© 2006 prentice hall, inc.15 – 1 operations management chapter 15 – short-term scheduling ©...

© 2006 Prentice Hall, Inc. 15 – 1

Operations ManagementOperations ManagementChapter 15 – Short-Term SchedulingChapter 15 – Short-Term Scheduling

© 2006 Prentice Hall, Inc.

PowerPoint presentation to accompanyPowerPoint presentation to accompany Heizer/Render Heizer/Render Operations Management, 8e Operations Management, 8e


Strategic Importance of Strategic Importance of Short-Term SchedulingShort-Term Scheduling

Effective and efficient scheduling Effective and efficient scheduling can be a competitive advantagecan be a competitive advantage Faster movement of goods through a Faster movement of goods through a

facility means better use of assets facility means better use of assets and lower costsand lower costs

Additional capacity resulting from Additional capacity resulting from faster throughput improves customer faster throughput improves customer service through faster deliveryservice through faster delivery

Good schedules result in more Good schedules result in more reliable deliveriesreliable deliveries


Scheduling DecisionsScheduling Decisions

OrganizationOrganization Managers Must Schedule the FollowingManagers Must Schedule the Following

Arnold Palmer Arnold Palmer HospitalHospital

Operating room useOperating room usePatient admissionsPatient admissionsNursing, security, maintenance staffsNursing, security, maintenance staffsOutpatient treatmentsOutpatient treatments

University of University of MissouriMissouri

Classrooms and audiovisual equipmentClassrooms and audiovisual equipmentStudent and instructor schedulesStudent and instructor schedulesGraduate and undergraduate coursesGraduate and undergraduate courses

Lockheed-Martin Lockheed-Martin factoryfactory

Production of goodsProduction of goodsPurchases of materialsPurchases of materialsWorkersWorkers

Hard Rock CafeHard Rock Cafe Chef, waiters, bartendersChef, waiters, bartendersDelivery of fresh foodsDelivery of fresh foodsEntertainersEntertainersOpening of dining areasOpening of dining areas

Delta AirlinesDelta Airlines Maintenance of aircraftMaintenance of aircraftDeparture timetablesDeparture timetablesFlight crews, catering, gate, ticketing personnelFlight crews, catering, gate, ticketing personnelTable 15.1Table 15.1


Activity in SequencingActivity in Sequencing Sequence the following cars into as many work days as Sequence the following cars into as many work days as

needed. Garage can work on two cars simultaneouslyneeded. Garage can work on two cars simultaneously Assume Assume first come first servefirst come first serve sequencing; 8 hour sequencing; 8 hour

workday. Customers arrive in the following orderworkday. Customers arrive in the following order

DAY 1DAY 1

Car 3: Maintenance ; time needed 6 hoursCar 3: Maintenance ; time needed 6 hours

Car 4: Maintenance ; time needed 10 hoursCar 4: Maintenance ; time needed 10 hours

Car 1: Repair ; time needed 2 hoursCar 1: Repair ; time needed 2 hours

Car 2: Repair ; time needed 2.5 hoursCar 2: Repair ; time needed 2.5 hours

DAY 2DAY 2

Car 5: Maintenance ; time needed 3.5 hoursCar 5: Maintenance ; time needed 3.5 hours

Car 6: Repair ; time needed 3.5 hrsCar 6: Repair ; time needed 3.5 hrs Car 7: Maintenance ; time needed 4 hoursCar 7: Maintenance ; time needed 4 hours


Solution: SequencingSolution: Sequencing

Repair Track 2Repair Track 2

Car 4: Repair – 2 hoursCar 4: Repair – 2 hours

Car 5: Repair – 3.5 hoursCar 5: Repair – 3.5 hours

Car 7:Maintenance 2.5 hoursCar 7:Maintenance 2.5 hours


Car 3: Repair - 6 hoursCar 3: Repair - 6 hours

Car 1: Maintenance 2 hoursCar 1: Maintenance 2 hours


Repair Track 2 Repair Track 2



Car 7:Maintenance 1.5 hours Car 7:Maintenance 1.5 hours


Car 2: Maintenance 2.5 hoursCar 2: Maintenance 2.5 hours Car 6:Maintenance 3.5 hoursCar 6:Maintenance 3.5 hours

Day 1Day 1

Day 2Day 2

Day 3Day 3


Activity in Sequencing_2Activity in Sequencing_2 Schedule the following cars into 2 work days. Schedule the following cars into 2 work days.

Garage can work on two cars simultaneouslyGarage can work on two cars simultaneously Method: Garage controlled scheduling Method: Garage controlled scheduling

(First (First assignedassigned first serve; or capacity-based first serve; or capacity-based scheduling). 8 hours per day work time.scheduling). 8 hours per day work time.

