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7/13/2010

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Operations Planning Operations Planning and Schedulingand Scheduling14

14 – 1Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

For For Operations Management, 9eOperations Management, 9e by by Krajewski/Ritzman/Malhotra Krajewski/Ritzman/Malhotra © 2010 Pearson Education© 2010 Pearson Education

PowerPoint Slides PowerPoint Slides by Jeff Heylby Jeff Heyl

Across the OrganizationAcross the Organization

Operations planning and scheduling is the process of making sure that demand

d l l i b l t lland supply plans are in balance at all levelsSales and operations planning and schedulingRequires managerial inputs from all of the firm’s functions


firm’s functionsEach function is affected by the plan

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Across the OrganizationAcross the Organization

TABLE 14.1 | TYPES OF PLANS WITH OPERATIONS PLANNING AND| SCHEDULING

Term DefinitionSales and operations plan (S&OP)

A time-phased plan of future aggregate resource levels so that supply is in balance with demand throughout the organization

Aggregate plan Another term for the sales and operations plan

Production plan A manufacturing firm’s sales and operations plan that centers on production rates and inventory holdings

Staffing plan A sales and operations plan for a service firm, which centers on staffing and on other human resource-related f t


factorsResource plan An intermediate, more detailed, step in the planning

process that lies between S&OP and schedulingSchedule A detailed plan that allocates resources over shorter

time horizons to accomplish specific tasks

AggregationProduct families

Stages in Planning and SchedulingStages in Planning and Scheduling

Workforce Time

The relationship of operations plans and schedules to other plans

A business plan


pAn annual plan or financial plan Resource planningThe lowest planning level is scheduling

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Stages in Planning and SchedulingStages in Planning and Scheduling

Business orannual plan

Operationsstrategy

Figure 14.1 – The Relationship of Sales and Operations Plans and Schedules to Other Plans

• Master production scheduleResource Planning (manufacturing)

• Workforce scheduleResource Planning (services)

SalesPlan

OperationsPlan

Sales and Operations Plan

Forecasting Constraintmanagement


• Employee and equipment schedules• Production order schedules• Purchase order schedules

Scheduling• Employee schedules• Facility schedules• Customer schedules

Scheduling

Master production schedule• Material requirements planning

Workforce schedule• Materials and facility resources

Matching supply with demand becomes challenging when forecasts call for uneven

Managing DemandManaging Demand

challenging when forecasts call for uneven demand patternsDemand management, the process of changing demand patterns using one or more demand options


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Managing DemandManaging Demand

TABLE 14.2 | DEMAND AND SUPPLY OPTIONS FOR| OPERATIONS PLANNING AND SCHEDULING

Demand Options Supply Optionsp pp y pComplementaryproducts

Anticipation inventory

Promotional pricing Workforce adjustment (hiring or layoffs)Prescheduled appointments

Workforce utilization (overtime and undertime)

Reservations Part-time workers and subcontractorsRevenue management Vacation schedules


Backlogs Workforce schedulesBackorders Job and customer sequenceStockouts Expediting

Sales and Operations PlansSales and Operations Plans

Current machine capacities Plans for future capacities Workforce capacities

OperationsCustomer needs Demand forecasts Competition behavior

Distribution and marketing

Aggregate plan

Supplier capabilities Storage capacity Materials availability

Materials

o o ce capac t esCurrent staffing level

Cost data Financial condition of firm

Accounting and finance

Co pet t o be a o


New products Product design changes Machine standards

EngineeringLabor-market conditions Training capacity

Human resources

Figure 14.2 – Managerial Inputs from Functional Areas to Sales and Operations Plans

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Information inputsSupply options

Anticipation inventoryWorkforce adjustmentWorkforce utilizationPart-time workersSubcontractorsVacation schedules


Planning strategiesChase strategyLevel strategyMixed strategy


Constraints and costsSix steps in the sales and operations planning processprocess

