Adaptive Control in Production Scheduling

Copyright©IFAC Control Budapest, Hungary, 1980

Probl~nu

and Devices

ADAPTIVE CONTROL IN PRODUCTION SCHEDULING M. Girnt* and E. Szelke** *Development Institute of Machine Tool Works, Hungary "Computer and Automation Institute Hungarian Academy of Sciences, Budapest, Hungary

Abstract

The paper reports on a new method for solving perturbation prob-

lems in the course of production scheduling of cutting operations in the field of machine tool manufacture. It can perform this task by supplementing a previously prepared heuristic scheduling method with an algorithm which optimizes cutting parameters. The advantage of this new method is that one can adapt machining times to actual production situations and therefore meet due dates without a need for overtime operation. Keywords: production scheduling, adaptive control, cutting data optimization.

INTRODUCTION In the recent decades, two stages of develop-

After a short view of the applied heuristic

ment for boosting productivity were signifi-

scheduling method and the optimizing algorithm,

cant regarding cutting operations of machine

the new adaptive method will be exposed.

tool manufacture. In the sixties, efforts were concentrated on

HEURISTIC SCHEDULING METHODS

decreasing the setup times which constitute most of the machining time. As a result, be-

The general production control is accomplished

side of conventional manufacturing technology

by means of a complex hierarchy. The top

the NC technology appeared.

level of this hierarchy, the top management decides overall policy by estimating demands

The introduction of adaptive control for

and setting the tasks for a long time horizon,

machine tools during the seventies made it

say a year. At the middle level the tasks

possible to reduce the main part of the

will be decomposed into various plants with

processing time by changing cutting parameters.

a period of time, such as a quarter or a month. They are responsible for planning of

For solving disturbances in the course of

machines and manpower and due dates have been

production scheduling, the further demonstra-

established for the jobs or shop orders.

ted adaptive scheduling method utilizes the possibility of altering the main part of

The lower level of production control gets

processing time of cutting operations.

partly the shop orders with their due dates, partly the technological routing of the jobs with the available production facilities

First we present its application to manufacturing processes with non-adaptively control-

such as data from the middle level control.

led machine tools. Then we refer to its extens ion.

At the lower level the middle-level control

179

M. Girnt and E. Szelke

180

problems will be decomposed for short-term.

due dates. This is the reason of using

weekly and daily problems and the control

the so-called SLACK priority rule in its

goes down in this way to the shop-floor

decision strategy.

where the actual production takes place. To the use of SLACK rule a general assumpThe main task of this shop floor control is

tion should be taken for

the day-to-day scheduling. Certain jobs or

a job is completed through

shop orders are released to the shop and

operations for which the following data

any job. Namely. n

different

certain items are assigned to particular

should have been selected from the standard

machines for accomplishment

data-base (the order list. the list of

at a specified

time according to certain production objec-

facilities and the technological routing

tives. One of these objectives is to meet due

of jobs):

dates of the jobs subject to fixed resources and technological precedence relations concerning the operations. Further. we deal with scheduling jobs to meet their due dates at the shop-floor level.

D

the due date of the job

t

the make span of the last operation

n

of the job 1 . . - the time measure of lap-phasing 1.J

i th

between the

and the

jth

operations.

In respect of operation research the production scheduling of machine tool workshops is generally a job-shop class scheduling problem. For solving problems of this class. both exact analytical and heuristic methods are known from the special literature. The exact models of job-shop scheduling problems are very simplified approaches of the real job-shop situations. Their handling needs a lot of computational effort. For this reason, heuristic methods are very important to obtain solutions for scheduling problems in practice. By means of certain intuitive logical rules they simplify finding near optimum sequences of jobs on machines. They consider a shop to be basically a network of queues. The rules of interest. the so-called priority rules. resolve the conflicts among the jobs waiting for a

Our former heuristic scheduling method performs the scheduling task in two phases. In the initial phase the

:atest possible

starting times

(T ) will be determined i for each operation of every job. This is

carried out by putting the operations in reverse order from the due date of the job on imagined time axes as it is shown in Figure I. This is a preparation to the use of SLACK-rule. In the decision making phase the machine which is going to be available earliest in the shop will be selected and loaded. All the jobs waiting just for this machine are taken into consideration. The job with the smallest slack time from the queue will be allocated to this machine.

machine. They assign each job a priority index which is a scalar value. The basic

· Th e s 1ac k t1me.

Si'

f or any

tenet is that the job with the minimum

can be computed by the equation:

. 1.th operat10n

priority index of those waiting for a particular machine should be processed first. After the preceding survey we can outline the

S.

