti. Instead, compare the two ratios like fractions. To compare a/b and c/d, compare ad and bc.

Time Complexity: O(N log N) Space Complexity: O(N)

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Gui Y Tang D Zhu H Zhang Y Zhang Z (2023) Dynamic scheduling for flexible job shop using a deep reinforcement learning approach Computers and Industrial Engineering 10.1016/j.cie.2023.109255 180 :C Online publication date: 1-Jun-2023 https://dl.acm.org/doi/10.1016/j.cie.2023.109255
Zeiträg Y Figueira J (2023) Automatically evolving preference-based dispatching rules for multi-objective job shop scheduling Journal of Scheduling 10.1007/s10951-023-00783-9 26 :3 (289-314) Online publication date: 29-Apr-2023 https://dl.acm.org/doi/10.1007/s10951-023-00783-9
Zeiträg Y Figueira J Horta N Neves R (2022) Surrogate-assisted automatic evolving of dispatching rules for multi-objective dynamic job shop scheduling using genetic programming Expert Systems with Applications: An International Journal 10.1016/j.eswa.2022.118194 209 :C Online publication date: 15-Dec-2022 https://dl.acm.org/doi/10.1016/j.eswa.2022.118194
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This study explores the due-date performance of job shop control systems which base job due dates on a time-phased representation of the workload and the machine capacity in the shop. The performance is measured by the mean and the standard deviation of ...

Due Date Assignment for Production Systems

This paper is concerned with the study of the constant due-date assignment policy in a dynamic job shop. Assuming that production times are randomly distributed, each job has a penalty cost that is some non-linear function of its due-date and its actual ...

A Simulation Study of Predictable Due-Dates

This paper describes a simulation study of assigning attainable or predictable due-dates in hypothetical labor and machine constrained job shop settings of varying size and structure. Several predictable due-date assignment rules are developed based on ...

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Linthicum, MD, United States

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inventory/production: policies
production/scheduling: job shop
simulation: application

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Shiue Y Lee K Su C (2018) Real-time scheduling for a smart factory using a reinforcement learning approach Computers and Industrial Engineering 10.1016/j.cie.2018.03.039 125 :C (604-614) Online publication date: 1-Nov-2018 https://dl.acm.org/doi/10.1016/j.cie.2018.03.039
Wang Y (2018) Adaptive job shop scheduling strategy based on weighted Q-learning algorithm Journal of Intelligent Manufacturing 10.1007/s10845-018-1454-3 31 :2 (417-432) Online publication date: 7-Nov-2018 https://dl.acm.org/doi/10.1007/s10845-018-1454-3
Askin R Hanumantha G (2017) Automated lead time estimation for manufacturing networks with dynamic demand 2017 13th IEEE Conference on Automation Science and Engineering (CASE) 10.1109/COASE.2017.8256232 (994-999) Online publication date: 20-Aug-2017 https://dl.acm.org/doi/10.1109/COASE.2017.8256232
Xiang Li Dongni Li Xuhui Wu Hong Zheng Yin Y (2017) A cooperative co-evolution approach for a line-seru conversion problem 2017 IEEE Congress on Evolutionary Computation (CEC) 10.1109/CEC.2017.7969468 (1406-1411) Online publication date: 5-Jun-2017 https://dl.acm.org/doi/10.1109/CEC.2017.7969468
Chen T Wang Y (2017) A nonlinearly normalized back propagation network and cloud computing approach for determining cycle time allowance during wafer fabrication Robotics and Computer-Integrated Manufacturing 10.1016/j.rcim.2015.11.005 45 :C (144-156) Online publication date: 1-Jun-2017 https://dl.acm.org/doi/10.1016/j.rcim.2015.11.005
Hart E Sim K (2016) A hyper-heuristic ensemble method for static job-shop scheduling Evolutionary Computation 10.1162/EVCO_a_00183 24 :4 (609-635) Online publication date: 1-Dec-2016 https://dl.acm.org/doi/10.1162/EVCO_a_00183
Afèche P Baron O Kerner Y (2013) Pricing Time-Sensitive Services Based on Realized Performance Manufacturing & Service Operations Management 10.1287/msom.2013.0434 15 :3 (492-506) Online publication date: 1-Jul-2013 https://dl.acm.org/doi/10.1287/msom.2013.0434

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IMAGES

Job Sequencing With Deadlines
Jobs Sequencing Problem N jobs on 3 Machines
Job Sequencing Problem
Job Sequencing Introduction
Example to illustrate job sequencing.
Job Sequencing With Deadline. The sequencing of jobs on a single…

VIDEO

JOB SEQUENCING||CONCEPTS & TERMINOLOGY||OPERATIONS RESEARCH|| Lecture
Optimization Techniques MCQ Part 7 Job Sequencing Johnson Algorithm
Assignment Method
Job Sequencing using Greedy Method
Job Sequencing Problem
[NEW] EXAMPLE PROBLEM- 2: JOB SEQUENCING WITH DEADLINES PROBLEM IN GREEDY METHOD