TABLE 14.3 | TYPES OF COSTS WITH SALES AND OPERATIONS PLANNING

Cost DefinitionRegular time Regular-time wages plus benefits and pay for vacationsOvertime Wages paid for work beyond the normal workweek exclusive

of fringe benefitsHiring and layoff Cost of advertising jobs interviews training programs scrap


Hiring and layoff Cost of advertising jobs, interviews, training programs, scrap caused by inexperienced employees, exit interviews, severance pay, and retraining

Inventory holding Capital, storage and warehousing, pilferage and obsolescence, insurance, and taxes

Backorder and stockout Costs to expedite past-due orders, potential cost of losing a customer

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Figure 14.3 – Sales and Operations Plan for Make-to-Stock Product Family


Finalize Executive C

Update S&OP spreadsheets

3

Demand planning

2

Gather data

1


Finalize and

communicate6

Executive S&OP

meeting5

Consensus meeting

4

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Using SpreadsheetsUsing Spreadsheets


Figure 14.4 – Manufacturer’s Plan Using a Spreadsheet and Mixed Strategy

Using Chase and Level StrategiesUsing Chase and Level Strategies

EXAMPLE 14.1A large distribution center must develop a staffing plan that minimizes total costs using part-time stockpickersminimizes total costs using part time stockpickersFirst level strategy that meets demand with the minimum use of undertime and not consider vacation schedulingEach part-time employee can work a maximum of 20 hours per week on regular timeInstead of paying undertime, each worker’s day is shortened during slack periods and overtime can be used during peak periods


periods

1 2 3 4 5 6 Total

Forecasted demand 6 12 18 15 13 14 78

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Currently, 10 part-time clerks are employed. They have not been subtracted from the forecasted demand shown. Constraints and cost information are as follows:a. The size of training facilities limits the number of new hires

in any period to no more than 10.b. No backorders are permitted.c. Overtime cannot exceed 20 percent of the regular-time

capacity in any period. The most that any part-time employee can work is 1.20(20) = 24 hours per week.

d. The following costs can be assigned:


d. The following costs can be assigned:

Regular-time wage rate $2,000/time period at 20 hrs/weekOvertime wages 150% of the regular-time rateHires $1,000 per personLayoffs $500 per person


SOLUTIONa. Chase StrategyThi t t i l i l dj ti th kfThis strategy simply involves adjusting the workforce as needed to meet demand, as shown in Figure 14.5. Rows in the spreadsheet that do not apply (such as inventory and vacations) are hidden. The workforce level row is identical to the forecasted demand row. A large number of hirings and layoffs begin with laying off 4 part-time employees immediately because the current staff is 10 and the staff level required in period 1 is only 6. However, many employees, such as college students prefer part-time work The total cost is $173 500 and


students, prefer part-time work. The total cost is $173,500, and most of the cost increase comes from frequent hiring and layoffs, which add $17,500 to the cost of utilized regular-time costs.

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Figure 14.5 – Spreadsheet for Chase Strategy


b. Level StrategyIn order to minimize undertime, the maximum use of overtime possible must occur in the peak period. For this particular levelpossible must occur in the peak period. For this particular level strategy (other workforce options are possible), the most overtime that the manager can use is 20 percent of the regular-time capacity, w, so

1.20w = 18 employees required in peak period (period 3)

w = = 15 employees181.20


A 15-employee staff size minimizes the amount of undertime for this level strategy. Because the staff already includes 10 part-time employees, the manager should immediately hire 5 more. The complete plan is shown in Figure 14.6. The total cost is $164,000.

