AN EFFECTIVE APPROACH FOR REAL-WORLD
PRODUCTION PLANNING
Jesuk Ko
Department of Industrial and Information Engineering, Gwangju University
592-1 Jinwol-dong, Nam-gu, Gwangju 503-703, Korea
Keywords: Realistic scheduling, Combinatorial optimisation, Constraint logic programming
Abstract: This paper shows an application of constraint logic-b
ased approach to the realistic scheduling problem.
Operations scheduling, often influenced by diverse and conflicting constraints, is strongly NP-hard problem
of combinatorial optimisation. The problem is complicated further by real scheduling environments, where a
variety of constraints in response are critical aspects for the application of a solution. Constraint logic
programming technique well armed with the major function of constraint handling and solving mechanisms
can be effectively applied to solve real-world scheduling problems. In this study, the scheduling problem
addressed, based on a dye house involving jobs associated with the colouring of different fibres, is
characterized by various constraints like colour precedence, dye machine allocation and time constraints.
The solution procedure used takes into account a number of dye house performance measures which include
on-time delivery and resource utilisation. The results indicate that constraint-based scheduling is
computationally efficient in schedule generation in that a solution can be found within a few seconds.
Furthermore, solutions produced always minimise the mean tardiness and maximise the utilisation of dyeing
facilities.
1 INTRODUCTION
Competitive manufacturing requires the efficient use
of facilities to meet the cost and time requirements
of customers. This is addressed by the scheduling of
work orders within the manufacturing system. The
generic operations scheduling problem may be
defined as assigning various jobs or work orders to
resources over time windows in order to complete a
set of jobs or orders for a given period. Many real-
world manufacturing situations are particularly
subject to difficult scheduling problems because
they must satisfy many constraints for a successful
solution. Most of the realistic scheduling problems
belong to the class of nondeterministic polynomial
(NP)-complete (Garey and Johnson, 1979), which
implies that an optimal solution is not solvable in
polynomial time. As highly combinatorial search
problems, real-world scheduling problems are
computationally complex. Much of the complexity
comes from the need to attend to a large and diverse
set of objectives, requirements and preferences that
originate from many different sources in the plant-
wide situation (Smith et al., 1986). In the large-scale
scheduling environments, reducing complexity is
especially crucial to obtain feasible schedules within
acceptable response time.
The prime concern of scheduling in reality relies
to
tally on its applicability, subject to various
scheduling constraints which must be satisfied for a
solution to be valid. Also the quality of a completed
schedule may be evaluated according to a variety of
constraints, including the degree to which the due
dates of the orders are met, the total amount of time
required to complete the operation sequences, and
the utilisation of the resources. The motivation of
this study is to systematically address all constraints
encountered in scheduling environments, and to
demonstrate the use of constraint manipulation as a
solving mechanism over a scheduling domain. The
goal of this paper is to show an intelligent
scheduling methodology that is capable of solving
operations scheduling problems within realistic,
broadly constrained environments. In the process,
constraint logic based scheduling approach that
combines a declarative representation of solution
domain with a constraint handling and solving
mechanism is proposed.
114
Ko J. (2004).
AN EFFECTIVE APPROACH FOR REAL-WORLD PRODUCTION PLANNING.
In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 114-120
DOI: 10.5220/0001127101140120
Copyright
c
 SciTePress

2 THE TARGET PROBLEM
The target problem addressed by the constraint
logic-based approach is scheduling an efficient
operations sequence in the dye house of a socks
manufacturing company. On the whole, the
production process of socks making is divided into
five divisions. The first process in sock
manufacturing is knitting using machines to turn raw
materials (called yarn), such as wool, nylon and
cotton, into semi-finished goods. The types of socks
produced range from fine gauge business socks,
right down to heavy cushion foot sports socks. The
next phase is seaming, or toe closing. Jobs are
required to go through three separate operations in
this area. They are: (i) turning the socks inside out
for sewing, (ii) sewing of the toe line, and (iii)
turning back to the right side and expanding the toe
line - to avoid having a large chunky over-locking
line at the toe of the sock. After the toe closing
operation socks are sent to the dye house for
colouring or finishing. The socks are dyed in
machines most suited to the fibre type. Wool takes
about 4 hours to dye, while cotton can take up to 8
hours. There are 4 different dyeing machine groups
in a dye house. The next process area is pressing.