Car 3: Maintenance Car 3: Maintenance ; time needed ; time needed 6 hours6 hours

Car 4: Maintenance Car 4: Maintenance ; time needed ; time needed 10 hours10 hours

Car 1: Repair Car 1: Repair ; time needed ; time needed 2 hours2 hours

Car 2: Repair Car 2: Repair ; time needed ; time needed 2.5 hours2.5 hours

Car 5: Maintenance Car 5: Maintenance ; time needed ; time needed 3.5 hours3.5 hours

Car 6: Repair Car 6: Repair ; time needed ; time needed 3.5 hrs3.5 hrs

Car 7: Maintenance Car 7: Maintenance ; time needed ; time needed 4 hours 4 hours


Solution: Sequencing _2Solution: Sequencing _2 Schedule for days 1 and 2. Notice one track for longSchedule for days 1 and 2. Notice one track for long

duration work and the other for fast jobs!duration work and the other for fast jobs!





Car 1: Repair - 2 hoursCar 1: Repair - 2 hours

Car 5: Maintenance 3.5 hoursCar 5: Maintenance 3.5 hours




Car 7:Maintenance 4.0 hoursCar 7:Maintenance 4.0 hours

Repair Track 2 Repair Track 2


Fast turnaround jobsFast turnaround jobs Long turnaround jobsLong turnaround jobs

Day 2Day 2

Day 1Day 1


DefinitionsDefinitions Scheduling is the assignment of Scheduling is the assignment of due datesdue dates

to specific work or jobs.to specific work or jobs.

Loading is the Loading is the assignment of jobsassignment of jobs to work to work centers.centers.

Sequencing: Determining Sequencing: Determining the order in the order in which jobswhich jobs should be done at each work should be done at each work center center so that due dates are metso that due dates are met..

Input-Output control: Any technique that Input-Output control: Any technique that enables managers to manage workflows at enables managers to manage workflows at each work center each work center by comparing work added by comparing work added to work completedto work completed..


Figure 15.1Figure 15.1

Positioning Positioning SchedulingScheduling


Defining SchedulingDefining Scheduling

Scheduling deals with the assignment of Scheduling deals with the assignment of activities (activities (demanddemand) to resources () to resources (supplysupply) ) (or vice-versa) and timing of activities. (or vice-versa) and timing of activities. E.g.E.g. supply could be production capacity of a firmsupply could be production capacity of a firm))

Types of scheduling situationsTypes of scheduling situations Type I: Supply options (M) are fewer Type I: Supply options (M) are fewer

than demand options (N)than demand options (N)

Type II: Supply options (M) are equal to Type II: Supply options (M) are equal to demand options (N)demand options (N)

Type III: Supply options (M) exceed the Type III: Supply options (M) exceed the number of demand options (N)number of demand options (N)


Objectives of SchedulingObjectives of Scheduling Goals of schedulingGoals of scheduling

Type I: Supply options (M) are fewer than Type I: Supply options (M) are fewer than demand options (N)demand options (N)

Assign scarce supply to demand to minimize cost or Assign scarce supply to demand to minimize cost or maximize benefitsmaximize benefits

Type II: Supply options (M) are equal to Type II: Supply options (M) are equal to demand options (N)demand options (N)

Assign supply to demand to minimize cost or Assign supply to demand to minimize cost or maximize benefits for total processmaximize benefits for total process

Type III: Supply options (M) exceed the Type III: Supply options (M) exceed the number of demand options (N)number of demand options (N)

Scheduling is done for limited capacity and excess Scheduling is done for limited capacity and excess capacity is outsourced.capacity is outsourced.


Methods of SchedulingMethods of Scheduling Forward scheduling conceptForward scheduling concept

Scheduling begins as soon as customer Scheduling begins as soon as customer requests and requirements are known requests and requirements are known

Scheduling begins from the Scheduling begins from the estimated start dateestimated start date of the project and of the project and works forwardworks forward to determine the to determine the start and finish dates for each of the activities that start and finish dates for each of the activities that make up the order.make up the order.

Backward scheduling conceptBackward scheduling conceptScheduling begins from the expected Scheduling begins from the expected delivery datedelivery date and works backwards to determine the finish and start and works backwards to determine the finish and start dates for the activities that make up the order.dates for the activities that make up the order.

[Usually this method is available for projects that have long [Usually this method is available for projects that have long completion times, large number of units or parts, and have completion times, large number of units or parts, and have the completion of project on or before the delivery deadline the completion of project on or before the delivery deadline as a key objective]as a key objective] . .


Loading_Activity_ALoading_Activity_A We own a hotel which has a large ballroom. We have to We own a hotel which has a large ballroom. We have to

schedule activities for schedule activities for two Saturdays in Maytwo Saturdays in May. The closing time . The closing time of the ballroom each Saturday is 10 pm. Which activities of the ballroom each Saturday is 10 pm. Which activities would you schedule? would you schedule? We charge per hour for the time a client We charge per hour for the time a client spend using roomspend using room. No charges for cleaning and preparation . No charges for cleaning and preparation times.times.

