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Operations Planning and Scheduling

Chapter 10

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What is Operations Planning and Scheduling?

Operations planning and scheduling

The process of balancing supply with demand, from the aggregate level down to the short-term scheduling level

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Operations Planning and Scheduling

TYPES OF PLANS WITH OPERATIONS PLANNING AND SCHEDULING
Term	Definition
Sales and operations plan (S&OP)	A time-phased plan of future aggregate resource levels so that supply is in balance with demand
Aggregate plan	Another term for the sales and operations plan
Production plan	A sales and operations plan for a manufacturing firm 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 factors
Resource plan	An intermediate step in the planning process that lies between S&OP and scheduling
Schedule	A detailed plan that allocates resources over shorter time horizons to accomplish specific tasks

Table 10.1

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Levels in Operations Planning and Scheduling

Level 1: Sales and Operations Planning

Aggregation

Services or products
Workforce
Time

Information inputs
Relationship to other plans

Business Plan
Annual Plan

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Levels in Operations Planning and Scheduling

Business or

annual plan

Job and facility scheduling
Workforce scheduling
Equipment/jobs scheduling

Scheduling

Materials requirements planning
Services resource planning

Resource Planning

Sales

Plan

Operations

Plan

Sales and Operations Plan

Forecasting

Operations

strategy

Constraint

management

Figure 10.2

Level 1

Level 2

Level 3

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Levels in Operations Planning and Scheduling

Level 2: Resource Planning

A process that takes sales and operations plans; process time standards, routings, and other information on how services or products are produced; and then plans the timing of capacity and material requirements.

Level 3: Scheduling

A process that takes the resource plan and translates it into specific operational tasks on a detailed basis.

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S&OP Supply Options

Anticipation Inventory
Workforce Adjustment
Workforce Utilization
Part-Time Workers
Subcontractors
Vacation Schedules

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S&OP Strategies

Chase Strategy

A strategy that involves hiring and laying off employees to match the demand forecast

Level Strategy

A strategy that keeps the workforce constant, but varies its utilization via overtime, undertime, and vacation planning to match the demand forecast

Mixed Strategy

A strategy that considers the full range of supply options

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S&OP Strategies

TYPES OF COSTS WITH SALES AND OPERATIONS PLANNING
Cost	Definition
Regular time	Regular-time wages plus benefits and pay for vacations
Overtime	Wages paid for work beyond the normal workweek exclusive of fringe benefits
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

Table 10.2

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S&OP Strategies

Figure 10.3

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S&OP Strategies

Finalize

and communicate

6

Executive S&OP meeting

5

Consensus meeting

4

Update

S&OP spreadsheets

3

Demand planning

2

Gather data

1

Steps in Sales and Operations Planning Process

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Spreadsheet for a Manufacturer

Figure 10.4

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Example 10.1

A large distribution center must develop a staffing plan that minimizes total costs using part-time stockpickers (using chase and level plans)
For the level strategy, need to meet demand with the minimum use of undertime and not consider vacation scheduling
Each part-time employee can work a maximum of 20 hours per week on regular time
Instead of paying undertime, each worker’s day is shortened during slack periods and overtime can be used during peak periods

	1	2	3	4	5	6	Total
Forecasted demand	6	12	18	15	13	14	78

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Example 10.1

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; demand must be met each period.

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:

Regular-time wage rate $2,000/time period at 20 hrs/week

Overtime wages 150% of the regular-time rate

Hires $1,000 per person

Layoffs $500 per person

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Example 10.1

a. Chase Strategy

This strategy simply involves adjusting the workforce as needed to meet demand.
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.
The total cost is $173,500.

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Example 10.1

Figure 10.5

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Example 10.1

b. Level Strategy

In order to minimize undertime, the maximum use of overtime possible must occur in the peak period.
The most overtime that the manager can use is 20 percent of the regular-time capacity, w, so

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 total cost is $164,000.

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

w =

= 15 employees

18

1.20

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Example 10.1

Figure 10.6

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Application 10.1

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, must 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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Application 10.1

Use a chase strategy for the Barberton Municipal Division that varies the workforce level without using overtime.

