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Transactions on Information and Communications Technologies vol 8, © 1995 WIT Press, www.witpress.com, ISSN 1743-3517
A case-based expert system for scheduling
problems with sequence dependent set up times
B.L. MacCarthy, P. Jou
Department of Manufacturing Engineering and Operations
Management, University of Nottingham, Nottingham NG7 2RD,
Abstract
Scheduling is an important application area for expert systems. However, the
development of expert systems in scheduling poses many problems and many
different approaches have been attempted in prototype systems. This paper
discusses the use of case-based reasoning (CBR) in the development of expert
scheduling systems. The design and development of an expert system using CBR
is described. The application area is an important class of scheduling problems those involving sequence dependent set up times. This type of problem is
important in many production environments and arises frequently in the process
industries. The paper addresses general problems and research issues related to
the application of CBR to scheduling problems.
1 Introduction
Scheduling is defined by Baker [1] as the allocation of resources over time
to perform a collection of tasks. In classical deterministic scheduling theory a
set of jobs must be completed on a set of machines in a manner which optimizes
some performance measure. All the parameters are assumed to be known in
advance. In the classical theory this often reduces to a sequencing problem.
Since the paper of Johnson [2] on the two-machine flowshop problem, the
sequencing literature has grown enormously. Many such deterministic models
have been studied over the past forty years in operational research (OR).
However, the relevance of this research to production management practice
has been questionable. Harrison [3] pointed out that long lead times, excessive
inventories, poor due date performance and low customer service levels are
problems still faced by many manufacturing managers and production
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controllers. Most researchers would admit that scheduling research has not
given the kind of payback that the volume of research deserved (MacCarthy and
Liu [4]).
In general, from a combinatorial perspective, scheduling problems are NPhard and real scheduling environments tend to have further layers of complexity.
Parunak [5] describes scheduling complexity, showing that existing techniques
address only isolated parts of the problem. Charalambous and Hindi [6] state
that classical scheduling fails to meet practical requirements in three ways :
models are oversimplified, approaches cannot deal with multiple objectives and
heuristics cannot be integrated into the mathematical models.
Scheduling environments are inherently dynamic, uncertain and complex
and consequently are difficult to cope with. Different environments require
different techniques. The two main research themes in the literature are OR and
artificial intelligent (AI) approaches. OR employs a modelling approach where
the emphasis is on algorithmic and heuristic solution methods. However there
is a considerable gap between the OR research literature and real scheduling
problems (MacCarthy and Liu [4]).
Many AI scheduling prototype systems have been reported - ISA.
DEVISER, ISIS, ISIS-2, OPIS, OPAL, FIXER and PLANNET (White [7]).
However, many problem areas arise in using AI approaches in scheduling
(White [7] and Grant [8]). A key insight of AI scheduling work is the
importance of constraints and constraint modelling (Grant [8] and Fox et al [9]).
Charalambous and Hindi [6] reviewed 20 systems, noted that the majority were
still prototypes and concluded that hybrid solution may be the way forward.
The combination of OR and AI approaches may enhance scheduling system
capability significantly.
Case-based reasoning (CBR) is an important development in AI in the last
decade with a number of important successful applications (Kolodner [10]). This
paper discusses the application of CBR to scheduling problems. The approach
is discussed in relation to an important class of practical scheduling problems.
The approach allows the utilization of both OR and AI techniques. A generic
control strategy is described for a CBR based expert system for the problem
domain. Important research issues in system design and implementation are
highlighted.
2 Case-based Expert Systems in Scheduling
Sadeh [11] describes as a major challenge, the development of a scheduling
tool that can: meet more precisely actual constraints and objectives; be used for
on-line real-time scheduling; allow users to manipulate the schedule interactively
to reflect user-dependent preferences and constraints. The user must be helped
if critical situations arise e.g. : where the user may have little or no experience.
The most appropriate technology available, as Paul [12] indicated, to address
such intellectually demanding tasks is expert system technology. The first
requirement in using an expert system approach is that the relevant knowledge
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must exist. If there is insufficient heuristic or episodic knowledge an expert
system approach cannot be applied. In scheduling problems, theoretical
knowledge and some heuristics exists. Unfortunately, practical knowledge and
experience may be of limited value. A number of review papers have been
published in this area (Steffen [13], Kusiak and Chen [14], Charalambous and
Hindi [6], Noronha and Sarma [15]). It is clear that most researchers use rules
in knowledge representation and constraint directed search in control strategies.
Ye and Hughes [16] note that job shop scheduling can be viewed as a constraint
satisfaction problem.