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Figure 14.6 – Spreadsheet for Level Strategy

Application 14.1Application 14.1

The Barberton Municipal Division of Road Maintenance is charged with road repair in the city of Barberton and surrounding area. Cindy Kramer, road maintenance director,

t b it t ffi l f th t b d tmust submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Kramer estimates that the labor hours required for the next four quarters are 6,000, 12,000, 19,000, and 9,000, respectively. Each of the 11 workers on the workforce can contribute 520 hours per quarter. Overtime is limited to 20 percent of the regular-time capacity in any quarter. Subcontracting is not permitted.Payroll costs are $6,240 in wages per worker for regular time


worked up to 520 hours, with an overtime pay rate of $18 for each overtime hour. Although unused overtime capacity has no cost, unused regular time is paid at $12 per hour. The cost of hiring a worker is $3,000, and the cost of laying off a worker is $2,000.

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Use a chase strategy for the Barberton Municipal Division that varies the workforce level without using overtime. Undertime gshould be minimized, except for the minimal amount mandated because the quarterly requirements are not integer multiples of 520 hours. (Students complete highlighted sections)


Quarter1 2 3 4 Total


1 2 3 4 TotalForecasted demand (hrs)

6,000 12,000 19,000 9,000 46,000

Workforce level (workers)

12 91

Undertime (hours) 240 1,320Overtime (hours) 0 0Utilized time 6,000 46,000

37

2400

19,000

18

3600

9,000

24

4800

12,000


(hours), ,

Hires (workers) 1 26Layoffs (workers) 0 19

,

130

,

019

,

120

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What is the total cost of this plan?

Costs per Quarter1 2 3 4 Total

Utilized time $72,000 $552,000Undertime 2,880 15,840Overtime 0 0Hires 3,000 78,000L ff 0 38 000

$144,0005,760

036,000

0

$228,0002,880

039,000

0

$108,0004,320

00

38 000


Layoffs 0 38,000Total Cost $683,840

0 0 38,000


Find a level plan for the Barberton Municipal Division that allows no delay in road repair and minimizes undertime. O ti b d t it li it i t Gi th t thOvertime can be used to its limits in any quarter. Given that the demand peaks in quarter 3, we get:

1.20w =

w = 30.45 or 31 employees

36.54 employee-period equivalents 19,000

520 =


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Forecasted demand (hrs)

6,000 12,000 19,000 9,000 46,000

Workforce level (workers)

31

Undertime (hours) 10,120Overtime (hours) 0Utilized time 6,000

31

4,1200

12,000

31

02,880

16,120

31

7,1200

9,000

124

21,3602,880

43,120


Utilized time (hours)

6,000

Hires (workers) 20Layoffs (workers) 0

12,000

00

16,120

00

9,000

00

43,120

200


What is the total cost of this level workforce plan?


Utilized time $72,000 $517,440Undertime 121,440 256,320Overtime 0 51,840Hires 60,000 60,000

$108,00085,440

00

$193,4400

51,8400

$144,00049,440

00


Layoffs 0 0Total Cost $885,600

000

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A mixed strategy considers and implements a fuller range of reactive alternatives than any one “pure” strategy.Now propose a plan of your own for the Barberton Municipal Division. Use the chase strategy as a base, but find a way to decrease the cost of hiring and layoffs by selectively using some overtime. (Students complete highlighted sections)



Forecasted demand 6 000 12 000 19 000 9 000 46 000


Forecasted demand 6,000 12,000 19,000 9,000 46,000Workforce level Undertime (hours)Overtime (hours)Utilized time (hours)Hires (workers)Layoffs (workers)

12240

06,000

10

851,0802,880

43,1202013

24480

012,000

120

310

2,88016,120

70

18360

09,000

013


y ( )

Several solutions are possible. The key idea in creating this one is hiring only 7 employees in quarter 3, while using overtime to its maximum limit and eliminating undertime for that quarter. Hiring fewer in quarter 3 allows the number of layoffs in quarter 4 to drop to only 13, down from 19.

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What is the cost of your mixed strategy plan?


