1. Roberta Russell & Bernard W. Taylor, III
Chapter 16
Scheduling
Operations Management - 5th Edition
Roberta Russell & Bernard W. Taylor, III

2. Lecture Outline Objectives in Scheduling Loading / Assignment
Sequencing
Monitoring
Theory of Constraints
Employee Scheduling

3. What is Scheduling? Last stage of planning before production occurs
Specifies when labor, equipment, facilities are needed to produce a product or provide a service

4. Another Definition of Scheduling
Scheduling concerns the allocation of limited resources to tasks over time. It is a decision-making process that has as a goal the optimization of one or more objectives
Michael Pinedo – Scheduling: Theory, Algorithms, and Systems
I like this definition better.

5. Managers Must Schedule the Following
Scheduling Decisions
Organization
Managers Must Schedule the Following
Arnold Palmer Hospital
Operating room use
Patient admissions
Nursing, security, maintenance staffs
Outpatient treatments
University of Missouri
Classrooms and audiovisual equipment
Student and instructor schedules
Graduate and undergraduate courses
Lockheed-Martin factory
Production of goods
Purchases of materials
Workers
Hard Rock Cafe
Chef, waiters, bartenders
Delivery of fresh foods
Entertainers
Opening of dining areas
Delta Airlines
Maintenance of aircraft
Departure timetables
Flight crews, catering, gate, ticketing personnel

6. Objectives in Scheduling
Meet customer due dates
Minimize job lateness
Minimize response time
Minimize completion time
Minimize time in the system
Minimize overtime
Maximize machine or labor utilization
Minimize idle time
Minimize work-in-process inventory

7. Shop Floor Control Loading Sequencing Monitoring
Check availability of material, machines and labor
Sequencing
Release work orders to shop and issue dispatch lists for individual machines
Monitoring
Maintain progress reports on each job until it is complete

8. Loading Process of assigning work to limited resources
Perform work on most efficient resources
Use assignment method of linear programming to determine allocation

9. Assignment Problem Example
WebStar, Inc. has 4 projects to complete
They have 4 programmers, each with varying degrees of expertise
On average, it costs $100 per hour
Assign a single worker to a single project in order to minimize total cost
Processing PROJECT
Estimates (hr)
Bryan
Kari
Noah
Chris

10. Formulation Indices DATA Variables i = project index j = worker index
n = total number of projects (and workers)
DATA
COSTij = cost of having project i assigned to worker j
Variables
xij = indicates if project i assigned to worker j
totcost = total cost of assignments

11. Formulation, cont’d. Objective Constraints min totcost =
for i = 1, …, n
(assign only one worker to a project)
for j = 1, …, n
(assign only one project to a worker)
xij binary

12. Another Example
Spring Weekend is coming up and Joe has 3 commitments to keep:
Go out one night with his girlfriend
Go out one night with his UConn friends
Go out one night with his HS friends
He has estimated his costs for each commitment as shown on the next slide
Help Joe decide which night he should spend with each group of friends

13. Joe’s Costs Girlfriend UConn Friends HS Friends Thursday $30 $50 $100
Friday
$40
$60
$90
Saturday
$80

14. Joe’s Dilemma Formulated
Let
???
Objective Function
Subject to

15. Sequencing Prioritize jobs assigned to a resource
If no order specified use first-come first-served (FCFS)
Many other sequencing rules exist
Each attempts to achieve an objective

16. Sequencing Rules FCFS - first-come, first-served
LCFS - last come, first served
DDATE - earliest due date
CUSTPR - highest customer priority
SETUP - similar required setups
SLACK - smallest slack
CR - critical ratio
SPT - shortest processing time
LPT - longest processing time

17. Critical Ratio Rule CR considers both time and work remaining CR = =
If CR > 1, job ahead of schedule
If CR < 1, job behind schedule
If CR = 1, job on schedule
time remaining due date - today’s date
work remaining remaining processing time

18. Sequencing Jobs Through One Process
Flowtime (completion time)
Time for a job to flow through the system
Makespan
Time for a group of jobs to be completed
Tardiness
Difference between a late job’s due date and its completion time

19. Sequencing Jobs Through Two Serial Process
Johnson’s Rule
List time required to process each job at each machine. Set up a one-dimensional matrix to represent desired sequence with # of slots equal to # of jobs.
Select smallest processing time at either machine. If that time is on machine 1, put the job as near to beginning of sequence as possible.
If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible.
Remove job from list.
Repeat steps 2-4 until all slots in matrix are filled and all jobs are sequenced.

20. Johnson’s Rule A B C D E JOB PROCESS 1 PROCESS 2 A 6 8 B 11 6 C 7 3

21. Johnson’s Rule (cont.) E A D B C Completion time = 41
Process 1
(sanding) 5 11 20 31 38
Process 2
(painting) 15 23 30 37 41
Idle time
Completion time = 41
Idle time = =10

22. Guidelines for Selecting a Sequencing Rule
SPT most useful when shop is highly congested
Use SLACK for periods of normal activity
Use DDATE when only small tardiness values can be tolerated
Use LPT if subcontracting is anticipated
Use FCFS when operating at low-capacity levels
Do not use SPT to sequence jobs that have to be assembled with other jobs at a later date

23. Monitoring Work package Gantt Chart Input/Output Control
Shop paperwork that travels with a job
Gantt Chart
Shows both planned and completed activities against a time scale
Input/Output Control
Monitors the input and output from each work center

24. Theory of Constraints Not all resources are used evenly
Concentrate on the “bottleneck” resource
Synchronize flow through the bottleneck
Use process and transfer batch sizes to move product through facility

25. TOC Scheduling Procedure
Identify bottleneck
Schedule job first whose lead time to the bottleneck is less than or equal bottleneck processing time
Forward schedule the bottleneck machine
Backward schedule the other machines to sustain the bottleneck schedule
Transfer in batch sizes smaller than the process batch size

26. Drum, Buffer, Rope
The drum is the beat of the system and provides the schedule or pace of production
The buffer is the inventory necessary to keep constraints operating at capacity
The rope provides the synchronization necessary to pull units through the system
Another idea from TOC.

27. Employee Scheduling Labor is very flexible resource
Scheduling workforce is complicated repetitive task
Assignment method can be used
Heuristics are commonly used

28. Employee Scheduling Heuristic
Let N = no. of workers available Di = demand for workers on day i X = day working O = day off
Assign the first N - D1 workers day 1 off. Assign the next N - D2 workers day 2 off. Continue in a similar manner until all days are have been scheduled
If number of workdays for full time employee < 5, assign remaining workdays so consecutive days off are possible
Assign any remaining work to part-time employees
If consecutive days off are desired, consider switching schedules among days with the same demand requirements

29. Employee Scheduling DAY OF WEEK M T W TH F SA SU MIN NO. OF
WORKERS REQUIRED
Homer
Marge
Bart
Lisa
Maggie

30. Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU
MIN NO. OF
WORKERS REQUIRED
Homer O X X O X X X
Marge O X X O X X X
Bart X O X X O X X
Lisa X O X X X X O
Maggie X X O X X X O
Completed schedule satisfies requirements but has no consecutive days off

31. Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU
MIN NO. OF
WORKERS REQUIRED
Homer O O X X X X X
Marge O O X X X X X
Bart X X O O X X X
Lisa X X X O X X O
Maggie X X X X O X O
Revised schedule satisfies requirements with consecutive days off for most employees