T. - t 1

1

(i=I.2 •...• n)

1

main characteristics of our former heuristic

is the release time of the .th machine appropriate to the 1 operation

scheduling method Cl). It is suitable to

and

solve job-shop scheduling problems of shop-floor level. Its main objective is to keep

where

X.

tx. 1

is the above-mentioned latest .th possible starting time of the 1 operation. T.

1

Adaptive Control in Production Scheduling

ALGORITHM FOR OPTIMIZING CUTTING

tool

(minute)

T - tool life

PARAMETERS

181

(minute)

Kt - tool cost/tool life

(Ft).

Cutting processes are considered optimum comin~

processes when they use cutting parameters

It is evident that the only solutions

by which the economic ends are approached the

into account during the optimizing procedure

best of all.

are those which satisfy the cons taints concerning the workpiece-apparatus-tool-machine

Economic ends of this sort may be: - to minimize the cost of the cutting process

tool ensemble. The feed rate constraints the revolution per time constraints, efficiency constrains, the constraints on cutting force

- to reach the maximum of machining

etc. altogether constitute a system of con-

productivity (that is, to approach the

straints. The optimizing algorithm is put

shortest processing time).

down in papers [2,3,4J, so here we do not enter into details.

There is a basic problem in the field of optimizing cutting data. Although the pro cessing time and the joining cost decrease

The investigation of the above objective functions makes it clear that two different

by increasing the depth of cut, the feed

values can be derived from them for the main

rate and the cutting speed, however, the

part of the processing time by the same systeo

tool wear boosts together with an increase

of constraints. One value,

of the idle time and cost. Assuming fixed depth of cut during the cutting process, the following objectives can be stated for the optimization problem (considering the simple case of machining by

t , which is k derived from the £irst objective function,

minimizes machining cost, the other value, tT'

can be derived from the second objective

function maximizes productivity. It is conceivable that

one tool): - the objective function for minimal and an inequality of the same sense is

machining cost I

K

B'L(ns

t

+

h

_c_) nsT

LK t + __ nsT

valid for full machining times, while the (Ft/piece)

setup

the objective function for the maximum productivity t

=

Itch L(ns + nsf)

(minute)

constant.

it is reasonable to specify first the use of cutting parameters which result in minimal machining cost. If during machining certain perturbations occur, we can change to parameters corresponding to the Maximal produc-

K

- cutting cost

B

- minute cost at the machine (Ft/minute)

L

- length of cut

n

- number of revolution5 per minute

s

- feed rate

(I/minute)

ch

times of machines etc., are nearly

During the design of a machining procedure,

where

t

side parts of machining times, that is the

(mm/revolution)

- the changing time of the worn-out

tivity, which can be utilized for minimizinc the influence of perturbations.

M. Girnt and E. Szelke

182

THE ADAPTIVE PRODUCITON

times of operations, the setup times

SCHEDULING HETHOD

and lap-phasing for each operation.

The production scheduling methods now in use

The double value of the processing times is

generally provide a time-schedule of manu-

the clue of our adaptive scheduling method:

facturing operations based on fixed and pre-determined processing times. These timevalues are obtained from a previous normative calculation performed in factories.

the highest value of processing time by minimum machining cost the lowest value of processing time by maximum productivity.

It is well-known from practice that the

They should be previously obtained by using

implementation of such time-schedules is not

the optimizinr algorithm.

free from perturbations like the overloading of certain machines or the delayed start of

In the initial phase of the

scheduling the

certain jobs. Some of the current scheduling

latest possible start of each job-operation

methods attempt to eliminate these perturba-

will be determined by the use of the highest

tions by making use of overtime work and over-

value of each processing time. This is a

level capacities.

preparation

to the use of the SLACK priority

rule, which was previously detailed. During The idea of using a new method to compensate the above-mentioned perturbations is derived from the possibilities offered by the preced-

the development phase of the scheduling algorithm the following procedure should be repeated from point 1 to point 6:

ing optimization algorithm of technological parameters. He take advanta['e of the possibility

of alterinp the Bachining

ti~e

by adapti-

vely controlling the main part of the processing time.

1. selection of the earliest available

machine in the shop; 2. consideration of every job waiting just for this machine; 3. allocation of the job from the queue

In the case of manufacturing processes with

with the smallest SLACK priority index;

non-adaptively controlled machine tools, at

the loading of the machine is carried

the start our method applies the highest

out on the basis of the highest values

value of the processing time permitted by the

of the processing times;

optimization algorithm. The perturbations

4. trouble-shooting, that is, a revealinc

will be discovered by a simulation technique

of the job lateness and the lack of

in the course of the scheduling process.

capacity (it will be further detailed);

vfuenever one of the above-mentioned perturba-

if any of these troubles occurs, go to

tions occurs, the value of the machining time

pointS,otherwise point 6

follows;

will be reduced to the required extent. The

5. new loading of the machine with the

lower limit of the reduction is defined by

smallest values of the o!,eration

the algorithm optimizing cutting parameters.

ing

proc~s-

times;

6. as long as job operations are to be Our due-date oriented adaptive scheduling method requires the following input-data from the middle-level production control:

scheduled or the scheduling period is not finished, return to point I, otherwise the procedure terminates.