Event A: 9 am - 1 pm, Cleanup needed after event 2 Event A: 9 am - 1 pm, Cleanup needed after event 2 hrs.hrs.

Event B: 4 pm – 7 pm, preparation needed before Event B: 4 pm – 7 pm, preparation needed before event 0.5 hours. Cleanup needed after event 1 hrs.event 0.5 hours. Cleanup needed after event 1 hrs.

Event C: 5 pm - 10 pm, preparation needed before Event C: 5 pm - 10 pm, preparation needed before event 1 hours. Cleanup after event 2 hrs.event 1 hours. Cleanup after event 2 hrs.

Event D: 9 am -12 pm, preparation needed before Event D: 9 am -12 pm, preparation needed before event 1 hours. Cleanup after event 1 hrs.event 1 hours. Cleanup after event 1 hrs.

Event E: 11 am – 8 pm, preparation needed before Event E: 11 am – 8 pm, preparation needed before event 2 hours. Cleanup after event 2 hrs.event 2 hours. Cleanup after event 2 hrs.


Activity_A Scheduling Criteria and OptionsActivity_A Scheduling Criteria and Options Option1Option1

Event A: 9 am - 1 pm AND Event B: 4 – 7 pmEvent A: 9 am - 1 pm AND Event B: 4 – 7 pm

Event D: 9 am -12 pm AND Event C: 5 - 10 pm.Event D: 9 am -12 pm AND Event C: 5 - 10 pm. Option 2Option 2

Event A: 9 am - 1 pm AND Event C 5 - 10 pm.Event A: 9 am - 1 pm AND Event C 5 - 10 pm.

Event D: 9 am -12 pm AND Event B: 4 – 7 pmEvent D: 9 am -12 pm AND Event B: 4 – 7 pm Option 3 Option 3

Event A: 9 am - 1 pm AND Event B OR Event C Event A: 9 am - 1 pm AND Event B OR Event C

Event E: 11 am – 8 pmEvent E: 11 am – 8 pm

Scheduling Criteria: Why did we schedule the way we did? We Scheduling Criteria: Why did we schedule the way we did? We are tried to maximize the utilization of the ballroom are tried to maximize the utilization of the ballroom (maximize utilization)!(maximize utilization)!

Other criteria; Min. Cost, Min. waiting time or Work in progress Other criteria; Min. Cost, Min. waiting time or Work in progress (WIP)(WIP)


Comparing Options_Activity_AComparing Options_Activity_A Option1Option1

Event A: 9 am - 1 pm AND Event B: 4 – 7 pmEvent A: 9 am - 1 pm AND Event B: 4 – 7 pm

Event D: 9 am -12 pm AND Event C: 5 - 10 pm.Event D: 9 am -12 pm AND Event C: 5 - 10 pm. Option 2Option 2

Event A: 9 am - 1 pm AND Event C 5 - 10 pm.Event A: 9 am - 1 pm AND Event C 5 - 10 pm.

Event D: 9 am -12 pm AND Event B: 4 – 7 pmEvent D: 9 am -12 pm AND Event B: 4 – 7 pm Option 3 Option 3

Event A: 9 am - 1 pm AND Event B OR Event C Event A: 9 am - 1 pm AND Event B OR Event C

Event E: 11 am – 8 pmEvent E: 11 am – 8 pm

OPTION 3: Less switching costs, maximize utilization, OPTION 3: Less switching costs, maximize utilization,

minimize waiting times, maximize profitsminimize waiting times, maximize profits


Activity_SchedulingActivity_SchedulingIf you could change one thing in the operations scheduling of this If you could change one thing in the operations scheduling of this

case, what would you change?case, what would you change? We own a hotel which has a large ballroom. We have to schedule We own a hotel which has a large ballroom. We have to schedule

activities for activities for two Saturdays in Maytwo Saturdays in May. The closing time of the . The closing time of the ballroom each Saturday is 10 pm. Which activities would you ballroom each Saturday is 10 pm. Which activities would you schedule? We charge per hour for time spent in room. No schedule? We charge per hour for time spent in room. No charges for cleaning and preparation times.charges for cleaning and preparation times. Event A: 9 am - 1 pm, Cleanup needed after event 2 hrs.Event A: 9 am - 1 pm, Cleanup needed after event 2 hrs. Event B: 4 pm – 7 pm, preparation needed before event 0.5 Event B: 4 pm – 7 pm, preparation needed before event 0.5

hours. Cleanup needed after event 1 hrs.hours. Cleanup needed after event 1 hrs. Event C: 5 pm - 10 pm, preparation needed before event 1 Event C: 5 pm - 10 pm, preparation needed before event 1

hours. Cleanup after event 2 hrs.hours. Cleanup after event 2 hrs. Event D: 9 am -12 pm, preparation needed before event 1 Event D: 9 am -12 pm, preparation needed before event 1

hours. Cleanup after event 1 hrs.hours. Cleanup after event 1 hrs. Event E: 11 am – 8 pm, preparation needed before event 2 Event E: 11 am – 8 pm, preparation needed before event 2

hours. Cleanup after event 2 hrs.hours. Cleanup after event 2 hrs.