Undertime should be minimized, except for the minimal amount mandated because the quarterly requirements are not integer multiples of 520 hours.

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Application 10.1

	Quarter
	1	2	3	4	Total
Forecasted demand (hrs)	6,000	12,000	19,000	9,000	46,000
Workforce level (workers)	12				91
Undertime (hours)	240				1,320
Overtime (hours)	0				0
Utilized time (hours)	6,000				46,000
Hires (workers)	1				26
Layoffs (workers)	0				19

37
240
0
19,000
13
0

18
360
0
9,000
0
19

24
480
0
12,000
12
0

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Application 10.1

What is the total cost of this plan?

Costs per Quarter
	1	2	3	4	Total
Utilized time	$72,000				$552,000
Undertime	2,880				15,840
Overtime	0				0
Hires	3,000				78,000
Layoffs	0				38,000
			Total Cost		$683,840

$144,000
5,760
0
36,000
0

$228,000
2,880
0
39,000
0

$108,000
4,320
0
0
38,000

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Application 10.2

Find a level plan for the Barberton Municipal Division that allows no delay in road repair and minimizes undertime.
Overtime can be used to its limits in any quarter.
Given that the demand peaks in quarter 3:

1.20w =

w = 30.45 or 31 employees

36.54 employee-period equivalents

19,000

520

=

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Application 10.2

Quarter
	1	2	3	4	Total
Forecasted demand (hrs)	6,000	12,000	19,000	9,000	46,000
Workforce level (workers)	31
Undertime (hours)	10,120
Overtime (hours)	0
Utilized time (hours)	6,000
Hires (workers)	20
Layoffs (workers)	0

31
4,120
0
12,000
0
0

31
0
2,880
16,120
0
0

31
7,120
0
9,000
0
0

124
21,360
2,880
43,120
20
0

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Application 10.2

What is the total cost of this level workforce plan?

Costs per Quarter
	1	2	3	4	Total
Utilized time	$72,000				$517,440
Undertime	121,440				256,320
Overtime	0				51,840
Hires	60,000				60,000
Layoffs	0				0
			Total Cost		$885,600

$108,000
85,440
0
0
0

$193,440
0
51,840
0
0

$144,000
49,440
0
0
0

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Application 10.3

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.

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Application 10.3

Quarter
	1	2	3	4	Total
Forecasted demand	6,000	12,000	19,000	9,000	46,000
Workforce level
Undertime (hours)
Overtime (hours)
Utilized time (hours)
Hires (workers)
Layoffs (workers)

12
240
0
6,000
1
0

85
1,080
2,880
43,120
20
13

24
480
0
12,000
12
0

31
0
2,880
16,120
7
0

18
360
0
9,000
0
13

The key idea in this plan 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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Application 10.3

Costs per Quarter
	1	2	3	4	Total
Utilized time	$72,000	$144,000	$193,440	$108,000	$517,440
Undertime
Overtime
Hires
Layoffs
			Total Cost

What is the cost of your mixed strategy plan?

12,960
51,840
60,000
26,000
$668,240


2,880
0
3,000
0

5,760
0
36,000
0

0
51,840
21,000
0

4,320
0
0
26,000

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Scheduling

Scheduling

The function that takes the operations and scheduling process from planning to execution.

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Scheduling

Job and Facility Scheduling

Gantt progress chart
Gantt workstation chart

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Scheduling

Gantt Progress Chart

Nissan

Ford

Pontiac

Job

4/20

4/22

4/23

4/24

4/25

4/26

4/21

4/17

4/18

4/19

Current date

Start activity

Finish activity

Scheduled activity time

Actual progress

Nonproductive time

Figure 10.7

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Scheduling

Operating Room A

Workstation

7am

Operating Room B

Operating Room C

12 pm

8am

9am

10am

11am

1pm

2pm

3pm

4pm

5pm

6pm

Time

Dr. Gary Case

Dr. Jeff Dow

Dr. Madeline Easton

Dr. Dan Gillespie

Dr. Jordanne Flowers

Dr. Jon Adams

Dr. Aubrey Brothers

Dr. Alaina Bright

Gantt Workstation Chart

Figure 10.8

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Scheduling

Workforce Scheduling –

A type of scheduling that determines when employees work

Constraints

Technical constraints
Legal and behavioral considerations
Psychological needs of workers