Utilized time $72,000 $144,000 $193,440 $108,000 $517,440UndertimeOvertimeHires

12,96051,84060,000

2,8800

3,000

5,7600

36,000

051,84021,000

4,32000


LayoffsTotal Cost

26,000$668,240

0 0 0 26,000

SchedulingScheduling

Takes operations and scheduling process from planning to execution and requires

th i d t f hgathering data from sources such as demand forecasts, resource availability from the sales and operations plan, and specific constraints from employees and customers. Generates a work schedule for employees or sequences of jobs or

t t k t ti


customers at workstations.

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Gantt ChartsGantt Charts

The job or activity progress chartThe workstation chart

Ford

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

Current date

Start activity

Finish activity

Scheduled activity time


Nissan

Pontiac

Figure 14.7 – Gantt Progress Chart for an Auto Parts Company

activity time

Actual progress

Nonproductive time

Gantt ChartsGantt Charts

Workstation 7am 12 pm8am 9am 10am 11am 1pm 2pm 3pm 4pm 5pm 6pm

Time

Operating Room A

Operating Room B

pm p p p p p p

Dr. Gary Case Dr. Jeff Dow Dr. Madeline Easton

Dr. Jon Adams Dr. Aubrey Brothers Dr. Alaina Bright


Operating Room C

Dr. Dan GillespieDr. Jordanne Flowers

Figure 14.8 – Gantt Workstation Chart for Operating Rooms at a Hospital

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Scheduling EmployeesScheduling Employees

Translate the staffing plan into specific schedules of work for each employeeConstraints

Technical constraintsLegal and behavioral considerationsPsychological needs of workers

Rotating schedule


Rotating scheduleFixed schedule

Scheduling EmployeesScheduling Employees

Steps in developing a workforce scheduleStep 1: Find all the pairs of consecutive daysStep 2: If a tie occurs, choose one of the tied

pairs, consistent with the provisions written into the labor agreement

Step 3: Assign the employees for the selected pair of days off

Step 4: Repeat steps 1 – 3 until all of the


Step 4: Repeat steps 1 3 until all of the requirements have been satisfied

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Developing a Workforce ScheduleDeveloping a Workforce Schedule

EXAMPLE 14.2The Amalgamated Parcel Service is open seven days a week. The schedule of requirements isThe schedule of requirements is

Day M T W Th F S Su

Required number of employees 6 4 8 9 10 3 2

The manager needs a workforce schedule that provides two consecutive days off and minimizes the amount of total slack


consecutive days off and minimizes the amount of total slack capacity. To break ties in the selection of off days, the scheduler gives preference to Saturday and Sunday if it is one of the tied pairs. If not, she selects one of the tied pairs arbitrarily.


SOLUTIONFriday contains the maximum requirements, and the pair S – Su has the lowest total requirements. Therefore, Employee 1 ishas the lowest total requirements. Therefore, Employee 1 is scheduled to work Monday through Friday.Note that Friday still has the maximum requirements and that the requirements for the S – Su pair are carried forward because these are Employee 1’s days off. These updated requirements are the ones the scheduler uses for the next employee.The day-off assignments for the employees are shown in the f ll i t bl


following table.

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Developing a Workforce ScheduleDeveloping a Workforce ScheduleScheduling Days Off

M T W Th F S Su Employee Comments

6 4 8 9 10 3 2 1 The S–Su pair has the lowest total requirements. Assign Employee 1 to a M-F schedule.



3 1 5 6 7 3 2 4 The M–T pair has the lowest total requirements. Assign Employee 4 to a W-Su schedule.



2 0 2 3 4 1 0 7 The S–Su pair has the lowest total requirements Assign



1 0 1 2 3 1 0 8 Four pairs have the minimum requirement and the lowest total. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 8 to a M-F schedule.

0 0 0 1 2 1 0 9 Arbitrarily choose the Su–M pair to break ties because the S–Su pair does not have the lowest total requirements. Assign Employee 9 to a T-S schedule.

0 0 0 0 1 0 0 10 Choose the S–Su pair according to the tie-breaking rule. Assign Employee 10 to a M-F schedule.