Activity_SchedulingActivity_SchedulingIf you could change one thing in the operations scheduling of this If you could change one thing in the operations scheduling of this

case, what would you change?case, what would you change?

Demand Options:Demand Options: Charge for cleaning timeCharge for cleaning timeSet minimum reservation timeSet minimum reservation time

Capacity Options:Capacity Options:Build new ballroomBuild new ballroomExtend working hours per dayExtend working hours per day


Scheduling CriteriaScheduling Criteria

Types of scheduling/sequencing criteriaTypes of scheduling/sequencing criteriaGoal-based approachesGoal-based approaches

Minimize cost, waiting timesMinimize cost, waiting times

Minimize work-in-processMinimize work-in-process

Maximize profitsMaximize profits

Priorities-based approachesPriorities-based approaches First-come first serve or Last-in-first-outFirst-come first serve or Last-in-first-out

Longest processing timeLongest processing time

Earliest due dateEarliest due date

Shortest processing timeShortest processing time


Job Loading MethodsJob Loading Methods

Types of scheduling methodsTypes of scheduling methodsArbitrary approachesArbitrary approaches

Useful when there are no constraints of Useful when there are no constraints of resources (Supply exceeds demand)resources (Supply exceeds demand)

Rule-based approachesRule-based approaches Useful when there are constraints of resourcesUseful when there are constraints of resources

Priorities-based approachesPriorities-based approaches Useful when there are constraints of resources Useful when there are constraints of resources

and there are priorities among suppliers or and there are priorities among suppliers or customerscustomers


Assignment Method Assignment Method (Type II Scheduling)(Type II Scheduling)

A special class of linear programming models A special class of linear programming models that assign tasks or jobs to resourcesthat assign tasks or jobs to resources

Objective is to minimize cost or timeObjective is to minimize cost or time

Only one job (or worker) is assigned to one Only one job (or worker) is assigned to one machine (or project)machine (or project)


Assignment MethodAssignment Method

1.1. Create zero opportunity costs by repeatedly subtracting Create zero opportunity costs by repeatedly subtracting the lowest costs from each row and columnthe lowest costs from each row and column

2.2. Draw the minimum number of vertical and horizontal Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the table. If the lines necessary to cover all the zeros in the table. If the number of lines equals either the number of rows or the number of lines equals either the number of rows or the number of columns, proceed to step 4. Otherwise number of columns, proceed to step 4. Otherwise proceed to step 3.proceed to step 3.

3.3. Subtract the smallest number not covered by a line from Subtract the smallest number not covered by a line from all other uncovered numbers. Add the same number to all other uncovered numbers. Add the same number to any number at the intersection of two lines. Return to any number at the intersection of two lines. Return to step 2.step 2.

4.4. Optimal assignments are at zero locations in the table. Optimal assignments are at zero locations in the table. Select one, draw lines through the row and column Select one, draw lines through the row and column involved, and continue to the next assignment.involved, and continue to the next assignment.


Assignment ExampleAssignment Example

AA BB CCJobJob

R-34R-34 $11$11 $14$14 $ 6$ 6

S-66S-66 $ 8$ 8 $10$10 $11$11

T-50T-50 $ 9$ 9 $12$12 $ 7$ 7

TypesetterTypesetter

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 8$ 8 $ 0$ 0

S-66S-66 $ 0$ 0 $ 2$ 2 $ 3$ 3

T-50T-50 $ 2$ 2 $ 5$ 5 $ 0$ 0


Step 1a - RowsStep 1a - Rows

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 6$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 3$ 3

T-50T-50 $ 2$ 2 $ 3$ 3 $ 0$ 0


Step 1b - ColumnsStep 1b - Columns

Least numbersLeast numbersper rowper row

Least numbersLeast numbersper columnper column



Step 2 - LinesStep 2 - Lines

AA BB CCJobJob

R-34R-34 $ 5$ 5 $ 6$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 3$ 3

T-50T-50 $ 2$ 2 $ 3$ 3 $ 0$ 0


Because only two lines Because only two lines are needed to cover all are needed to cover all the zeros, the solution the zeros, the solution is is not optimal (it is not optimal (it is fewer than the number fewer than the number of jobs to assign)of jobs to assign)

Step 3 - SubtractionStep 3 - Subtraction

AA BB CCJobJob

R-34R-34 $ 3$ 3 $ 4$ 4 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 5$ 5

