সময়সূচী তৈরি MCQ Quiz in বাংলা - Objective Question with Answer for Scheduling - বিনামূল্যে ডাউনলোড করুন [PDF]

Positive lateness is called Tardiness

Total Tardiness = 10 days 

Concept: Following are the steps:

Step 1: First find the optimal sequence using Johnson’s rule

Step 2: Draw a table showing in and out time for each job using the processing time.

Step 3: Calculate the asked values.

Calculation:

Step 1: Using Johnson’s rule the optimal sequence is A-D-C-B

Sequencing of ‘N’ Jobs on Two Machine

In this type of problem, we consider that two machines are A and B and the assumption is that the processing order is fixed. Each of the jobs numbered i = 1, 2, 3, -----, n has processing times A_i and B_i respectively. The problem is to find a processing order for different jobs and to ensure that the ideal time for both the machines is minimized. In other words, the aim is to maximize machine utilization. This is achieved by using Jhonson’s Algorithm.

Step(i): Find out the minimum of A_i and B_i. If the minimum is A_k then process the k^th job in the beginning. If the minimum is B_r then process the r^th job in the end.

Step(ii): When a particular job is placed in a sequence strike it off.

Step(iii): If A_k = B_r then in this case process the k^th job first and r^th job last.

If both equal values occur on machine A then select the one which has lowest value on B first. If both values occur on machine B then select the one with the lowest value on A first.  

Step 2:

Make span time = 43 minutes

Explanation:

Job Shop Scheduling:

• Job shop scheduling involves planning, allocating, and managing resources and tasks to ensure optimal utilization of resources and minimization of waiting times in a production environment.
• This process is critical in manufacturing and service industries where multiple jobs need to be processed on various machines.
• In job shop scheduling, jobs with different processing requirements are assigned to specific machines in a sequence that optimizes resource utilization and minimizes job waiting times.
• The sequence in which jobs are processed can significantly impact overall efficiency and productivity.

Advantages of Optimal Scheduling:

• Maximized resource utilization by ensuring machines and workers are continuously engaged.
• Reduced waiting times for jobs, leading to faster turnaround and improved customer satisfaction.
• Minimized production costs by reducing idle times and improving workflow efficiency.

Disadvantages of Suboptimal Scheduling:

• Increased waiting times and delays, leading to missed deadlines and customer dissatisfaction.
• Underutilization of resources, resulting in higher operational costs.
• Increased complexity in managing and rescheduling tasks, leading to inefficiencies.

Shortest Processing Time (SPT):

• The Shortest Processing Time (SPT) rule is a widely used heuristic in job shop scheduling because it tends to minimize the average waiting time for jobs.
• By processing jobs with shorter durations first, the overall flow of work is smoother, and bottlenecks are reduced, leading to optimal resource utilization.

Why SPT is Optimal:

• The Shortest Processing Time (SPT) rule works effectively because it prioritizes jobs that can be completed quickly, thereby freeing up resources faster for subsequent tasks. This approach reduces the time that jobs spend waiting to be processed, leading to a lower average waiting time and improved resource utilization.

Additional InformationFirst In, First Out (FIFO)

• This scheduling rule processes jobs in the order they arrive, regardless of their processing times. While FIFO is simple to implement and fair in terms of job order, it does not consider the processing time of each job. This can lead to longer waiting times, especially if a job with a long processing time arrives early and blocks subsequent shorter jobs.

Earliest Due Date (EDD)

• This rule prioritizes jobs based on their due dates, with jobs having the earliest due dates scheduled first. Although EDD can be useful in meeting deadlines, it does not necessarily optimize resource utilization or minimize waiting times. Jobs with shorter processing times might still be delayed, leading to inefficiencies.

Longest Processing Time (LPT) first

• This rule schedules jobs with the longest processing times first. While this can sometimes help in balancing the load across machines, it often leads to increased waiting times for shorter jobs. As a result, it is generally less effective in minimizing average waiting times compared to the SPT rule.

Applying shortest processing time rule and arranging according.

