Toma de fotografías de las microestructuras de los distintos materiales

T h e flo w time o f a jo b through a simple shop comprises processing time and

waiting time. T h e waiting time w ill depend on the priority given to this jo b in

com petition with other jobs through the fa cility, and on the provision o f capacity

to cope with the workload.

C onw ay et al (1 1 ) approached the multi-stage scheduling problem by means o f

tw o extreme cases:

( i ) pure jo b shop - in w hich a jo b leavin g a machine is equ ally likely to

go to any other machine in the shop, and

( i i ) pure flo w shop - in w hich there is o n ly one path through the shop that

all jo b s w ill follow.

T o distinguish these cases from alternative routing, it should be noted that the

w h ole route is d ecid ed before the first operation in both cases. Thus, there is no

"ch o ice" o f route at the end o f any operation.

A special case in multiple machine problems concerns the handling o f parallel

processors, or multiprocessors.

T h e type o f scheduling problem most closely related to alternative routing is

concerned with 'parallel processors' o r 'multiprocessors’. In these problems, more

than one processor is available to carry out the same operation, by relaxing the

rule stated in 2.3.11, i.e. that there is only one machine available o f each machine

type.

T h e interest in multiprocessors is not confined to manufacturing facilities.

An alogies may be drawn w ith packet movement in data communications

networks, vehicle control in transportation networks and task assignment in

multiprocessor computer systems. These examples all require dynamic solutions,

where a controller observes the network and the route chosen depends on the state

o f the network at the time when a routing decision is required. Dynamic routing

is discussed in sections 3.7 and 3.10.

In general three classes o f multiprocessor problems have been studied - identical,

uniform or unrelated machines. W hen the machines are identical, the processing

t i n » is the same on all machines. When the machines are uniform, the processing

times vary in a uniform manner, but i f the machines are unrelated, the processing

times vary arbitrarily between machines.

T h e first point to consider when scheduling multiprocessors is whether a jo b may

be divided am ong 2 or more machines. I f not, (batch splitting w ill not be allowed

in this w ork), then n jobs must be d ivided into m distinct subsets (w h ere n is the

number o f jobs and m is the number o f machines).

C offm an (1 8 ) describes a schedule fo r multiprocessors as com prising m blocks or

subsets, where the tasks in each block are ordered by a permutation to yield the

order o f task executions fo r a processor.

C onw ay et al (1 1 ) show that to m inim ise the flo w time, the jobs should be divided

among the machines so as to balance the workload as far as possible, using S P T as

the dispatching rule, and also balancing the distribution o f lon g and short jobs

between machines. A lthough the simplest equations demand identical machines,

the principle o f balancing the workload among non-identical machines still holds

and processing times on different machines may be v iew ed as a m atrix o f n jobs

by m machines (fig .8 ) where p y gives the time to perform a single operation i on

machine j.

A regular measure o f performance m ay still be m inimised using the S P T rule. I f a

jo b can be divided between 2 o r m ore machines, better schedules are possible

(because o f the reduced processing tim e, reduced idle times, reduced waiting

tim es) but determination o f the schedules is more difficult. C on w ay et al prove

clear advantages fo r simultaneous processing ranging from a minimum o f 25%

reduction in average flo w time, fo r 2 machines, to a maxim um o f 50% , for many

machines, in the idealised, identical machine, identical jo b condition. Ignoring

the penalties o f multiple set-up and tooling, C onw ay e t al con sider that any

schedule can be im proved by taking advantage o f parallel operations on identical

machines.

In the next sections, some o f the analytical techniques w hich have been used to

tackle scheduling problems w ill be described.

It is worth restating that most practical production environments have the

fo llo w in g features:

( i ) T h e y are dynamic - jobs are continually arriving and m oving through

the network.

( i i ) T h e y are stochastic - although expected operation times are known

beforehand, operator or material or machine o r tool problems can

cause significant variations.

(ii i ) G o o d due date achievement and flo w time performance is required.

Generally a range o f performance measures w ou ld be used in a

production facility including W I P level, due date achievement, lead

tim e, unit cost, quality, machine utilisation.

In addition, investigation o f alternative routing demands that rules stated in 2.3.10

and 2.3.11 be relaxed, such that

( i v ) Job routing is not necessarily fix ed at the start

( v ) M ore than one machine o f the same type may be present