EVOLUTIONARY APPROACH FOR DYNAMIC SCHEDULING

IN MANUFACTURING

Ana Madureira, Carlos Ramos

Instituto Superior de Engenharia do Porto, GECAD & Computer Science Department, Porto, Portugal

Sílvio do Carmo Silva

Universidade do Minho, Dept. de Produção e Sistemas, Braga, Portugal

Keywords: Dynamic scheduling, Extended

Job-Shop Scheduling, Manufacturing, Genetic Algorithms

Abstract: This paper presents a simple and general framework explor

ing the potential of evolutionary algorithms,

which is of practical utility, embedded in a simple framework to solve difficult problems in dynamic

environments. The proposed evolutionary approach is in line with reality and away from the approaches that

deal with static and classic or basic Job-Shop scheduling problems. In fact, in real world, where problems

are essentially of dynamic and stochastic nature, the traditional methods or algorithms are of very little use.

This is the case with most algorithms for solving the so-called static scheduling problem for different setting

of both single and multi-machine systems arrangements. This reality, motivated us to concentrate on tools,

which could deal with such dynamic, disturbed scheduling problems, both for single and multi-machine

manufacturing settings, even though, due to the complexity of these problems, optimal solutions may not be

possible to find. We decided to address the problem drawing upon the potential of Genetic Algorithms to

deal with such complex situations.

1 INTRODUCTION

Evolutionary algorithms have often been shown to

be effective for difficult combinatorial optimisation

problems appearing in various industrial,

economical, and scientific domains. Prominent

examples of such problems are scheduling,

timetabling, network design, transportation and

distribution problems, vehicle routing, travelling

salesperson, other graph problems, satisfiability,

packing problems, planning problems, and general

mixed integer programming.

Considering that natural evolution is a process of

ntinuous adaptation, it seemed us appropriate to

consider Genetic Algorithms for tackling real Non-

Deterministic Scheduling Problems. Thus, the GA

based scheduling system developed adapts the

resolution of the static and deterministic problem to

the dynamic one in which changes may occur

continually. A population regenerating mechanism is

put forward, for adapting the population of solutions,

according to disturbances, to a new population,

which increases or decreases according to new job

arrivals or cancellations.

It is widely accepted that manufacturing scheduling

roblems are generally difficult or hard to solve to

optimality (Baker, 1974), (French, 1982) and

(Blazewick, 2001). Most of the approximation

methods proposed for the Job-Shop Scheduling

Problems are oriented methods, i.e. developed

specifically for the problem in consideration. Some

examples of this class of methods are the priority

rules (Baker, 1974), (French, 1982) (Blazewick,

2001) and the Shifting Bottleneck proposed in

(Adams, 1988).

The problem of finding good solutions to scheduling

oblems is very important to real manufacturing

systems because the production rate and production

costs are very dependent on the schedules used for

controlling the flow of work through the system.

Most research in scheduling focuses on optimisation

of static and dynamic deterministic problems where

all problem data are known before scheduling starts.

However many real world optimisation problems are

non-deterministic, in which changes may occur

continually.

288

Madureira A., Ramos C. and do Carmo Silva S. (2004).

EVOLUTIONARY APPROACH FOR DYNAMIC SCHEDULING IN MANUFACTURING.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 288-291

DOI: 10.5220/0001145002880291

 SciTePress

Due to their dynamic nature, real scheduling

problems have an additional complexity in relation

to static ones. In many situations these problems,

even for apparently simple situations, are hard to

solve, i.e. the time required to compute an optimal

solution increases exponentially with the size of the

problem (Morton and Pentico, 1993).

Recently the scheduling problem in dynamic

environments have been investigated by a number of

authors especially in the evolutionary community,

see for example, (Jain, 1999), (Dimopoulos et al.,

2000) and (Madureira, 2002).

The proposed approach deals with these two cases of

dynamic scheduling: deterministic and stochastic.

For such class of problems, the goal is no longer to

find a single optimum, but rather to continuously

adapt the solution to the changing environment. The

purpose of this paper is to describe an approach

based on GA for solving dynamic scheduling

problems.

The paper is structured as follows: section 2

provides a description of the scheduling problem to

be solved. In section 3, we describe a method based

on GA for the resolution of the Extended Job-Shop

Scheduling Problems (EJSSP) and describe an

approach to solve the Non-deterministic version of

the Extended Job-Shop Scheduling Problems.

Finally, some conclusions are drawn and some ideas

for future work are presented.

