Production Scheduling P.C. Chang, IEM, YZU.1

• Production Scheduling: operations scheduling with applications in

manufacturing and services

Pei-Chann ChangRM 2614, tel. 2305, iepchang@saturn.yzu.edu.tw

Industrial Engineering and ManagementYuan Ze University, Taiwan

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Literature

Book:Operations Scheduling with applicationsin 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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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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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.