1. Production Scheduling: operations scheduling with applications in manufacturing and services
Pei-Chann Chang
RM 2614, tel. 2305,
Industrial Engineering and Management
Yuan Ze University, Taiwan

2. Literature Book: Operations Scheduling with applications
in manufacturing and services
Authors: M. Pinedo, X. Chao
Handouts, also downloadable from website

3. Exam The following methods must be studied thoroughly
(one or two questions about these will be in the exam):
adaptive search
branch-and-bound, beam-search
shifting bottleneck
Aside from the discussed chapters from the book,
the handouts must be well studied.

4. Scheduling: definition
Allocation of jobs to scarce resources
the types of jobs and resources depend on the specific situation
Combinatorial optimization problem
maximize/minimize objective
subject to constraints

5. Application of Scheduling
Sales Dept.
Production Dept.
Inventory Dept.
order
shipping
Production Management Dept.
customer
Problem：Complexity↑、Machine ↑ 、Order ↑ 、Variety ↑

6. Application of Scheduling
MTO (Make to Order)
MTS (Make to Stock)
Produce way
Supply way
Inventory
semi-finished goods
BTO (Build to Order)
Time Demand
Short
Medium
Long
Tendency of Business:
BTO (Build To Order) CTO (Configuration To Order)

7. Theory of Production Scheduling
Shop Type
Single Machine
Parallel Machine
(Flow Shop : Uni-direction)
(Job Shop : Multi-direction)
(Open Shop: No direction)
Total identical
Partial identical M1 M2 M3 M4 M1 M2 M3 M4

8. Theory of Production Scheduling
Job Type
Dependent Job
order
product
operation
b. Independent Job
part
assembly

9. Theory of Production Scheduling
Objective Function
1. Completion time - Min Max Ci
2. Tardiness Min Tmax
Note：Reasonable Due Date
3. Flow time Min F
Objectives

10. Application areas Manufacturing, e.g.: Services, e.g.:
job shop / flow shop scheduling
workforce scheduling
tool scheduling
Services, e.g.:
Hotel / airline reservation systems
Hospitals (operating rooms)
Transportation and distribution, e.g.:
vehicle scheduling, and routing
railways

11. Application areas (cont.)
Information processing and communications:
CPU’s, series and parallel computing
call centers
Time-tabling, e.g.:
lecture planning at a University
soccer competition
flight scheduling
Warehousing, e.g.:
AGV scheduling, and routing
Maintenance, e.g.:
scheduling maintenance of a fleet of ships

12. Scheduling in manufacturing
Due to increasing market competition, companies strive to:
shorten delivery times
increase variety in end-products
shorten production lead times
increase resource utilization
improve quality, reduce WIP
prevent production disturbances (machine breakdowns)
--> more products in less time!

13. Scheduling in services
Workforce Scheduling in
Call Centers
Hospitals
Employment agencies
Schools, universities
Reservation Systems in
Airlines
Hotels
Car Rentals
Travel Agencies
Postal services

14. Important objectives to be displayed
Due Date Related
Number of late jobs
Maximum lateness
Average lateness, tardiness
Productivity and Inventory Related
Total Setup Time
Total Machine Idle Time
Average Time Jobs Remain in System, WIP
Resource usage
resource shortage

15. Important characteristics of optimization techniques
Quality of Solutions Obtained (How Close to Optimal?)
Amount of CPU-Time Needed (Real-Time on a PC?)
Ease of Development and Implementation (How much time needed to code, test, adjust and modify)
Implementation costs
(Are expensive LP-solvers required?)

16. Our approach Scheduling problem Problem formulation Model
Solve with algorithms
Conclusions

17. Theory of Production Scheduling
Methodology
Mixed Integer Linear Programming
Dynamic Programming
Branch and Bound
Constraint Programming
Heuristics
Genetic Algorithm
Neural Network
Simulated Annealing
Tabu Search
Ant Colony
Evolutionary Algorithm
Fuzzy Logistics . 　
#jobs
Time
NP problem

18. Future Development Alternate Routing Multiple Objectives
Machine break down -Rescheduling

19. Topic 1
Setting up the Scheduling Problem

20. Modeling Three components to any model: 1. Decision variables
This is what we can change to affect the system, that is, the variables we can decide upon
2. Objective function
E.g, cost to be minimized, quality measure to be maximized
3. Constraints
Which values the decision variables can be set to

21. Decision “Variables” Three basic types of solutions:
A sequence: a permutation of the jobs
A schedule: allocation of the jobs in a more complicated setting of the environment
A scheduling policy: determines the next job given the current state of the system

22. Model Characteristics
Multiple factors:
Number of machine and resources,
configuration and layout,
level of automation, etc.
Our terminology:
Resource = machine (m)
Entity requiring the resource = job (n)

23. reading order and times in mins.
Example:
Scheduling Problem:
The data for the newspaper reading problem
Ask: What is the earliest time they may leave?
Reader
get up at
reading order and times in mins.
Algy
8:30
F.T(60)
G (30)
D.E (2)
S (5)
Bertie
8:45
G (75)
D.E (3)
F.T(25)
S (10)
Charles
D.E (5)
G (15)
F.T(10)
S (30)
Digby
9:30
S (90)
F.T (1)
G (1)
D.E (1)

24. Sol: Estimation based on jobs (persons): Jobs J1 Algy 8:30 +
( )
= 10:07 J2
Bertie
8:45 +
( )
= 10:38 J3
Charles
( )
= 09:45 J4
Digby
9:30 +
( )
= 11:03
Lower Bound 1
(Jobs base bound)

25. Sol: Estimation based on machine (newspaper): machines M1 F.T 8:30 +
( )
= 10:06 M2 S.
9:15 +
( )
= 11:30 M3
G.T
8:45 +
( )
= 10:46 M4
D.E
( )
= 08:56
Why?
Lower Bound 2
(machine base bound)
LB = Max(LB1, LB2) = Max(11:03, 11:30) = 11:30

26. HW. How many different schedules, feasible and infeasible are there?
What is the earliest time that Algy and his friends can leave for the country?
Digby decides that the delights for a day in the country are not for him, He will spend the morning in bed. What is the earliest time that Algy, Bertie and Charles may leave ?
Do you need to list every feasible solution when solving prob.2 & 3? If not, please explain in detail the procedure to your answer without listing every feasible solution.