T-50T-50 $ 0$ 0 $ 1$ 1 $ 0$ 0


The The smallest uncovered smallest uncovered number is 2number is 2 so this is so this is subtracted from all other subtracted from all other uncovered numbers and uncovered numbers and added to numbers at the added to numbers at the intersection of linesintersection of lines



Because three lines are Because three lines are needed to cover all the needed to cover all the numbers, the solution numbers, the solution is optimal and job is optimal and job assignments can now assignments can now be madebe made

Step 2 - LinesStep 2 - Lines

AA BB CCJobJob

R-34R-34 $ 3$ 3 $ 4$ 4 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 $ 5$ 5

T-50T-50 $ 0$ 0 $ 1$ 1 $ 0$ 0


Start by assigning S-66 for Start by assigning S-66 for worker B. worker B. Job T-50 must go to worker A.Job T-50 must go to worker A. This leaves R-34 to worker C as This leaves R-34 to worker C as this is the least cost assignment this is the least cost assignment for worker C.for worker C.

Step 4 - AssignmentsStep 4 - Assignments

AA BB CCJobJobR-34 $ 3$ 3 $ 4$ 4 $ 0S-66 $ 0$ 0 $ 0 $ 5$ 5T-50 $ 0 $ 1$ 1 $ 0$ 0




Step 4 - AssignmentsStep 4 - Assignments

AA BB CCJobJobR-34 $ 3$ 3 $ 4$ 4 $ 0S-66 $ 0$ 0 $ 0 $ 5$ 5T-50 $ 0 $ 1$ 1 $ 0$ 0


From the original cost table

Minimum cost = $6 + $10 + $9 = $25

AA BB CCJobJob

R-34R-34 $11$11 $14$14 $ 6$ 6

S-66S-66 $ 8$ 8 $10$10 $11$11

T-50T-50 $ 9$ 9 $12$12 $ 7$ 7


Costs TableCosts Table


Opportunity Loss: Example 2 (Deriving Opportunity Loss: Example 2 (Deriving Opportunity Loss Table)Opportunity Loss Table)

AA BB CCJobJob

R-34R-34 $11$11 $14$14 $ 6$ 6

S-66S-66 $ 8$ 8 $10$10 $11$11

T-50T-50 $ 9$ 9 $12$12 $ 7$ 7


AA BB CCJobJobR-34R-34 $$15-$1115-$11 $15-$14$15-$14 $15-$6$15-$6

S-66S-66 $15-$8$15-$8 $15-$10$15-$10 $15-$11$15-$11

T-50T-50 $14-$9$14-$9 $14-$12$14-$12 $14-$7$14-$7


(Sales – Costs) Table(Sales – Costs) Table

AA BB CCJobJob

R-34R-34 $ 4$ 4 $ 1$ 1 $ 9$ 9

S-66S-66 $ 7$ 7 $ 5$ 5 $ 4$ 4

T-50T-50 $ 5$ 5 $ 2$ 2 $ 7$ 7


Assume that the fixed sale price Assume that the fixed sale price for each job is as follows :for each job is as follows :R-34 = $ 15 /unit;R-34 = $ 15 /unit;S-66 = $ 15 /unit;S-66 = $ 15 /unit;T-50 = $ 14 /unit;T-50 = $ 14 /unit;

Opportunity Loss TableOpportunity Loss Table

Assignment Costs TableAssignment Costs Table


Assignment: Example 2 (Deriving Assignment: Example 2 (Deriving Opportunity Loss Table)Opportunity Loss Table)

The table has profit margins that are earned for each unit made. To The table has profit margins that are earned for each unit made. To find the optimal assignment, use the method but subtract the highest find the optimal assignment, use the method but subtract the highest score of each row not the least one. score of each row not the least one.

AA BB CCJobJob

R-34R-34 $ 4$ 4 $ 1$ 1 $ 9$ 9

S-66S-66 $ 7$ 7 $ 5$ 5 $ 4$ 4

T-50T-50 $ 5$ 5 $ 2$ 2 $ 7$ 7


Opportunity Loss TableOpportunity Loss TableAA BB CC

JobJob

R-34R-34 --$ 5$ 5 -$ 8-$ 8 $ 0$ 0

S-66S-66 $ 0$ 0 -$ 2-$ 2 -$ 3-$ 3

T-50T-50 --$ 2$ 2 -$ 5-$ 5 $ 0$ 0


AA BB CCJobJob

R-34R-34 --$ 5$ 5 -$ 6-$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 -$ 3-$ 3

T-50T-50 --$ 2$ 2 -$ 3-$ 3 $ 0$ 0

TypesetterTypesetterTake highest number from each columnTake highest number from each columnand subtract from all the numbersand subtract from all the numbersin the column. in the column. Note -2 is the highest number in column B! Note -2 is the highest number in column B!