2 PROBLEM DEFINITION

Most real-world multi-operation scheduling

problems can be described as dynamic and restricted

or relaxed versions of the classic Job-Shop

scheduling combinatorial optimisation problem

(Morton and Pentico, 1993). In a Job-Shop problem

each job has a specified processing order through the

machines, i.e. a job is composed of an ordered set of

operations each of which is to be processed, during a

given time, i.e. the operation processing time, in a

machine of the system. In the classic Job-Shop

Scheduling Problems (JSSP) several constraints on

jobs and machines are considered: machines are

always available and never break down; there are no

precedence constraints among operations of the

different jobs; the operations processing can not be

interrupted and each machine can process only one

job at a time; each job can be processed only on a

machine at a time; setup times are independent of

the schedules and are included in processing times;

technological constraints are deterministic and

known in advance.

In practice, many scheduling problems include

further constraints. This means that problems can

become more complex and more general, i.e. non-

basic (Portmann, 1997). Thus, for example,

precedence constraints among operations of the

different jobs are common because, most of the

times, mainly in discrete manufacturing, products

are made of several components that can be seen as

different jobs whose manufacturing must be

coordinated. This non-basic JSSP, focused in our

work, which we called Extended Job-Shop

Scheduling Problem (EJSSP), has major extensions

and differences in relation to the classic or basic

JSSP (Madureira et al., 2002).

3 THE PROPOSED APPROACH

The scheduling approach presented in this section is

applicable to both static and dynamic manufacturing

environments for any optimizing criteria that are

possible to establish. It is based on the

decomposition of the problems into Single Machine

Scheduling Problems(SMSP), one for each machine

involved in processing, ant later integration for

obtaining a solution to the original problem, i.e. to

the Extended JSSP.

This work is concerned with the solution of problem

instances of the EJSSP. It starts focusing on the

solution of the dynamic deterministic JSSP

problems. For solving these we developed a

framework, leading to a dynamic scheduling system

having as a fundamental scheduling tool a GA-based

scheduling method with two main pieces of

intelligence. One such piece is a GA-based method

for deterministic scheduling. This includes a Genetic

Algorithm for single machine problems and an inter-

machine activity coordination mechanism that

attempts to ensure a good feasible solution for the

deterministic EJSSP. The other piece is a

rescheduling mechanism that includes a method for

population regeneration under dynamic

environments, increasing or decreasing it according

new job arrivals or cancellations.

This approach to solve the dynamic EJSSP consists

on generating a predictive schedule in advance using

the information available. When disruptions occur in

the system during the execution, the predictive

schedule is modified or revised in order to consider

the recent modifications.

3.1 Dynamic Deterministic EJSSP

Initially, we start by decomposing the deterministic

EJSSP problem into a series of deterministic Single

Machine Scheduling Problems. We assume the

existence of different and known job release times r

prior to which no processing of the job can be done

EVOLUTIONARY APPROACH FOR DYNAMIC SCHEDULING IN MANUFACTURING

289

and, also, job due dates d

. Based on these, release

dates and due dates are determined for each SMSP

and, subsequently, each such problem is solved

independently by the Genetic Algorithm.

Afterwards, the solutions obtained for each SMSP

are integrated to obtain a solution to the main

problem instance, i.e. the instance of the EJSSP. The

integration of the SMSP solutions may give an

unfeasible schedule to the EJSSP. This is why

schedule repairing may be necessary to obtain a

feasible solution. The repairing mechanism named

Inter-Machine Activity Coordination Mechanism

(IMACM) carries this out (Madureira et al., 2002).

The repairing is carried out through coordination of

machines activity, having into account job operation

precedence and other problem constraints. This is

done keeping job allocation order, in each machine,

unchanged. The IMACM mechanism establishes the

starting and the completion times for each operation.

It ensures that the starting time for each operation is

the highest of the two following values: the

completion time of the immediately precedent

operation in the job, if there is only one, or the

highest of all if there are more, and the completion

time of the immediately precedent operation on the

machine.

3.2 Dynamic Non-Deterministic

EJSSP

For non-deterministic problems some or all

parameters are uncertain, i.e. are not fixed as we

assumed in the deterministic problem. Non-

determinism of variables has to be taken into

account in real world problems. For generating

acceptable solutions in such circumstances our

approach starts by generating a predictive schedule,

using the available information and then, if

perturbations occur in the system during execution,

the schedule may have to be modified or revised

accordingly, i.e. rescheduling is performed.

Therefore, in this process, an important decision

must be taken, namely that of deciding if and when

rescheduling should happen. The decision strategies

for rescheduling may be grouped into three

categories: continuous, periodic and hybrid

rescheduling. In the continuous one rescheduling is

done whenever an event modifying the state of the

system occurs. In periodic rescheduling, the current

schedule is modified at regular time intervals, taking

into account the schedule perturbations that have

occurred. Finally, for the hybrid rescheduling the

current schedule is modified at regular time intervals

if some perturbation occurs.

