The classical job shop scheduling problem (jsp), Mechanical Engineering

The Classical Job Shop Scheduling Problem (Jsp)

A  job  shop  scheduling  problem  occupies  the  determination  of  beginning  time  for  all operations in a finite and specified set, N. Related along with each operation i ε N there is a processing time pi. The operations in set N are portioned in n equally exclusive and exhaustive subsets Jk, here Jk is termed as job k. The operations in set N are portioned also into m equally exhaustive and exclusive subsets Mr, where Mr is the set of operations to be processed upon machine r. Also specified are the precedence associations, and the operations in a job or technological constraints. A pair (i, j), i, j ∈ Jk, imply that operation i precedes operation j in job k. Assume that Ak = {(i, j) | i, j ∈ Jk and I must precede j} indicate the set of pairs that illustrate the technological constraints related with job k. Related with every operation i ∈ N there is a processing time pi. The traditional job shop scheduling problem is to calculating the processing order of the operations in Mr, for r = 1, 2, . . . , m, such as several objective function is optimized.

This problem contains finding the vector of operation begin times, t = (t1, t2, . . . , t¦N¦), which minimizes a specified objective function Z (t). The difficulty can be formulated mathematically as given below:

(JSP): Minimize Z (t) Subjected to

 ti - 1 tj ≥ pj,                                         (i, j) ∈ Ak, k = 1, 2, . . . , n                 . . . (1)

ti  - tj ≥ pj V tj - ti ≥ pi,                          i, j, ∈ Mr, r = 1, 2, . . . , m                 . . . (2)

ti ≥ 0,                                                               i ∈ N.                                   . . . (3)

Eq. (1) makes sure that the technological constraints are satisfied. The disjunctive relation in Eq. (2) makes sure that the ability constraints on the machines are not violated that is a machine can process individual operation at a time. JSP is well identifying that it belongs to a class of the most complicated combinatorial optimization problems and it has been extensively studied.

Usual assumptions made in job shop scheduling comprise the following figure:

A1

Each job needs only one machine at a time, that is Mr ∩ Ms = φ, r ≠ s.

A2

One job processes by one machine at a time, that is | Jk ∩ Mr   | = 1, k = 1, . . . , n and r = 1, . . . , m. also this shows that a job visits each machine exactly once, that is two operations in similar job cannot use similar machine.

A 3

The  order  in  that  a  job  visits  various  machines  is  predetermined  via technological constraints, that is the set A = A1 ∪ A2 ∪ . . . ∪ An, is specified and fixed. Ak can be seemed like the machine routing or process plan for job k.

A4

No explicit consideration is specified to auxiliary resources as like: material handling, buffer space and tooling.

                                               414_The Classical Job Shop Scheduling Problem (Jsp).png

                                                 Figure: Typical Assumption Made in Job Shop Scheduling

These assumptions are suitable for manufacturing environments that is, which human intervention is important and the equipment utilized is hard automation or manual. This is also suitable in environments characterized via batch production, in that every part type has a fixed and determined process plan. A specified workstation or machine is pre- assigned to execute each step in the process plan.

Posted Date: 3/5/2013 7:02:28 AM | Location : United States







Related Discussions:- The classical job shop scheduling problem (jsp), Assignment Help, Ask Question on The classical job shop scheduling problem (jsp), Get Answer, Expert's Help, The classical job shop scheduling problem (jsp) Discussions

Write discussion on The classical job shop scheduling problem (jsp)
Your posts are moderated
Related Questions
First we focus on the inner region fluid (0 (solid body rotation) around the z-axis. The steady incompressible velocity field is given by ur=0 utheta=rw uz= 0. The pressure at th

ARC BLOW In certain cases depending upon where the return path connections are given for the arc current, the arc may be deflected towards a direction of weaker electro magnet

Desgin of furnce - combustion chamber: • Deside on type of furnace :need review of furnace types (grete,fluidized bed,puluerised coal or other. • Sectch of furnace design with

Autocad screen- The autocad Screen basic chapter of Autocad course it will show the display of Autocad on computer screen

Friction: you have learnt laws of friction and problems involving dry friction. The relative sliding motion of one body on another body is resisted by forces called as frictio

Explain how chips are prepared in cutting and how are they classified with sketches. What are the factors responsible for creation of different forms of chips?

Effective communication is an itergral aspect in the mechanical engineering field, base on arguement

Calculate total deflection -two close-coiled helical springs: Two close-coiled helical springs are compressed among two parallel plates by a load of 1000 N. The springs contai

Torque of Multiple and Different Sized Fasteners: First tighten all fasteners by the help of free hand. Then torque big fasteners first followed by torque of smaller fasteners in

what are the essentials of a good steam generator?