Scheduling Days Off

M T W Th F S Su Employee Comments



The S–Su pair has the lowest total requirements. Assign Employee 1 to a M-F schedule.

6 4 8 9 10 3 2 1







The S–Su pair has the lowest total requirements. Assign Employee 2 to a M-F schedule.The S–Su pair has the lowest total requirements. Assign Employee 3 to a M-F schedule.

5 3 7 8 9 3 2 2

4 2 6 7 8 3 2 3














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In this example, Friday always has the maximum requirements and should be avoided as a day off. The final schedule for the employees is shown in the following table.

Final Schedule

Employee M T W Th F S Su Total

1 X X X X X off off

2 X X X X X off off

3 X X X X X off off

4 off off X X X X X

5 X X X X X off off

6 off off X X X X X

7 X X X X X ff ff


7 X X X X X off off

8 X X X X X off off

9 off X X X X X off

10 X X X X X off off

Capacity, C 7 8 10 10 10 3 2 50

Requirements, R 6 4 8 9 10 3 2 42

Slack, C – R 1 4 2 1 0 0 0 8

Sequencing Jobs at a WorkstationSequencing Jobs at a Workstation

Priority sequencing rulesFirst-come, first-served (FCFS)

Performance measuresFlow time

First come, first served (FCFS)Earliest due date (EDD)

Flow time = Finish time


Past due (also referred to as tardiness)+ Time since job arrived at workstation

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Using the FCFS RuleUsing the FCFS Rule

EXAMPLE 14.3Currently a consulting company has five jobs in its backlog. The time since the order was placed, processing time, andThe time since the order was placed, processing time, and promised due dates are given in the following table. Determine the schedule by using the FCFS rule, and calculate the average days past due and flow time. How can the schedule be improved, if average flow time is the most critical?

Customer Time Since Order Arrived (days ago)

Processing Time (days)

Due Date(days from now)

A 15 25 29


A 15 25 29

B 12 16 27

C 5 14 68

D 10 10 48

E 0 12 80


SOLUTIONa. The FCFS rule states that Customer A should be the first one

in the sequence, because that order arrived earliest—15in the sequence, because that order arrived earliest 15 days ago. Customer E’s order arrived today, so it is processed last. The sequence is shown in the following table, along with the days past due and flow times.

Customer Sequence

Start Time

(days)


Finish Time

(days)

Due Date

Days Past Due

Days Ago Since Order

Arrived

Flow Time

(days)

A


B

C

D

E

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SOLUTIONa. The FCFS rule states that Customer A should be the first one

in the sequence, because that order arrived earliest—15in the sequence, because that order arrived earliest 15 days ago. Customer E’s order arrived today, so it is processed last. The sequence is shown in the following table, along with the days past due and flow times.

15 40+ 25 = 25 29 00

Customer Sequence

Start Time

(days)


Finish Time

(days)

Due Date

Days Past Due


Arrived

Flow Time

(days)

A


27 14 12 53

41 + 10 = 51 48 3 10 61

51 + 14 = 65 68 0 5 70

65 + 12 = 77 80 0 0 77

25 + 16 = 41B

C

D

E


The finish time for a job is its start time plus the processing time. Its finish time becomes the start time for the next job in the sequence, assuming that the next job is available for i di t i Th d t d f j b i (0) ifimmediate processing. The days past due for a job is zero (0) if its due date is equal to or exceeds the finish time. Otherwise it equals the shortfall. The flow time for each job equals its finish time plus the number of days ago since the order first arrived at the workstation. The days past due and average flow time performance measures for the FCFS schedule are

Average days past due = = 3 4 days0 + 14 + 3 + 0 + 0


Average days past due =

Average flow time =

= 3.4 days

= 60.2 days

5

40 + 53 + 61 + 70 + 775

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b. The average flow time can be reduced. One possibility is the sequence shown in the following table.