11 22

33


Assignment: Example 2 (Deriving Assignment: Example 2 (Deriving Opportunity Loss Table)Opportunity Loss Table)

Draw lines across the zeros. As only two lines cross all the zeros,Draw lines across the zeros. As only two lines cross all the zeros,solution is not yet optimal.solution is not yet optimal.

Opportunity Loss TableOpportunity Loss Table

AA BB CCJobJob

R-34R-34 --$ 5$ 5 -$ 6-$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 -$ 3-$ 3

T-50T-50 --$ 2$ 2 -$ 3-$ 3 $ 0$ 0


Take highest number from uncrossed Take highest number from uncrossed cells and subtract it from all other cells and subtract it from all other uncrossed numbers in each column.uncrossed numbers in each column.Add the number to number on the intersectionAdd the number to number on the intersectionIntersection to get table 5.Intersection to get table 5.This is not an optimal solution – 2 lines This is not an optimal solution – 2 lines through all zerosthrough all zeros

44


Opportunity Loss: Example 2Opportunity Loss: Example 2

Assign C to R-34; assign A to T-50; Assign C to R-34; assign A to T-50; assign B to S-66; assign B to S-66; The profit margin of the assignmentThe profit margin of the assignmentis taken from first table:is taken from first table:= = $5 + $ 5 + $ 9 = $ 19$5 + $ 5 + $ 9 = $ 19

AA BB CCJobJob

R-34R-34 $ 4$ 4 $ 1$ 1 $ 9$ 9

S-66S-66 $ 7$ 7 $ 5$ 5 $ 4$ 4

T-50T-50 $ 5$ 5 $ 2$ 2 $ 7$ 7


Gross Margin - Opportunity Loss TableGross Margin - Opportunity Loss Table

11AA BB CC

JobJob

R-34R-34 --$ 3$ 3 -$ 4-$ 4 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 -$ 5-$ 5

T-50T-50 $ 0$ 0 -$ 1-$ 1 $ 0$ 0

TypesetterTypesetter 55

AA BB CCJobJob

R-34R-34 --$ 5$ 5 -$ 6-$ 6 $ 0$ 0

S-66S-66 $ 0$ 0 $ 0$ 0 -$ 3-$ 3

T-50T-50 --$ 2$ 2 -$ 3-$ 3 $ 0$ 0

TypesetterTypesetter 44

Largest Largest uncrosseduncrossednumbernumberTable 5 now has three lines Table 5 now has three lines

going through all the zeros. An going through all the zeros. An optimal assignment can now be optimal assignment can now be Made for our problem!Made for our problem!


Gantt Load Chart Method Gantt Load Chart Method (Type III Scheduling)(Type III Scheduling)

Day Monday Tuesday Wednesday Thursday FridayWork Center

Metalworks

Mechanical

Electronics

Painting

Job 349

Job 349

Job 349

Job 408

Job 408

Job 408

ProcessingProcessing UnscheduledUnscheduled Center not availableCenter not available

Job 350

Job 349

Job 295



Plan 1: Gantt Staffing Chart (Type III Plan 1: Gantt Staffing Chart (Type III Scheduling)Scheduling)

MonMon TueTue WedWed ThuThu FriFri SatSat SunSun

BillBill OffOff OffOff

MaryMary OffOff OffOff

SueSue OffOff OffOff

WillWill OffOff OffOff

BobBob OffOff OffOff

MonMon OffOff OffOff

JoshJosh OffOff OffOff

1. Required Capacity1. Required Capacity 55 55 66 55 88 99 99

2. Max available staff2. Max available staff 77 77 77 77 77 77 77

3. Max off duty limits3. Max off duty limits 22 22 11 22 -1-1 -2-2 -2-2

4. 4. ScheduledScheduled off-duty off-duty 33 33 22 33 22 11 00

5. Extra staff needed5. Extra staff needed 11 11 11 11 33 33 22

Scheduled off duty minus Max. off duty limit ( row 4. Minus row 3.)Scheduled off duty minus Max. off duty limit ( row 4. Minus row 3.)

ScheduleSchedule

What would you advise the manager to do?What would you advise the manager to do?


Plan 2: Gantt Staffing Chart (Type III Plan 2: Gantt Staffing Chart (Type III Scheduling)Scheduling)

MonMon TueTue WedWed ThuThu FriFri SatSat SunSun

BillBill OffOff OffOff

MaryMary OffOff OffOff

SueSue OffOff OffOff

WillWill OffOff OffOff

BobBob OffOff OffOff

MonMon OffOff OffOff

JoshJosh OffOff OffOff

1. Required Capacity1. Required Capacity 55 55 66 55 88 99 99

2. Max available staff2. Max available staff 77 77 77 77 77 77 77

3. Max off duty staff3. Max off duty staff 22 22 11 22 -1-1 -2-2 -2-2

4. Scheduled off-duty 4. Scheduled off-duty 11 22 11 22 22 33 33

5. Extra staff needed5. Extra staff needed -1-1 00 00 00 33 55 55

4. Minus 34. Minus 3

ScheduleSchedule

This solution shifts all temp staff requirement to This solution shifts all temp staff requirement to weekendsweekends

What could be the benefit/problem with this plan?What could be the benefit/problem with this plan?


