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

Find the value of force to move a system: Th e system of particles shown in the figure given below is initially at rest. Find the value of force F which should be applied so

Cases of equilibrium: What are cases of equilibrium? Sol.: As a result of the acting forces, the body may be having one of the following states: (1) The body can mo

In conveyor belts calculations, if it is required of me to calculate "The Power transmitted by the drive,at the specific efficiency" Which power are they reffering to?

Characteristics of the secondary circuit The dimensions of the secondary circuit in secondary loop determine to a large extent, the performance of these machines. The secondary

a) Describe Quality. What are various quality measures. b) A steel chairs manufacturer is also the quality inspector in his manufacturing unit this parameter of a chair being de

Applications. The  welding  process  finds  widespread  applications  in almost all branches of industry and construction. fabrication and creation of steel structures

Plate clutch warpage: Place plate clutch on surface plate and check for warpage. Ensure that0.20 mm feeler gauge does not slide freely.

(a) Write short note on following : (i) Ericsson cycle (ii) Diesel cycle (iii) Stirling cycle (b) The swept volume of a diesel cycle engine working on dual cycle is 0.0

In this assignment you will apply what you have learned in previous training. Consider the part in figure, which constructed from a solid tube. The bracket is supported at surface