Lecture 3 manufacturing scheduling concepts
Download
1 / 21

Lecture 3: - PowerPoint PPT Presentation


  • 199 Views
  • Updated On :

Lecture 3: Manufacturing Scheduling Concepts. Outline. Jobs & Operations Characteristics & notation Resources/machines Setup/transition cost Objective functions Complexity. M 1. M 2. M 3. S ij. C ij. S ij – starting time of job j on machine i C ij – completion time of job j.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Lecture 3: ' - Angelica


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 3 manufacturing scheduling concepts l.jpg

Lecture 3: Manufacturing Scheduling Concepts

© J. Christopher Beck 2005


Outline l.jpg
Outline

  • Jobs & Operations

    • Characteristics & notation

  • Resources/machines

    • Setup/transition cost

  • Objective functions

  • Complexity

© J. Christopher Beck 2005


Slide3 l.jpg

M1

M2

M3

Sij

Cij

Sij – starting time of job j on machine i

Cij – completion time of job j

Jobs

rj

dj

wj

pij

pij – processing time of job j on machine i

rj – release date of job j

dj – due date of job j

wj – weight of job j

© J. Christopher Beck 2005


Jobs operations l.jpg
Jobs & Operations

  • Often jobs are made up of a set of operations

rj

dj

wj

p2j

p0j

p3j

p1j

precedence constraints

© J. Christopher Beck 2005


Example house building l.jpg
Example: House Building

Excavate

Floor joists

Foundations

4 wks

2 wks

3 wks

Exterior plumbing

3 wks

© J. Christopher Beck 2005


Resources machines l.jpg
Resources/Machines

  • Jobs may need resources

    • Mixing machine, back-hoe, cement mixer

  • May be multiple similar resources are available and you need to choose one

© J. Christopher Beck 2005


House building resources l.jpg
House Building Resources

Excavate

Floor joists

Foundations

4 wks

2 wks

3 wks

requires

Carpenter

Exterior plumbing

Backhoe

Backhoe operator

Dump truck

3 wks

© J. Christopher Beck 2005


Resources setup l.jpg
Resources & Setup

  • If 2 jobs need the same resource (and the resource can only do 1 thing at a time), then the jobs must be sequenced

  • May be a time or cost for a resource to change jobs (“sequence dependent setup”)

© J. Christopher Beck 2005


Objectives l.jpg
Objectives

  • Minimize maximum completion time (aka “makespan”)

    • Min Cmax

    • Cmax = max(C1, … Cn)

  • Minimize maximum lateness

    • Min Lmax

    • Lmax = max(C1 – d1, … Cn – dn)

© J. Christopher Beck 2005


Objectives10 l.jpg
Objectives

  • Minimize total weighted tardiness

    • Min ΣwjTj

    • Tj = max(Cj – dj, 0)

© J. Christopher Beck 2005


Slide11 l.jpg

Exercise 2.1

a) Draw precedence graph

b) Calculate

makespan


Hard problems vs easy problems l.jpg
Hard Problems vs. Easy Problems

  • Exercise 2.1b was “easy”

  • Adding resources would have made it hard

  • Hard & easy have precise mathematical definitions

  • You need to have, at least, an intuitive understanding of what this means

© J. Christopher Beck 2005


Hard vs easy l.jpg
Hard vs Easy

  • Easy:

    • Sort n numbers

    • Solve a system of linear equations

  • Hard:

    • Schedule a factory, deliver packages, schedule buses, …

© J. Christopher Beck 2005


Hard vs easy14 l.jpg
Hard vs Easy

  • f (n): the number of “basic operations” needed to solve the problem with input size n

  • Easy: f (n) is polynomial in n

    • O(n), O(n log n), O(n2), …

  • Hard: f (n) is exponential in n

    • O(2n), …

© J. Christopher Beck 2005






Hard vs easy19 l.jpg
Hard vs Easy

  • 10301 operations required in worst case

  • Age of universe: 1018 seconds

  • Fastest Computer today: 1014 op/sec

  • Let’s say we get a computer 1018 times faster (a sextillion times faster)

    • 1033 op/sec

  • It may still take 10250 times longer than the age of the universe to solve the problem!

© J. Christopher Beck 2005


Hard vs easy20 l.jpg
Hard vs Easy

  • If it is going to take 10250 times the age of the universe to schedule a factory, why bother?

© J. Christopher Beck 2005


Hard vs easy21 l.jpg
Hard vs Easy

  • If it is going to take 10250 times the age of the universe to schedule a factory, why bother?

    • May be we can do it in a reasonable time in most cases?

    • May be we can get a good (but not necessarily best possible) solution in a reasonable amount of time?

© J. Christopher Beck 2005


ad