1. OPERATIONS SCHEDULING AND SEQUENCING
CHAPTER 14
DAVID A. COLLIER AND JAMES R. EVANS

2. LO1 Explain the concepts of scheduling and sequencing.
LO2 Describe staff scheduling and appointment system decisions.
LO3 Explain sequencing performance criteria and rules.
LO4 Describe how to solve single- and two-resource sequencing problems.
LO5 Explain the need for monitoring schedules using Gantt charts.

3. jean Rowecamp, clinical coordinator of nursing services, was faced with a deluge of complaints by her nursing staff about their work schedules and complaints by floor supervisors about inadequate staffing. The nurses complained they were having too many shift changes each month. Supervisors said they had too many nurses during the days and not enough at night and on the weekends. It seems that nothing she did would satisfy everyone. The nurses were unionized, so she couldn’t schedule them more than 7 consecutive working days and the nurses required at least 16 hours between shift changes. Nurses were constantly making “special requests” for personal time off, despite the negotiated procedures for bidding for shifts and vacation times. Jean lamented that she became an administrator and longed for the days before she had these responsibilities.

4. What do you think?
As a student, how do you schedule your homework, school projects, and study activities? What criteria do you use?

5. Understanding Scheduling and Sequencing
Scheduling refers to the assignment of start and completion times to particular jobs, people, or equipment.
Examples: Scheduling restaurant employees, airline crews and planes, sports teams, factory jobs.
Sequencing refers to determining the order in which jobs or tasks are processed.
Examples: Emergency room patients, automobile models on an assembly line, outgoing flights on runways.

7. Scheduling Applications and Approaches
Scheduling applies to all aspects of the value chain, from planning and releasing orders in a factory, determining work shifts for employees, and making deliveries to customers.
Tools:
Spreadsheets
Software packages
Web-based tools

8. Scheduling Applications and Approaches
Staff scheduling attempts to match available personnel with the needs of the organization by:
Accurately forecasting demand and translating it into the quantity and timing of work to be done.
Determining the staffing required to perform the work by time period.
Determining the personnel available and the full- and part-time mix.
Matching capacity to demand requirements and developing a work schedule that maximizes service and minimizes costs.

9. Scheduling Applications and Approaches
Staff scheduling problem:
Given minimum worker requirements for each day of the week, schedule employees so that each has two consecutive days off and all demand requirements are met.
Method:
Locate the set of at least two consecutive days with the smallest requirements, circle the requirements for these days, and assign a worker to all days not circled. Subtract 1 from the requirement of each day not circled, removing existing circles, and repeat this process until all requirements are satisfied.

10. Employee 1: New requirements: Employee 2:
Example: T.R. Accounting Service is developing a workforce schedule for three weeks from now, and has forecast demand and translated it into the following minimum personnel requirements for the week.
Day Mon Tue Wed Thur Fri Sat Sun
Min Personnel
Employee 1:
New requirements:
Employee 2:

11. Exhibit 14.1 Staff Scheduling Procedure for T.R. Accounting Service
Employee 3:
New requirements:
Remaining assignments:

12. Exhibit 14.2 Final Accountant Schedule

13. Scheduling Applications and Approaches
Appointment Systems
Appointments can be viewed as a reservation for service time and capacity.
Four decisions:
Determine the appointment time interval.
Determine the length of each workday and time off-duty.
Decide how to handle overbooking.
Develop customer appointment rules that maximize customer satisfaction.

15. Sequencing
Sequencing is required when several activities must be processed using a common resource.
Sequencing criteria:
Process-focused performance criteria (flow time and makespan)
Customer-focused due date criteria (lateness and tardiness)
Cost-based criteria

16. Fi = ∑pij + ∑wij = Ci - Ri [14.1]
Sequencing
Flow time is the amount of time a job spent in the shop or factory.
Fi = ∑pij + ∑wij = Ci - Ri [14.1]
Where:
Fi  Flow time of job i
∑pij  Sum of all processing times of job i at workstation or area j (run  setup times)
∑wij  Sum of all waiting times of job i at workstation or area j
Ci  Completion time of job i
Ri  Ready time for job i where all materials, specifications, and so on are available