Gantt Schedule Chart Gantt Schedule Chart ExampleExample


Job Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

A

B

C

NowNow

Maintenance

Start of an Start of an activityactivity

End of an End of an activityactivity

Scheduled Scheduled activity time activity time allowedallowed

Actual work Actual work progressprogress

Nonproduction Nonproduction timetime

Point in time Point in time when chart is when chart is reviewedreviewed


SequencingSequencing

Specifies the order in which jobs should be Specifies the order in which jobs should be performed at work centersperformed at work centers

Priority rules are used to dispatch or Priority rules are used to dispatch or sequence jobssequence jobs

FCFS: First come, first servedFCFS: First come, first served

SPT: Shortest processing timeSPT: Shortest processing time

EDD: Earliest due dateEDD: Earliest due date

LPT: Longest processing timeLPT: Longest processing time


Sequencing ExampleSequencing Example

JobJob

Job Work Job Work (Processing) Time(Processing) Time

(Days)(Days)

Job Due Job Due DateDate

(Days)(Days)

AA 66 88

BB 22 66

CC 88 1818

DD 33 1515

EE 99 2323

Apply the four popular sequencing rules Apply the four popular sequencing rules to these five jobsto these five jobs


Sequencing: FCFS ExampleSequencing: FCFS Example

Job Job Sequ-Sequ-enceence

Job Job Work Work

(Proce(Processing) ssing) TimeTime

Wait Wait TimesTimes

Flow Flow TimeTime


Job Job LatenessLateness

AA 66 00 66 88 00

BB 22 66 88 66 22

CC 88 88 1616 1818 00

DD 33 1616 1919 1515 44

EE 99 1919 2828 2323 55

2828 2828 4949 7777 1111

FCFS: Sequence A-B-C-D-E (assume that all jobsFCFS: Sequence A-B-C-D-E (assume that all jobs arrived on same day in the sequence given).arrived on same day in the sequence given).



FCFS: Sequence A-B-C-D-EFCFS: Sequence A-B-C-D-E

Average completion time = = 77/5 = 15.4 daysTotal flow timeNumber of jobs

Utilization = = 28/77 = 36.4%Total job work time

Total flow time

Average number of jobs in the system = = 77/28 = 2.75 jobs/month

Total flow timeTotal job work time

Average job lateness = = 11/5 = 2.2 daysTotal late daysNumber of jobs



Job Job SequenceSequence

Job Work Job Work (Processing) (Processing)

TimeTimeFlow Flow TimeTime



BB 22 22 66 00

DD 33 55 1515 00

AA 66 1111 88 33

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6565 99

SPT (Shortest processing time): Sequence B-D-A-C-ESPT (Shortest processing time): Sequence B-D-A-C-E

The sequence changes with the priority ruleThe sequence changes with the priority rule



SPT: Sequence B-D-A-C-ESPT: Sequence B-D-A-C-E

Average completion time = = 65/5 = 13 daysTotal flow timeNumber of jobs


Total flow time

Average number of jobs in the system = = 65/28 = 2.32

jobs/months










BB 22 22 66 00

AA 66 88 88 00

DD 33 1111 1515 00

CC 88 1919 1818 11

EE 99 2828 2323 55

2828 6868 66

EDD EDD (Earliest due date)(Earliest due date) : Sequence B-A-D-C-E : Sequence B-A-D-C-E



EDD: Sequence B-A-D-C-EEDD: Sequence B-A-D-C-E



Total flow time

Average number of jobs in the system = = 68/28 = 2.43 jobs/

month










EE 99 99 2323 00

CC 88 1717 1818 00

AA 66 2323 88 1515

DD 33 2626 1515 1111

BB 22 2828 66 2222

2828 103103 4848

LPT (Longest processing time): Sequence E-C-A-D-BLPT (Longest processing time): Sequence E-C-A-D-B



LPT: Sequence E-C-A-D-BLPT: Sequence E-C-A-D-B



Total flow time

Average number of jobs in the system = = 103/28 = 3.68 jobs




Summary Sequencing ExamplesSummary Sequencing Examples

RuleRule

Average Average Completion Completion Time (Days)Time (Days)

Utilization Utilization (%)(%)

Average Number Average Number of Jobs in of Jobs in

System per System per monthmonth

Average Average Lateness Lateness

(Days)(Days)

FCFSFCFS 15.415.4 36.436.4 2.752.75 2.22.2

SPTSPT 13.013.0 43.143.1 2.322.32 1.81.8

EDDEDD 13.613.6 41.241.2 2.432.43 1.21.2

LPTLPT 20.620.6 27.227.2 3.683.68 9.69.6

Summary of RulesSummary of Rules


Comparison of Comparison of Sequencing RulesSequencing Rules

No one sequencing rule excels on all No one sequencing rule excels on all criteriacriteria