Customer Start Processing Finish Due Days Days Ago Flow Sequence Time

(days)Time (days) Time

(days)Date Past

DueSince Order

ArrivedTime

(days)

D

E

C

B

A



b. The average flow time can be reduced. One possibility is the sequence shown in the following table.

Customer Start Processing Finish Due Days Days Ago Flow

0 + 10 = 10

Sequence Time (days)

Time (days) Time (days)

Date Past Due

Since Order Arrived

Time (days)

D

E

C

B

A

0 0 0 25 48

22 + 14 = 36 68 0 5 41

36 + 16 = 52 27 25 12 64

52 + 25 = 77 29 48 15 92

48 0 10 20

10 + 12 = 22 80 0 0 22


This schedule reduces the average flow time from to 60.2 to 47.8 days—a 21 percent improvement. However, the past due times for jobs A and B have increased.


Average flow time =

= 14.6 days

= 47.8 days

0 + 0 + 0 + 25 + 485

20 + 22 + 41 + 64 + 925

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Software SupportSoftware Support

Computerized scheduling systems are available to cope with the complexity of p p yworkforce schedulingSoftware is also available for sequencing jobs at workstationsAdvance planning and scheduling (APS) systems


Revisit Example 14.3, where the consulting company has five jobs in its backlog. Create a schedule using the EDD rule, calculating the average days past due and flow time. In this

d EDD t f th FCFS l ?


Customer Sequence

Start Time

(days)


Finish Time

(days)

Due Date

Days Past Due


Arrived

Flow Time

(days)

B

case, does EDD outperform the FCFS rule?

SOLUTION

0 + 16 = 16 27 0 12 28


A

D

C

E

41 + 10 = 51 48 3 10 61

51 + 14 = 65 68 0 5 70

65 + 12 = 77 80 0 0 77

16 + 25 = 41 29 12 15 56

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Customer Sequence

Start Time

(days)


Finish Time

(days)

Due Date

Days Past Due


Arrived

Flow Time

(days)

B


0 + 16 = 16 27 0 12 28B

A

D

C

E

0 16 16

41 + 10 = 51 48 3 10 61

51 + 14 = 65 68 0 5 70

65 + 12 = 77 80 0 0 77

27 0 12 28

16 + 25 = 41 29 12 15 56

The days past due and average flow time performance measures for the EDD schedule are

0 + 12 + 3 + 0 + 0


By both measures, EDD outperforms the FCFS. However, the solution found in part (b) of Example 14.3 still has the best average flow time of only 47.8 days.


Average flow time =

= 3.0 days

= 58.4 days

0 12 3 0 05

28 + 56 + 61 + 70 + 715

Solved Problem 1Solved Problem 1

The Cranston Telephone Company employs workers who lay telephone cables and perform various other construction tasks. The company prides itself on good service and strives to

l t ll i d ithi th l i i d i hi hcomplete all service orders within the planning period in which they are received.Each worker puts in 600 hours of regular time per planning period and can work as many as an additional 100 hours of overtime. The operations department has estimated the following workforce requirements for such services over the next four planning periods:


Planning Period 1 2 3 4

Demand (hours) 21,000 18,000 30,000 12,000

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Cranston pays regular-time wages of $6,000 per employee per period for any time worked up to 600 hours (including undertime). The overtime pay rate is $15 per hour over 600 h Hi i t i i d tfitti l thours. Hiring, training, and outfitting a new employee costs $8,000. Layoff costs are $2,000 per employee. Currently, 40 employees work for Cranston in this capacity. No delays in service, or backorders, are allowed. Use the spreadsheet approach to answer the following questions:

a. Prepare a chase strategy using only hiring and layoffs. What are the total numbers of employees hired and laid off?

b D l kf l th t th l l t t


b. Develop a workforce plan that uses the level strategy, relaying only on overtime and undertime. Maximize the use of overtime during the peak period so as to minimize the workforce level and amount of undertime.

c. Propose an effective mixed-strategy plan.d. Compare the total costs of the three plans.


a. The chase strategy workforce is calculated by dividing the demand for each period by 600 hours, or the amount or regular-time work for one employee during one period. This

t t ll f t t l f 20 k t b hi d d 40 tstrategy calls for a total of 20 workers to be hired and 40 to be laid off during the four-period plan. Figure 14.9 shows the “chase strategy” solution that OM Explorer’s Sales and Operations Planning with Spreadsheets solver produces. We simply hide any unneeded columns and rows in this general-purpose solver.