17. Sequencing M = C - S [14.2] Where: M = Makespan of a group of jobs
Makespan is the time needed to process a given set of jobs.
M = C - S [14.2]
Where:
M = Makespan of a group of jobs
C = Completion time of last job in the group
S = Start time of first job in the group

18. Sequencing
Lateness is the difference between the completion time and the due date (either positive or negative).
Tardiness is the amount of time by which the completion time exceeds the due date.
(Tardiness is defined as zero if the job is completed before the due date.)
Li = Ci - Di
Ti = Max (0, Li)
Where:
Li = Lateness of job i
Ti = Tardiness of job i
Di = Due date of job i
[14.3]
[14.4]

19. Sequencing Sequencing rules for a fixed set of jobs:
Shortest Processing Time (SPT)
SPT sequencing maximizes resource utilization and minimizes average flow time and work-in-process inventory.
Earliest Due Date (EDD)
EDD minimizes the maximum job tardiness and lateness.

20. Sequencing – Other Priority Rules
Priority rules when new jobs arrive intermittently:
First come-first served (FCFS).
Fewest number of operations remaining (FNO).
Least work remaining (LWR) – The sum of all processing times for operations not yet performed.
Least amount of work at the next process queue (LWNQ) – Amount of work awaiting the next process in a job’s sequence.

21. Applications of Sequencing Rules
Single-Resource Sequencing Problem
Process a set of jobs on a single processor.
SPT sequencing finds a minimal average flow time sequence.
FCFS rule works well when processing times are relatively equal.
EDD rule minimizes the maximum job tardiness and lateness.

22. Example: FCFS Rule Job Processing Time (days) Due Date 1 4 15 2 7 16

23. Example: SPT Rule Job Processing Time (days) Due Date 1 4 15 2 7 16

24. Example: EDD Rule Job Processing Time (days) Due Date 1 4 15 2 7 16

25. Exhibit 14.3 Comparison of Three Ways (By-the Numbers, SPT, and EDD) to Sequence the Five Jobs

26. Applications of Sequencing Rules
Two-Resource Sequencing Problem (Johnson’s Rule)
List the jobs and their processing times on Resources #1 and #2.
Find the job with the shortest processing time (on either resource).
If this time corresponds to Resource #1, sequence the job first; if it corresponds to Resource #2, sequence the job last.
Repeat steps 2 and 3, using the next-shortest processing time and working inward from both ends of the sequence until all jobs have been scheduled.

27. Example
Each job requires first a shearing operation (Resource #1) and then a punch-press operation (Resource #2).
Job 2 has the shortest processing time; since it is on Resource 2, schedule it last. Job 1 has the next shortest processing time; since it is on Resource 1, schedule it first:

28. Example
Next, both job 1 on the shear and job 3 on the punch press have the next shortest time. Choose job 1:
Continuing, choose job 3 and finally job 4:

29. If jobs are completed by order number, the punch press often experiences idle time awaiting the next job. The makespan is 37 days.
Exhibit Gantt Job Sequence Chart for Hirsch Product Sequence

30. Johnson’s Rule results in a reduction in makespan from 37 days to 27 days, as shown in the Gantt chart.
Exhibit Gantt Job Sequence Chart for Hirsch Product Sequence

31. Schedule Monitoring and Control
Schedule progress must be monitored on a continuing basis. Reschedules are a normal part of scheduling.
Gantt charts are useful tools for monitoring schedules. This helps to track jobs that are behind, on, or ahead of schedule.

32. Exhibit 14.6 Gantt Chart Example for Monitoring Schedule Progress

33. Balloons Aloha Case Study
Compute the average flow time, lateness, and tardiness for this group of jobs using Mr. Sailboat’s sequential order of 1 (first), 2, 3, 4, 5, and 6 (last).
In what order would the jobs be processed using the SPT rule? Compute the average flow time, lateness, and tardiness for this group of jobs.
Compare the answers in Questions 1 and 2.
What are your short-term recommendations for this set of six jobs? Explain how you arrived at them.
What are your long-term recommendations with respect to sequencing jobs at Balloons Aloha? Explain your reasoning.