Scheduling Options

Rotating schedule vs Fixed schedule

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Scheduling

Steps in developing a workforce schedule

Step 1: Find all the pairs of consecutive days

Step 2: If a tie occurs, choose one of the tied pairs, consistent with the provisions written into the labor agreement

Step 3: Assign the employee the selected pair of days off

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

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Example 10.2

The Amalgamated Parcel Service is open seven days a week. The 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 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.

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Example 10.2

Friday contains the maximum requirements, and the pair S – Su has 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.

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Example 10.2

Scheduling 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.
5	3	7	8	9	3	2	2	The S–Su pair has the lowest total requirements. Assign Employee 2 to a M-F schedule.
4	2	6	7	8	3	2	3	The S–Su pair has the lowest total requirements. Assign Employee 3 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.
3	1	4	5	6	2	1	5	The S–Su pair has the lowest total requirements. Assign Employee 5 to a M-F schedule.
2	0	3	4	5	2	1	6	The M–T pair has the lowest total requirements. Assign Employee 6 to a W-Su schedule.
2	0	2	3	4	1	0	7	The S–Su pair has the lowest total requirements. Assign Employee 7 to a M-F schedule.
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.

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

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.

6	4	8	9	10	3	2	1

5	3	7	8	9	3	2	2

4	2	6	7	8	3	2	3

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.
3	1	4	5	6	2	1	5	The S–Su pair has the lowest total requirements. Assign Employee 5 to a M-F schedule.
2	0	3	4	5	2	1	6	The M–T pair has the lowest total requirements. Assign Employee 6 to a W-Su schedule.
2	0	2	3	4	1	0	7	The S–Su pair has the lowest total requirements. Assign Employee 7 to a M-F schedule.
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.

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Example 10.2

	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	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

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.

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Sequencing Jobs at a Workstation

Priority Sequencing Rules

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

Performance Measures

Flow Time

Flow time = Finish time + Time since job arrived at workstation

Past Due (Tardiness)

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Example 10.3

Currently a consulting company has five jobs in its backlog.
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
B	12	16	27
C	5	14	68
D	10	10	48
E	0	12	80

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Example 10.3

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

15	40

+	25	=	25

29	0

0

25

+	16	=	41

Customer Sequence	Start Time (days)	Processing Time (days)	Finish Time (days)	Due Date	Days Past Due	Days Ago Since Order Arrived	Flow Time (days)
A
B
D
C
E

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

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Example 10.3

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 immediate 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 =

Average flow time =

= 3.4 days

= 60.2 days

0 + 14 + 3 + 0 + 0

5

40 + 53 + 61 + 70 + 77

5

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Example 10.3

b. Using the STP rule, the average flow time can be reduced with this new sequence.

0	+	10	=	10

Customer Sequence	Start Time (days)	Processing Time (days)	Finish Time (days)	Due Date	Days Past Due	Days Ago Since Order Arrived	Flow Time (days)
D
E
C
B
A

Average days past due =

Average flow time =

= 14.6 days

= 47.8 days

0 + 0 + 0 + 25 + 48

5

20 + 22 + 41 + 64 + 92

5

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

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Application 10.4

A consulting company has five jobs in its backlog. A schedule was created using the FCFS rule and the average days past due was 3.4 days and the average flow time was 60.2 days. Create a new schedule using the EDD rule, calculating the average days past due and flow time. In this case, does EDD outperform the FCFS rule?