COMMENTS

Job Sequencing Problem
Learn how to solve the job sequencing problem, a classic optimization problem in computer science, with examples and algorithms on GeeksforGeeks.
7.1 Job Sequencing with Deadline
7.1 Job Sequencing with Deadline - Branch and Bound Abdul Bari 1M subscribers Subscribed 2.8K 332K views 6 years ago Job Sequencing using Branch and Bound PATREON : https://www.patreon.com ...
Job Assignment Problem using Branch And Bound
Solution 1: Brute Force. We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O (n!). Solution 2: Hungarian Algorithm. The optimal assignment can be found using the Hungarian algorithm.
3.2 Job Sequencing with Deadlines
3.2 Job Sequencing with Deadlines - Greedy Method Abdul Bari 1.01M subscribers 21K 1.4M views 6 years ago Job Sequencing with Deadlines 2 problems are solved ...more
Rules of Job Sequencing in Production
First-Come, First Serve - The first-come, first-served sequencing method processes orders in the order of their arrival at their production facility or resource. The arrival time is a key component and factor within the job sequencing rule, which is what separates it from methods such as longest processing time and shortest processing time.
Job Sequencing (Algorithm, Time Complexity, and Example) in Operating
In this tutorial, we will learn about the job sequencing algorithm, its time complexity, and example in Operating System.
Job Sequencing Problem (Greedy Algorithm)
Explanation for the article: http://www.geeksforgeeks.org/job-sequencing-problem-set-1-greedy-algorithm/This video is contributed by Illuminati.
Job Sequencing using Branch and Bound
Job Sequencing using Branch and Bound: Given n jobs with profit, execution time, and deadline, achieve the schedule which maximizes the profit.
Job Sequencing Problem with Deadline
In this tutorial we will learn about Job Sequencing Problem with Deadline. This problem consists of n jobs each associated with a deadline and profit and our objective is to earn maximum profit. We will earn profit only when job is completed on or before deadline. We assume that each job will take unit time to complete.
Applying Python Programming to the Traditional Methods of Job Sequencing
Job sequencing problems are used to determine a suitable or an appropriate order for a series of respective jobs that are to be performed to optimize some efficiency measure such as total elapsed time or overall cost, among other things. Efficiency in that type of circumstance is determined by the order or sequence in which the jobs are completed.
OPS chap 15 Flashcards
Cost for each job-machine combination appears in the table below. Perform the first two steps of the assignment method (subtract the smallest number in each row and subtract the smallest number in each column; then cover with straight lines).
Johnson's Rule in Sequencing Problems
Johnson's Rule in Sequencing Problems. The sequencing problem deals with determining an optimum sequence of performing a number of jobs by a finite number of service facilities (machine) according to some pre-assigned order so as to optimize the output. The objective is to determine the optimal order of performing the jobs in such a way that ...
Job Sequencing with Deadline
Job Sequencing with Deadline - Job scheduling algorithm is applied to schedule the jobs on a single processor to maximize the profits.
Job Sequencing and Scheduling
5.1 Job Sequencing and Scheduling in Semiconductor Manufacturing. The semiconductor manufacturing process typically consists of four stages: wafer fabrication, wafer probe, assembly, and final test [ 1 ]. Fab fabrication systems are complex and have typical characteristics such as fluctuating demand, jobs with various product types and ...
Hyper-Heuristic Coevolution of Machine Assignment and Job Sequencing
Three types of hyper-heuristic methods were proposed in this paper for coevolution of the machine assignment rules and job sequencing rules to solve the multi-objective dynamic flexible job shop scheduling problem, including the multi-objective cooperative coevolution genetic programming with two sub-populations, the multi-objective genetic ...
job sequencing|| repeated processing time || n jobs under 2 machines
Learn how to solve job sequencing problems with repeated processing time and two machines in this video tutorial.
Job Sequencing with Deadlines
Job Sequencing with Deadlines problem uses the greedy approach. Read about the algorithm of job sequencing with deadlines, its definition, algorithm, example, and more.
Sequencing Rules and Due-Date Assignments in a Job Shop
Recent research studies of job shop scheduling have begun to examine the interaction between sequencing priorities and the method of assigning due-dates. This paper surveys the tactical aspects of this interaction, focusing primarily on average tardiness as a measure of scheduling effectiveness. The discussion highlights several factors that ...
Job Sequencing Problem using Disjoint Set
Job Sequencing Problem using Disjoint Set. Given a set of n jobs where each job i has a deadline di >=1 and profit pi>=0. Only one job can be scheduled at a time. Each job takes 1 unit of time to complete. We earn the profit if and only if the job is completed by its deadline. The task is to find the subset of jobs that maximizes profit.
Job sequencing problem with deadline
Greedy method : Job sequencing problem with deadline explained with examples
Job Sequencing Problem
Job Sequencing Problem - Loss Minimization. We are given N jobs numbered 1 to N. For each activity, let Ti denotes the number of days required to complete the job. For each day of delay before starting to work for job i, a loss of Li is incurred. We are required to find a sequence to complete the jobs so that overall loss is minimized.
Sequencing Rules and Due-Date Assignments in a Job Shop
Abstract. Recent research studies of job shop scheduling have begun to examine the interaction between sequencing priorities and the method of assigning due-dates. This paper surveys the tactical aspects of this interaction, focusing primarily on average tardiness as a measure of scheduling effectiveness.
Sequencing Rules and Due-Date Assignments in a Job Shop
Recent research studies of job shop scheduling have begun to examine the interaction between sequencing priorities and the method of assigning due-dates. This paper surveys the