SPT does well on minimizing flow time and SPT does well on minimizing flow time and number of jobs in the systemnumber of jobs in the system

But SPT moves long jobs to the end which But SPT moves long jobs to the end which may result in dissatisfied customersmay result in dissatisfied customers

FCFS does not do especially well on any FCFS does not do especially well on any criteria (or does poorly on most criteria) criteria (or does poorly on most criteria) but it is perceived as fair by customersbut it is perceived as fair by customers

EDD minimizes latenessEDD minimizes lateness


Improving Performance of SystemImproving Performance of System

Changing setting of due datesChanging setting of due dates Changing process serial to parallel formChanging process serial to parallel form

BBAA CC EEDD

BBAA

CC

EE

DD


Example from Service IndustryExample from Service IndustryPatiePatientnt

Health Issue (Treatment time)Health Issue (Treatment time) First priorityFirst priority

appointmentappointment

Second prioritySecond priority

appointmentappointment

AA Pain in head (1 hr)Pain in head (1 hr) 8-9 am8-9 am 10-11 am10-11 am

FF Skin disease (1 hr)Skin disease (1 hr) 9-10 am9-10 am 10-11 am10-11 am

GG Sun burns (1 hr)Sun burns (1 hr) 10-11 am10-11 am 11-12 pm11-12 pm

BB Brain tumor (2 hrs)Brain tumor (2 hrs) 8-10 am8-10 am 10-12pm10-12pm

CC Depression (1 hr)Depression (1 hr) 2-3 pm2-3 pm 1-2 pm1-2 pm

II Pollen issues (2 hrs)Pollen issues (2 hrs) 2-4 pm2-4 pm 10-12 pm10-12 pm

DD Migraine pains (2 hrs)Migraine pains (2 hrs) 2-4 pm2-4 pm 8-10 am8-10 am

HH Skin cancer (2 hrs)Skin cancer (2 hrs) 8-10 am8-10 am 2-4 pm2-4 pm

EE Skin exam (1 hr)Skin exam (1 hr) 11-12 am11-12 am 2-3 pm2-3 pmThere are two doctors in a specialist clinic, one is a dermatologist the There are two doctors in a specialist clinic, one is a dermatologist the other is a neurologist. The patients call-in the order shown. Create a other is a neurologist. The patients call-in the order shown. Create a schedule for the clinic assuming that each specialist works 8-12 pm schedule for the clinic assuming that each specialist works 8-12 pm and 1-4pm daily. Assign slots to patients using and 1-4pm daily. Assign slots to patients using First come First serveFirst come First serve priority rule. Assume that the appointments slots are one hour each.priority rule. Assume that the appointments slots are one hour each.


Resolution from Service IndustryResolution from Service Industry

There are two doctors in a specialist clinic, one is a dermatologist the There are two doctors in a specialist clinic, one is a dermatologist the other is a neurologist. The patients call-in the order shown. Create a other is a neurologist. The patients call-in the order shown. Create a schedule for the clinic assuming that each specialist works 8-12 pm schedule for the clinic assuming that each specialist works 8-12 pm and 1-4pm daily. Assign slots to patients using and 1-4pm daily. Assign slots to patients using First come First serveFirst come First serve priority rule. Assume that the appointments slots are one hour each.priority rule. Assume that the appointments slots are one hour each.

Day 1Day 1 Day 2Day 28-98-9 9-109-10 10-1110-11 11-1211-12 1-21-2 2-32-3 3-43-4 8-98-9 9-109-10 10-1110-11 11-11-

1212

NurloNurlogistgist AA BB BB CC DD DD EE

AllerAllergistgist FF GG HH HH II II


Resolution from Service IndustryResolution from Service Industry

There are two doctors in a specialist clinic, one is a dermatologist the There are two doctors in a specialist clinic, one is a dermatologist the other is a neurologist. The patients call-in the order shown. Create a other is a neurologist. The patients call-in the order shown. Create a schedule for the clinic assuming that each specialist works 8-12 pm schedule for the clinic assuming that each specialist works 8-12 pm and 1-4pm daily. Assign slots to patients using and 1-4pm daily. Assign slots to patients using First come First serveFirst come First serve priority rule combined with SPT and LPT time slotspriority rule combined with SPT and LPT time slots

Day 1Day 1 Day 2Day 28-98-9 9-109-10 10-1110-11 11-1211-12 1-21-2 2-32-3 3-43-4 8-98-9 9-109-10 10-1110-11 11-11-

1212

NurloNurlogistgist BB AA EE CC DD

AllerAllergistgist HH FF GG II

© 2006 prentice hall, inc.15 – 1 operations management chapter 15 – short-term scheduling ©...

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