Customer	Time Since Order �Arrived (days ago)	Processing �Time (days)	Due Date �(days from now)
A	15	25	29
B	12	16	27
C	5	14	68
D	10	10	48
E	0	12	80

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Application 10.4

Customer Sequence	Start Time (days)	Processing Time (days)	Finish Time (days)	Due Date	Days Past Due	Days Ago Since Order Arrived	Flow Time (days)
B
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

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Application 10.4

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

By both measures, EDD outperforms the FCFS.

However, the solution found in Example 15.3 still has the best average flow time of only 47.8 days

Average days past due =

Average flow time =

= 3.0 days

= 58.4 days

0 + 12 + 3 + 0 + 0

5

28 + 56 + 61 + 70 + 77

5

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Software Support

Computerized scheduling systems are available to cope with the complexity of workforce scheduling.
Software is also available for sequencing jobs at workstations.
Advance planning and scheduling (APS) systems seek to optimize resources across the supply chain and align daily operations with strategic goals.

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Solved 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 complete 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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Solved Problem 1

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 hours. 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.

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

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.

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Solved Problem 1

a. Chase Strategy

Figure 10.9

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Solved Problem 1

b. Level Strategy

Figure 10.10

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Solved Problem 1

Figure 10.11

c. Mixed Strategy

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Solved Problem 1

d. Total Cost of Plans

CHASE = $1,050,000

LEVEL = $1,119,000

MIXED = $1,021,000

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Solved Problem 2

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. Bulger 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

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Solved Problem 2

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?

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Solved Problem 2

We use the method demonstrated in Example 15.2 to determine the number of clerks needed.

The minimum number of clerks is eight.

3	4	5	5	4	7	8

off	off	X	X	X	X	X

3	4	4	4	3	6	7

off	off	X	X	X	X	X

				Day
	M	T	W	Th	F	S	Su
Requirements
Clerk 1
Requirements
Clerk 2
Requirements
Clerk 3
Requirements
Clerk 4

3	4	3	3	2	5	6

X	X	X	off	off	X	X

2	3	2	3	2	4	5

X	X	X	off	off	X	X

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Solved Problem 2

1	2	1	3	2	3	4
X	off	off	X	X	X	X
0	2	1	2	1	2	3
off	off	X	X	X	X	X
0	2	0	1	0	1	2
X	X	off	off	X	X	X
0	1	0	1	0	0	1
X	X	X	X	off	off	X
0	0	0	0	0	0	0

				Day
	M	T	W	Th	F	S	Su
Requirements
Clerk 5
Requirements
Clerk 6
Requirements
Clerk 7
Requirements
Clerk 8
Requirements

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Solved Problem 2

b. Based on the results in part (a), the number of clerks on duty minus the requirements is the number of idle clerks available for other duties:

The slack in this schedule would indicate to Bulger the number of employees he might ask to work part time (fewer than 5 days per week).
For example, Clerk 7 might work Tuesday, Saturday, and Sunday and Clerk 8 might work Tuesday, Thursday, and Sunday.
That would eliminate slack from the schedule.

	M	T	W	Th	F	S	Su
Number on duty	5	4	6	5	5	7	8
Requirements	3	4	5	5	4	7	8
Idle clerks	2	0	1	0	1	0	0

10-58

1	2	1	3	2	3	4
X	off	off	X	X	X	X
0	2	1	2	1	2	3
off	off	X	X	X	X	X
0	2	0	1	0	1	2
X	X	off	off	X	X	X
0	1	0	1	0	0	1
X	X	X	X	off	off	X
0	0	0	0	0	0	0

1	2	1	3	2	3	4
X	off	off	X	X	X	X
0	2	1	2	1	2	3
off	off	X	X	X	X	X
0	2	0	1	0	1	2
X	X	off	off	X	X	X
0	1	0	1	0	0	1
X	X	X	X	off	off	X
0	0	0	0	0	0	0

1	2	1	3	2	3	4
X	off	off	X	X	X	X
0	2	1	2	1	2	3
off	off	X	X	X	X	X
0	2	0	1	0	1	2
X	X	off	off	X	X	X
0	1	0	1	0	0	1
X	X	X	X	off	off	X
0	0	0	0	0	0	0