• Production Scheduling:
operations scheduling
with applications in
manufacturing and services
Pei-Chann Chang
RM 2614, tel. 2305,
iepchang@saturn.yzu.edu.tw
Industrial Engineering and
Management
Yuan Ze University, Taiwan
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P.C. Chang, IEM, YZU.
Literature
Book: Operations Scheduling with applications
in manufacturing and services
Authors: M. Pinedo, X. Chao
Handouts, also downloadable from website
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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.
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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
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Application of Scheduling
Sales Dept.
order
Production Dept.
Inventory Dept.
Production Management Dept.
shipping
customer
Problem：Complexity↑、Machine ↑ 、Order ↑ 、Variety ↑
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Application of Scheduling
MTO (Make to Order)
Produce way
MTS (Make to Stock)
Supply way
Time Demand
Inventory semi-finished goods BTO (Build to Order)
Short
Medium
Long
Tendency of Business:
BTO (Build To Order)
CTO (Configuration To Order)
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Theory of Production Scheduling
I. Shop Type
a. Single Machine
Total identical
b. Parallel Machine
Partial identical
c. (Flow Shop : Uni-direction)
M1
M2
M3
M4
d. (Job Shop : Multi-direction)
M4
M1
M3
M2
e.
(Open Shop: No direction)
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Theory of Production Scheduling
II. Job Type
a.
Dependent Job
order
product
operation
b.
part
assembly
Independent Job
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Theory of Production Scheduling
III. Objective Function
Objectives
1. Completion time - Min Max Ci
2. Tardiness
- Min Tmax
Note：Reasonable Due Date
3. Flow time
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- Min F
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Application areas
• Manufacturing, 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
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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
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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!
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Scheduling in services
• Workforce Scheduling in
– Call Centers
– Hospitals
– Employment agencies
– Schools, universities
• Reservation Systems in
– Airlines
– Hotels
– Car Rentals
– Travel Agencies
• Postal services
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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
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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?)
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Our approach
Scheduling problem
Problem formulation
Model
Solve with algorithms
Conclusions
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Theory of Production Scheduling
IV. Methodology
a.
b.
c.
d.
e.
Mixed Integer Linear Programming
Dynamic Programming
Branch and Bound
Time
Constraint Programming
Heuristics
•
•
•
•
•
•
•
Genetic Algorithm
Neural Network
Simulated Annealing
Tabu Search
Ant Colony
Evolutionary Algorithm
Fuzzy Logistics
NP problem
10 20 30 40
#jobs
.
.
.
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Future Development

Alternate Routing

Multiple Objectives

Machine break down -Rescheduling
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Topic 1
• Setting up the Scheduling Problem
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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
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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
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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)
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Example:
Scheduling Problem:
The data for the newspaper reading problem
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
8:45
D.E (5)
G (15)
F.T(10)
S (30)
Digby
9:30
S (90)
F.T (1)
G (1)
D.E (1)
Ask: What is the earliest time they may leave?
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Sol:
Estimation based on jobs (persons):
J1 Algy 8:30 + (60+30+2+5)
J2 Bertie 8:45 + (75+3+25+10)
Jobs
J3 Charles 8:45 + (5+15+10+30)
J4
Digby
9:30 +
(90+1+1+1)
= 10:07
= 10:38
= 09:45
= 11:03
Lower Bound 1
(Jobs base bound)
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Sol:
Estimation based on machine (newspaper):
M1
M2
machines
M3
M4
F.T 8:30 +
Why?
S.
9:15 +
G.T 8:45 +
D.E
8:45 +
(60+25+10+1)
(5+10+30+90)
(30+75+15+1)
= 10:06
= 11:30
= 10:46
(2+3+5+1)
= 08:56
Lower Bound 2
(machine base bound)
LB = Max(LB1, LB2) = Max(11:03, 11:30) = 11:30
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HW.
1.
2.
3.
4.
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.
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