Scheduling

Scheduling

• Scheduling: The allocation of resources over time to accomplish specific tasks.

• Demand scheduling: A type of scheduling whereby customers are assigned to a definite time for order fulfillment.

• Workforce scheduling: A type of scheduling that determines when employees work.

• Operations scheduling: A type of scheduling in which jobs are assigned to workstations or employees are assigned to jobs for specified time periods.

Performance Measures• Job flow time: The amount of time a job spends in the

service or manufacturing system. Also referred to as throughput time or time spent in the system, including service.

• Makespan: The total amount of time required to complete a group of jobs.

• Past due (Tardiness): The amount of time by which a job missed its due date or the percentage of total jobs processed over some period of time that missed their due dates.

• Work-in-process (WIP) inventory: Any job that is waiting in line, moving from one operation to the next, being delayed, being processed, or residing in a semi-finished state.

• Total inventory: The sum of scheduled receipts and on-hand inventories.

• Utilization: The percentage of work time that is productively spent by an employee or machine.

Gantt Charts

• Gantt chart: Used as a tool to monitor the progress of work and to view the load on workstations.

The chart takes two basic forms: (1) the job or activity progress chart, and (2) the workstation chart.

• The Gantt progress chart graphically displays the current status of each job or activity relative to its scheduled completion date.

• The Gantt workstation chart shows the load on the workstations and the nonproductive time.

Gantt Progress ChartGantt Progress Chart

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Job 4/20 4/22 4/23 4/24 4/25 4/264/214/17 4/18 4/19

Current Current date date

Scheduled activity time

Actual progress

Start activity

Finish activity

Nonproductive time

Gantt Progress Chart for an Auto Parts Company

Gantt Workstation Chart Gantt Workstation Chart

Gantt Workstation Chart for Hospital Operating Rooms

Operations Scheduling

• Operations schedules are short-term plans designed to implement the master production schedule. Operations scheduling focuses on how best to use

existing capacity. Often, several jobs must be processed at one or more

workstations. Typically, a variety of tasks can be performed at each workstation.

• Job shop: A firm that specializes in low- to medium-volume production and utilizes job or batch processes.

• Flow shop: A firm that specializes in medium- to high-volume production and utilizes line or continuous processes.

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WorkstationWorkstation

Job Shop Dispatching

• Dispatching: A method of generating schedules in job shops whereby the decision about which job to process next is made using simple priority rules whenever the workstation becomes available for further processing.

• Priority sequencing rules: The rules that specify the job processing sequence when several jobs are waiting in line at a workstation.

Job Shop Dispatching• Earliest due date (EDD): A priority sequencing rule that specifies

that the job with the earliest due date is the next job to be processed.

• First-come, first-served (FCFS): A priority sequencing rule that specifies that the job arriving at the workstation first has the highest priority.

• Shortest processing time (SPT): A priority sequencing rule that specifies that the job requiring the shortest processing time is the next job to be processed.

• Critical ratio (CR): A ratio that is calculated by dividing the time remaining until a job’s due date by the total shop time remaining for the job. CR = (Due date – Today’s date)/Total shop time remaining(Due date – Today’s date)/Total shop time remaining– Total Shop Time = Setup, processing, move, and expected

waiting times of all remaining operations, including the operation being scheduled.

Scheduling Jobs for Multiple Workstations

• Priority sequencing rules can be used to schedule more than one operation. Each operation is treated independently.

• Identifying the best priority rule to use at a particular operation in a process is a complex problem because the output from one process becomes the input for another.

• Computer simulation models are effective tools to determine which priority rules work best in a given situation.

• When a workstation becomes idle, the priority rule is applied to the jobs waiting for that operation, and the job with the highest priority is selected.

• When that operation is finished, the job is moved to the next operation in its routing, where it waits until it again has the highest priority.

Scheduling Problems

• One machine, many jobs

• Two machines, many jobs

• Three machines, many jobs

• Many machines, many jobs

One machine, many jobs

• Total time is independent of sequence

• SPT minimizes average flow time

• Examples- Mumbai airport

Two machines, many jobs

• All Jobs follow same sequence – Johnson’s Rule

• Jobs have different sequence – Jackson’s Rule

• Johnson’s 3 machine rule

Johnson’s Rule• Johnson’s rule: A procedure that minimizes makespan

when scheduling a group of jobs on two workstations.• Step 1. Find the shortest processing time among the

jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily.

• Step 2. If the shortest processing time is on workstation 1, schedule the corresponding job as early as possible. If the shortest processing time is on workstation 2, schedule the corresponding job as late as possible.

• Step 3. Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.

Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first.

Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next.Eliminate M1 and the only job remaining to be scheduled is M4.

Example 16.5 Johnson’s RuleJohnson’s Rule at the at the Morris Machine Co.Morris Machine Co.

Time (hr)Time (hr)

MotorMotor Workstation 1Workstation 1 Workstation 2Workstation 2

M1M1 1212 2222M2M2 44 55M3M3 55 33M4M4 1515 1616M5M5 1010 88

Sequence = Sequence = M1M1M2M2 M3M3M4M4 M5M5

Shortest time is 3 hours at workstation 2, so schedule job M3 last.

Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last.

Workstation

M2 (4)

M1 (12)

M4 (15)

M5 (10)

M3 (5)

Idle—available for further work

0 5 10 15 20 25 30Day

35 40 45 50 55 60 65

Idle2 M2 (5)

M1 (22)

M4 (16)

M5 (8)

M3 (3)Idle

1

Gantt Chart for the Morris Machine Company Repair Schedule

The schedule minimizes the idle time of workstation 2 and gives the fastest repair time for all five motors.

No other sequence will produce a lower makespan.

Example 16.5 Johnson’s RuleJohnson’s Rule at the at the Morris Machine Co.Morris Machine Co.

Classwork

Job 1 2 3 4 5 6 7 8

A 4 5 8 10 6 5 10 6

B 8 10 2 4 5 7 6 6

Johnson’s 3 Machine Rule• Domination – Largest on B is not greater

than smallest on A or C. Domination guarantees optimality

• Conversion – Convert into a 2 M/C problem as M1 = A + B, M2 = B + C

• Find optimal sequence for this 2 machine problem

• Schedule on 3 machines based on the sequence above

Job 1 2 3 4 5 6A 8 6 10 7 9 7

B 7 4 6 5 5 4

C 13 12 11 12 13 10

M1 15 10 16 12 14 11

M2 20 16 17 17 18 14

Classwork