Case-based reasoning (CBR) was conceived in the late 1970's and the first
systems started to be built in the early 1980's by Schank's students (Kolodner
[10]). Riesbeck and Schank [17] provide an introduction to CBR. Watson and
Marir [18] give a detailed review of CBR and CBR tools.
At its simplest a case-based reasoning system focuses on previous situations
similar to the current one and uses them to help in solving a new problem.
Many management decision areas rely on previous experience and CBR has
many potential applications in managerial decision making. Although CBR does
have limitations it has many potential advantages. Experience may be re-used
for instance. CBR is also useful where information may be uncertain. Measures
of similarity may be used to retrieve cases and potential solution strategies. CBR
will usually require adaptation techniques to develop solution strategies for the
current temporal case. However it allows solutions to be proposed quickly for
problem domains which are not completely understood and it gives a means of
obtaining solutions when no algorithmic methods are available. On the negative
side cases may be used blindly without adequate validation and bias may be
introduced (Kolodner [10]).
The work described in this paper uses a CBR approach for the development
of an expert scheduling system for a particular application. In the proposed
system CBR is treated like a meta-rule in developing solution strategies. First,
simulation is used to generate cases including satisfied and unsatisfied schedules;
second, cases are retrieved to a temporal case base where matching is by
constraints; third, methods are selected from temporal case base by global
objectives and a relative ranking system. The problem domain is the class of
scheduling problems known as sequence dependent set up problems.
3 The Sequence Dependent Set Up Problem
Production scheduling in many industries must consider sequence dependent
set up constraints - environments in which the set up time is dependent on what
a machine is currently producing and what is scheduled to follow. This type of
scheduling problem is encountered frequently (Gupta [19], Srikar and Ghosh
[20], Selen and Heuts [21]) and in some industries these are the dominant
scheduling constraints, particularly in process industries e.g. paint manufacture,
printing, paper and container manufacture, and textile dyeing and weaving.
Though there has been extensive research on scheduling, much of this either
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totally ignores set up times, or considers them as being independent of the job
sequence.
Set up times occupy a substantial percentage of the available production
time on the manufacturing equipment in many industries. Daoud and Purcheck
[22] used statistical analysis of machine utilization to show that about 45% of
machine time is spent in tool changes between jobs. Reducing job set up times
can therefore make a substantial difference in machine utilization.
As an example, Zhou and Egbelu [23] present the following three machine,
four job problem. Figure 1 shows the machine and the processing time units,
respectively, required for each operation of each job.
Operation 1
Operation2
Operation 3 Operation4
Jobl
1 / 5
3 /9
2 /9
3 /9
Job2
1 / 9
2/ 15
1 / 13
1 / 7
Job3
3 /6
3 /6
—
Job4
2 /9
2 / 10
Figure 1 The machine and the processing time units
Operation5
2 / 12
-
-
-
-
-
In addition the set up times in changing between job operations for
machines 1, 2 and 3 were specified (not given here). Zhou and Egbelu [23]
proposed a solution approach integrating a scheduling algorithm with the
experience of an expert human scheduler. The approach performed reasonably
well. For the problem above which has an optimal schedule of 80 time units
(obtained from integer programming) the approach gave a solution of 82 time
units in attempting to minimize the maximum flow time (Fmax).
However this approach is applicable for one goal only. Other algorithms
would be necessary for other goals and there is no guarantee that this algorithm
will always do as well in other problems, even for maximum flow time.
Different goals might be necessary at different times and for different
circumstances. The specified constraints here are all hard constraints. In practice
some constraints may be soft and may be violated in some circumstances. The
data may be subject to inaccuracies. Some constraints may arise which are
temporary e.g. it may be desirable in this instance to complete job 1 before job2.
Only an expert system approach can handle this required level of functionality.
The approach adopted here is to use GBR techniques in developing such an
expert system.
4 Proposed System Structure
The structure of the proposed system combines 12 modules and 3 bases. An
overview of the top level architecture is illustrated in Figure 2. Some of the
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Figure 2 : System Architecture
main elements of expert system architecture are discussed here. The case base
consists of problem solving cases and data relevant to the problem domain. The
method base contains optimization and heuristic procedures relevant to sequence
dependent set up problems. The constraints module contains the relevant
constraints specified. The relaxation module is activated when all constraints
cannot be met. The case selector contains the principles that determine, for
different constraints, criteria and data, the selection of previous cases. The
temporal case module stores the cases that are selected by the case selector
module. The adaptor module adjusts variables after scheduling and rebuilds the
case base. This high level architecture facilitates interactive and reformulative
scheduling strategies by using combined heuristics and algorithms to generate
schedules, case-based reasoning to obtain more powerful and precise solution
strategies and interactive user manipulation of the variables that are time
dependent.