- the orderinf list of jobs with due dates and lot sizes

Let us explain how the trouble-shooting is 10ac1.in~

~chine

- the list of available machines

carried out. A fictitious

- the technological routing for jobs on

just available at time t (see Fizure 2) x has been started with all of the jobs

machines with a double value of processing

of the

Adaptive Control in Production Scheduling

183

waiting for it at time

lower values of processing times and the

increasin~ or~er

the machining process should be performed

t ' According to the x of the job's priorities,

this :' ic tit io,-,s loadine of the machine is

with the cutting parameters belonging to

carried out by the highest values of the

maximum productivity to eliminate these

processing times. By arranging the processing

perturbations.

times of the job operations into increasing order of their priority indices the values

In the future there will be also adaptively controlled machine

will be

tool~

for cuttine

o~e~­

ations in the workshop. In the case of using such machine tools, pre-determined values of processing time for the operations and the corresponding latest possible starting times of the job operations:

are out of question. In this case the completion time for each operation and the way of machining depend on the type of the adaptive control (ACC, ACO) and the geometrical-

1

n

•

-technological characteristics of the workpiece. The completion time of an operation

It obviously holds for these predetermined

will develop step-by-step during the machin-

values that,

ing process. This is the expected value of the processing time.

1]

<

1

2 <

1

<

n-] =

1

n'

During the extension of our method to this case, these facts are taken into consideration.

Denote by

t ,t , •.. , t _ , t the starting l 2 n l n times of these job operations determined by

the

~~clitious loadin~

procedure.

The first task is to determine the upper and the lower bounds for the expected value of the processing time for each operation. This should be performed by a simulation

Refer to

Figure 2,

it is clear that

algorithm which assumes that the main characteristics of the control mechanism applied

t

and the depth-of-cut distribution function

x

of the workpiece are known. Then the second task follows, namely the scheduling of the manufacturing process. Our adaptive scheduling t. +

J

T. J

procedure starts the computation with using the upper bound of the expected value of the processing time. lfuen a perturbation of the

t

n

t

n-I + Tn-I •

above-mentioned kind occurs during the scheduling process, it automatically switches

It is evident that the machine is not in a

over to using the lower bound of the expected

lack of capacity and the jobs are not late

processing time. Thus our method makes it

if for all indices

i=I,2, ... ,n,

possible to eliminate the

ef~ect

of pertur -

bations. T.

~

> t.

~

Our method is useful in situations where in Otherwise in a real scheduling process this

the manufacturing process it is not possible,

machine should have a lack of capacity and

for the sake of solving occurring problems

some jobs would be late. Therefore our

of production, to modify the technological

algorithm should turn to the use of the

sequence of operations.

184

M. Girnt and E. Szelke

It is applicable in the field of scheduling processes of traditional workshops, but it is particularly suitable in flexible manufacturing systems. In this case the main benefit from introducing a computer into the workshop is the increased control it gives to management over technology and scheduling. This new method and the applied optimization algorithm were developed at the Computer and Automation Institute of the Hungarian Academy of Sciences. The heuristic scheduling procedure prepared and applied previously is a result of the collaboration between the Computer and Automation Institute and the Development Institute of 11achine Tool Works.

REFERENCES [lJ

Girnt, M., Szelke, E., (1974)

Some

Experiences in the Field of Schedulding Medium Lot-size Production. COMPCONTROL'74

Conf., Szeged,

Proceedings (14S-ISS). (in Hungarian) [2J

Girnt, M., Somlo, J., Gylirki, J., etc. (1973)

ACO Systems for Machine

Tools. Computer and Automation Res. Inst. Hung. Ac.Sc. Report NOS. (in Hungarian) [3J

Horvath, M., Somlo, J.,

(1979)

Opti-

mization and Adaptive Control of Machining Processes. Mliszaki Konyvkiado, Budapest. [4J

Somlo, J., Nagy, J.,

(in Hungarian) (1976)

On a New

Approach to Cutting Data Optimization Problem. PROLAMAT'76, Stirling. Proceedings (293-30S).

Adaptive Control 1n Production Scheduling

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