                                                                                   \(= {\rm{\Sigma \;}}51\)

Average Tardiness \(= \frac{{51}}{8} = 6.375\;min\)

Explanation:

• Routing determines what work is to be done and where and how it will be done. Taking from raw material to the finished product, routing decides the path and sequence of operations to be performed on the job from one machine to another.
• Routing is essential in the Assembly industry

A production planning and control system has many functions to perform, some before the arrival of raw materials and tools, and others while the raw material undergoes processing.

There are four steps in the process of production planning and control:

Routing: Routing can be defined as the process of deciding the path (route) of work and the sequence of operations.

Scheduling: Scheduling function determines when an operation is to be performed, or when work is to be completed.

Dispatching: It is the action, doing or implementation stage. It comes after routing and scheduling. Dispatching means starting the process of production. It provides the necessary authority to start the work.

Expedition or follow-up: It is designed to keep track of the work effort. The aim is to ensure that what is intended and planned is being implemented. It maintains proper records of work, delays, and bottleneck. Such records can be used in the future to control production.

Explanation:

Scheduling:

Scheduling is done to determine the timing and order of operations to optimize the use of resources to meet production requirements.

Jobs are scheduled according to their priority there are several Priority rules existing for a job

Critical Ratio:

Critical ratio is calculated by dividing the time remaining until a job's due date by the total shop time remaining for the job.

Shop time is regarded as the setup time, processing time, and movement time and expected waiting times of all remaining operations, including the operation being scheduled.

\(Critical\;Ratio = \frac{{Demand\;Time}}{{Manufacturing\;Lead\;time}}\)

Where demand time is given by = Due date – Today’s date

If the critical ratio is less than one it means that job is behind the schedule, if the critical ratio is greater than one it shows that the job is running ahead of the schedule. The jobs with lowest critical ratio is scheduled next.

Shortest processing time rule:

That work is performed first which has shortest processing time.

Earliest due date rule:

Jobs are sequenced in increasing order of their due date.

Slack time remaining rule:

Jobs are sequenced in order of increasing slack time

Slack time = Due date – Processing Time

Concept:

Let the actual cases de denoted as demand (D)

And Forecasted cases be denoted as (F)

\({F_{t + 1}} = \;{F_t} + \;\alpha \left( {{D_t} - {F_t}} \right)\)       ---(1)       

Calculation:

For the month of April, given F =100

Soothing constant (α= 0.8)

By calculation as per (1), the following data is obtained

Mean absolute deviation (MAD)

\(MAD = \;\frac{{\mathop \sum \nolimits_{i = 1}^5 \left| {{e_i}} \right|}}{5} = 212.8128\)    (option b)

Running some forecast error (RSFE)

Now,

\(RSFE = \;\mathop \sum \limits_{i = 1}^5 {e_i} = 1064.064\)

Tracking signal (TS)

\(TS = \frac{{RSFE}}{{MAD}} = 5\)  (Option c)

Routing lays down the flow of work in the plant. It determines what work is to be done and where and how it will be done.

Use Johnson’s Algorithms solve.

Make a box like this & select the lowest number (say ‘1’ in this case). If the number belongs to ‘M₁’ place it on extreme left or else place it on the right side at the box.

Next lowest is ‘2’ on ‘M₂’, so place it in the Right

Next is ‘3’ on ‘M₁’, so place it on left

Next is ‘4’ on ‘M₂’, so place it on Right.

‘c’ is the only Remaining job so place it on the vacant position.

Hence the correct sequence is : BDCEA

Explanation:

Gantt chart:

• Gantt charts are mainly used to allocate resources to activities.
• Gantt chart is applicable for Production scheduling.
• The resources allocated to activities include staff, hardware, and software. Gantt charts are useful for resource planning.
• A Gantt chart is a special type of bar chart where each bar represents an activity. 
• This chart lists the tasks to be performed on the vertical axis, and time intervals on the horizontal axis.
• The bars are drawn along a timeline. The length of each bar is proportional to the duration of time planned for the corresponding activity.
• With the use of this chart, we can check the progress of project with
  • A visual display of the whole project,
  • Timelines and deadlines of all tasks,
  • Relationships and dependencies between the various activities,
  • Project phases

On Gantt Chart one can easily view

• ​The start date of the project
• What the project tasks are
• Who is working on each task
• When tasks start and finish
• How long each task will take
• How tasks group together, overlap and link with each other
• The finish date of the project