5 Research Issues in Developing, Testing and Implementing the
System
The expert system shell KAPPA-PC has been chosen as the implementation
tool for the system development because it allows object-oriented programming,
has a graphics user interface and is easy to interact with other software by
dynamic data exchange (DDE). The use of an object-oriented approach
considers modularity and reusability so that the system can be expanded in a
step by step manner. The system can communicate by DDE with graphical
software for plotting during run time.
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It is important that schedules reflect accurately the current environment
including the external constraints as well as the internal operational constraints.
The quality of scheduling is affected by the view of the user about the
combination of constraints that currently applies. During scheduling, there are
different sets of key constraints having direct impact on the quality of
scheduling. Constraints are not all of the same type or importance in scheduling.
Typical constraints include :
• time dependent constraints : specifying the variables which change with
time and their distribution functions.
• machine dependent constraints : limiting the types, the availability and
the capacity of machines that can operate on a job.
• precedence dependent constraints : existing between jobs or operations.
• sequence dependent constraints : existing between jobs, operations in a
job and machines.
• user dependent constraints : specifying personal preferences,
organizational objectives etc.
• environment dependent constraints : restricting physical location, layout,
handling and transportation etc.
It may be possible to satisfy some subset of constraints in scheduling but
some may conflict with each other. Relaxation of constraints may be necessary
in some instances and desirable in others. For instance, a due date - user
dependent constraint - may need to be relaxed (a so-called soft constraint) for
some jobs because of lack of availability in a machine dependent constraint.
Constraint relaxation is a suitable means of handling such a conflict. Some
constraints cannot be relaxed (a so-called hard constraint) e.g. precedence
constraints for job operations.
Constraints may change with time in such a manner that we are left with a
situation where constraints are not either strictly true or false. With this
uncertainty, it would be unwise to attempt to program constraints into rules in
the expert system. However, using constraint directed retrieval in case-based
reasoning may provide a workable approach. In previous scheduling expert
systems, the control module which generates the schedule acts like a black box.
Using constraint directed retrieval can allow users to define their constraints.
This allows system "tuning" via user's knowledge.
Although some researchers claim that knowledge acquisition is not a
problem in CBR (Watson and Marir [18]) the issue does arise in the
development of the system proposed here. An example is case indexing where
indices are assigned to cases in order to direct the case retrieval process. Rules
for indexing contain knowledge that determines which constraints will have an
impact on scheduling. In the proposed system the case selector is one of the
most important modules.
The system allows the user to set up his/her own priority of constraints in
the constraint directed retrieval of cases from the case base. This user view
allows relaxation of soft constraints and control over the degree of relaxation.
When creating a detailed user view, a temporal checking list is included to deal
Transactions on Information and Communications Technologies vol 8, © 1995 WIT Press, www.witpress.com, ISSN 1743-3517
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with the conflict or interaction of constraints. When the user specifies the
current constraints, the constraint module searches the case base for previous
cases in which constraints are in conflict. The searching result is kept in the
temporal checking list. Nearest-neighbour matching is applied by checking the
similarity of both constraints and performance measure values.
Simulation is used to generate cases for the case base when no cases exist
but just algorithms and heuristics in the method base. The starting point is to
generate data and obtain performance measures and case fitness values by
simulation and then incrementally build the case base. The structure of the case
base includes each constraint and performance measure types and their values.
The development environment first includes the single machine with
sequence dependent set up times problems. More complex flow-shop and jobshop environments follow from this initial work. Relevant algorithms and
heuristics are being programmed into the method base. Gradually, the system
hopes to cover job-shop environments and the heuristics will include
opportunistic scheduling approaches (Ow and Smith [24] and Sadeh [11]).
6 Conclusion and Future Work
Current work is concerned with the development and evaluation of different
algorithms and heuristics for the method base and the development of structures
for case representation and indexing in the proposed system. The methods for
the method base are being explored in order to exploit the full potential of the
algorithms and heuristics. The work has highlighted the need for fresh
comparative studies of different methods and different approaches for case
indexing. Control strategies to allow user interaction and reformulation are
being considered, particularly in order to utilize the user's knowledge of current
environmental conditions and factors. The research work so far has shown that
there are many opportunities for future work on improving the linkage of casebased reasoning to expert scheduling systems.
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