In the scheduling system for Extended JSSP,

implementing our approach, rescheduling is

necessary due to two classes of events (Madureira et

al., 2001a):

a) Partial events imply changes in jobs or

operations attributes such as processing times, due

dates and release times.

b) Total events, imply changes in neighbourhood

structure, resulting from either new job arrivals or

job cancellations.

While, on one hand, partial events only require

redefining job attributes and re-evaluation of the

objective function of solutions, total events, on the

other hand, require a change on solution structure

and size, carried out by inserting or deleting

operations, and also re-evaluation of the objective

function. Therefore, under a total event, the

modification of the current solution is imperative. In

this work, this is carried out by mechanisms

described in (Madureira et al., 2001b) for SMSP.

Considering the processing times involved and the

high frequency of perturbations, rescheduling all

jobs from the beginning should be avoided.

However, if work has not yet started and time is

available, then an obvious and simple approach to

rescheduling would be to restart the scheduling from

scratch with a new modified solution on which takes

into account the perturbation, for example a new job

arrival. When there is not enough time to reschedule

from scratch or job processing has already started, a

strategy must be used which adapts the current

schedule having in consideration the kind of

perturbation occurred.

The GA-based scheduling system, here proposed,

for non-deterministic EJSSP is structured, in three

modules, namely the modules for pre-processing,

scheduling and dynamic schedule adaptation:

1. Pre-Processing Module - The pre-processing

module deals with processing input information,

namely problem definition and instantiation of

algorithm components and parameters, such as, the

initial individual and population generation

mechanisms, size of population, genetic operators

and respective probabilities.

2. Scheduling Module - The scheduling module is

concerned with the application of the GA-based

scheduling method for deterministic EJSSP

presented above, considering that all release dates,

processing times and due dates are known in

advance. Whenever a new event occurs which

disturbs the schedule, in such a way that

rescheduling is to be done, the dynamic adaptation

module generates a new deterministic problem.

Then, the scheduling module solves this new

problem.

3. Dynamic Adaptation Module - The occurrence

of a partial event requires redefining job attributes

and a re-evaluation of the schedule objective

function. A change in job due date requires the re-

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calculation of the operation starting and completion

due times of all respective operations. However,

changes in the operation processing times only

requires re-calculation of the operation starting and

completion due times of the succeeding operations.

A new job arrival requires definition of the

correspondent operation starting and completion

times and a regenerating mechanism to integrate all

operations on the respective single machine

problems. In the presence of a job cancellation, the

application of a regenerating mechanism eliminates

the job operations from the SMSP where they

appear. After the insertion or deletion of positions,

neighbourhood regeneration is done by updating the

size of the neighbourhood and ensuring a structure

identical to the existing one. Then the scheduling

module can apply the search process for better

solutions with the new modified solution.

4 CONCLUDING REMARKS

In most practical environments, scheduling is an

ongoing reactive process where the presence of real

time information continually forces reconsideration

and revision of pre-established schedules.

The handling of uncertainty is an important issue in

real-world scheduling problems. Uncertainty can

arise through incomplete knowledge of the problem,

through incomplete knowledge of how the problem

will change over time or may be inherent to the

problem itself.

This work is concerned with the resolution of

realistic Job-Shop Scheduling Problems (EJSSP).

Thus, not only it focuses on the solution of the

dynamic EJSSP problem but also on both the

deterministic and non-deterministic versions of it.

Moreover, it is concerned with integrated scheduling

of jobs which are products composed by several

parts or components which may be submitted to a

number of manufacturing and multi level assembly

operations, having as the main criterion meeting due

dates. We call these problems Extended EJSSP.

Considering that natural evolution is a process of

continuous adaptation, it seemed us appropriate to

consider Genetic Algorithms for tackling real Non-

Deterministic Scheduling Problems. Thus, the GA

based scheduling system developed adapts the

resolution of the static and deterministic problem to

the dynamic one in which changes may occur

continually. A population regenerating mechanism is

put forward, for adapting the population of solutions,

according to disturbances, to a new population,

which increases or decreases according to new job

arrivals or cancellations.

We recognize the need for further testing,

particularly for better evaluation of the suitability the

proposed framework and mechanisms under

dynamic Extended Job-Shop environments. We also

recognize that this is not an easy task because it is

difficult to find in the literature test problems with

the job structure that we selected and think

important, in industrial practice, namely jobs made

from several parts to be manufactured and

assembled through several assembly operations and

stages.

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