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Figure 14.9 – Spreadsheet for Chase Strategy


b. The peak demand is 30,000 hours in period 3. As each employee can work 700 hours per period (600 on regular time and 100 on overtime), the workforce level of the level

t t th t i i i d ti i 30 000/700 42 86strategy that minimizes undertime is 30,000/700 = 42.86, or 43 employees. This strategy calls for three employees to be hired in the first quarter and for none to be laid off. To convert the demand requirements into employee-period equivalents, divide the demand in hours by 600. For example, the demand of 21,000 hours in period 1 translates into 35 employee-period equivalents (21,000/600) and demand in period 3 translates into 50 employee-period equivalents (30 000/600) Figure 14 10 shows OM Explorer’s


equivalents (30,000/600). Figure 14.10 shows OM Explorer s spreadsheet for this level strategy that minimizes undertime.

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Figure 14.10 – Spreadsheet for Level Strategy


c. The mixed-strategy plan that we propose uses a combination of hires, layoffs, and overtime to reduce total costs. The workforce is reduced by 5 at the beginning of the fi t i d i d b 8 i th thi d i d d d dfirst period, increased by 8 in the third period, and reduced by 13 in the fourth period. Figure 14.11 shows the results.


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Figure 14.11 – Spreadsheet for Mixed Strategy


d. The total cost of the chase strategy is $1,050,000. The level strategy results in a total cost of gy$1,119,000. The mixed-strategy plan was developed by trial and error and results in a total cost of $1,021,000. Further improvements are possible.


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The Food Bin grocery store operates 24 hours per day, 7 days per week. Fred Bulger, the store manager, has been analyzing the efficiency and productivity of store operations recently. B l d id d t b th d f h k t l k thBulger decided to observe the need for checkout clerks on the first shift for a one-month period. At the end of the month, he calculated the average number of checkout registers that should be open during the first shift each day. His results showed peak needs on Saturdays and Sundays.

Day M T W Th F S Su


Number of Clerks Required 3 4 5 5 4 7 8


Bulger now has to come up with a workforce schedule that guarantees each checkout clerk two consecutive days off but still covers all requirements.a. Develop a workforce schedule that covers all requirements

while giving two consecutive days off to each clerk. How many clerks are needed? Assume that the clerks have no preference regarding which days they have off.

b. Plans can be made to use the clerks for other duties if slack or idle time resulting from this schedule can be determined. How much idle time will result from this schedule, and on what days?


what days?

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SOLUTIONa. We use the method demonstrated in Example 14.2 to

determine the number of clerks needed. The minimumdetermine the number of clerks needed. The minimum number of clerks is eight.

3 4 5 5 4 7 8off off X X X X X3 4 4 4 3 6 7

DayM T W Th F S Su

RequirementsClerk 1Requirements


off off X X X X XClerk 2RequirementsClerk 3RequirementsClerk 4

3 4 3 3 2 5 6X X X off off X X2 3 2 3 2 4 5X X X off off X X


DayM T W Th F S Su1 2 1 3 2 3 4X off off X X X X0 2 1 2 1 2 3

off off X X X X X0 2 0 1 0 1 2X X off off X X X0 1 0 1 0 0 1X X X X ff ff X

RequirementsClerk 5RequirementsClerk 6RequirementsClerk 7RequirementsCl k 8


The minimum number of clerks is eight.

X X X X off off X0 0 0 0 0 0 0

Clerk 8Requirements

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