Production Scheduling: operations scheduling with applications in manufacturing and services
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Production Scheduling P.C. Chang, IEM, YZU.1
• Production Scheduling: operations scheduling with applications in
manufacturing and services
Pei-Chann ChangRM 2614, tel. 2305, [email protected]
Industrial Engineering and ManagementYuan Ze University, Taiwan
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Production Scheduling P.C. Chang, IEM, YZU.2
Literature
Book:Operations Scheduling with applicationsin manufacturing and services
Authors: M. Pinedo, X. Chao
Handouts, also downloadable from website
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Production Scheduling P.C. Chang, IEM, YZU.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.
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Production Scheduling P.C. Chang, IEM, YZU.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
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Production Scheduling P.C. Chang, IEM, YZU.5
Sales Dept.
Application of Scheduling
Production Dept. Inventory Dept.
Production Management Dept.
customer
order shipping
Problem: Complexity↑、Machine ↑ 、 Order ↑ 、 Variety ↑
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Application of Scheduling
Produce wayMTO (Make to Order)
MTS (Make to Stock)
Tendency of Business:
BTO (Build To Order)CTO (Configuration To Order)
Supply way Inventory
semi-finished goods
BTO (Build to Order)
Time Demand
Short Medium Long
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Theory of Production Scheduling
I. Shop Typea. Single Machine
b. Parallel Machine
c. (Flow Shop : Uni-direction)
d. (Job Shop : Multi-direction)
e. (Open Shop: No direction)
Total identical
Partial identical
M1 M2 M3 M4
M1
M2
M3M4
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Theory of Production Scheduling
II. Job Typea. Dependent Job
order
product
operation
b. Independent Job
part
assembly
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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 - Min F
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• 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
Application areas
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• 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
Application areas (cont.)
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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
Model
Conclusions
Problem formulation
Solve with algorithms
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Theory of Production Scheduling
IV. Methodology
10 20 30 40 #jobs
Time NP problem
a. Mixed Integer Linear Programmingb. Dynamic Programmingc. Branch and Boundd. Constraint Programminge. Heuristics
• Genetic Algorithm• Neural Network• Simulated Annealing• Tabu Search• Ant Colony• Evolutionary Algorithm• Fuzzy Logistics
.
.
.
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Production Scheduling P.C. Chang, IEM, YZU.18
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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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 functionE.g, cost to be minimized, quality measure to be maximized
3. ConstraintsWhich values the decision variables can be set to
Modeling
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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 co
mplicated setting of the environment
– A scheduling policy: determines the next job gi
ven 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
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 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)
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Sol:
Estimation based on jobs (persons):
Jobs
J1 Algy 8:30 + (60+30+2+5) = 10:07
J2 Bertie 8:45 + (75+3+25+10) = 10:38
J3 Charles 8:45 + (5+15+10+30) = 09:45
J4 Digby 9:30 + (90+1+1+1) = 11:03
Lower Bound 1(Jobs base bound)
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Sol:
Estimation based on machine (newspaper):
machines
M1 F.T 8:30 + (60+25+10+1) = 10:06
M2 S. 9:15 + (5+10+30+90) = 11:30
M3 G.T 8:45 + (30+75+15+1) = 10:46
M4 D.E 8:45 + (2+3+5+1) = 08:56
Lower Bound 2(machine base bound)
Why?
LB = Max(LB1, LB2) = Max(11:03, 11:30) = 11:30
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HW.
1. How many different schedules, feasible and infeasible are there?
2. What is the earliest time that Algy and his friends can leave for the country?
3. 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 ?
4. 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.