This operation provides a permanent setting of the
fibre and a clean, smooth texture for final
presentation for sale. After pressing, socks are
examined and packed.
In this paper, the focus is on the use of constraint
logic programming in the dye house scheduling of a
socks manufacturing factory. The significance of
scheduling in the dyeing division is grounded on the
fact that it determines the quality of final products
for the reason of dependencies among the sequence
of colours, fibre types, and dyeing capabilities of
machines. It also affects the productivity of the
whole manufacturing process due to a limited
number of facilities equipped being in operation. At
present, the production scheduling in each division
is handled manually. However, the shop floor is a
very dynamic environment and the scope and the
pertinent variables in scheduling far exceed any
human scheduler's capabilities. As for dye house
scheduling, the types of job schedules to be
produced range from a three-day scheduling to daily
scheduling, in alignment with the aspect of shop
floor such as a set of job orders released from the
previous stages, jobs to be delivered to the next
process within the deadline requested, urgent orders
to be scheduled for a short period of time and the
capacity (load limits) of dye house resources. The
human scheduler is only able to produce a rough
schedule; the actual shop floor operation still
depends on constant monitoring by the human
scheduler.
2.1 The Test Domain
The scheduling domain is derived from actual
manufacturing data. It is based on a general
operations scheduling but remains grounded in a
real-world application. The scheduling data used is
provided by the factory. The test domain is based on
a dye house covering the operations associated with
the colouring of four types of fibres. The key
characteristics of the problem are as follows:
▪ An order may consist of a set of sequenced
operations to be dyed on the specified machine.
▪ The dye house consists of four major dyeing
machine groups, defined in terms of their
processing capabilities.
▪ The socks are dyed in dye machines most suited
to the fibre type.
▪ The operation duration (processing times) ranges
from 4 hours to 8 hours.
▪ In view of its previous process, each job operation
has a requested start time to perform the operation.
▪ The number of colours at a dye house can be
broadly divided into nine major groupings.
▪ The job sequence within specific machines for
dyeing is constrained by the colour of the dyes
which are ordered from light to dark colours.
▪ Each job operation has a requested deadline to
meet the delivery of job order.
The descriptions of job operations at a typical
dye house are given in Table 1. A job is identified
by a unique job order (style) number, which is
recorded in the job order column. However on the
shop floor, a job is often identified by its operation
formula which is combined by its fibre and colour
used. Each job is assigned a requested start time and
due time. The remaining column shows a description
of the operation to be dyed (e.g., blue 69 etc.
represents fabric dyeing of different colours). The
predominant fibres to be dyed are 100% wool (WL)
and wool-blends (WB), and 100% cotton (CT) and
cotton-blends (CB).
AN EFFECTIVE APPROACH FOR REAL-WORLD PRODUCTION PLANNING
115

Table 1: A partial list of operation data at dye house for
scheduling.
Job Operation Processing Start Due Operation
order formula time (hrs) time time description
LP100173 WLB 4 0 12 wool : blue 69
SP132517 WBT 4 4 24 wol/bl : brown 8
EP180602 CTP 8 0 16 cotton : grey 57
EP148264 WBW 4 0 12 wol/bl : white 14
SP100770 CBG 8 4 24 cot/bl : green 75
SP113831 CBY 8 0 16 cot/bl : yellow 30
LP195812 WLU 4 4 20 wool : black 9
LP199860 CTK 8 0 16 cotton : cream 26
SP107015 WBR 4 4 20 wol/bl : red 42
2.2 The Schedule Constraints
The dye house scheduling problem involves the
following constraint types:
▪ Colour precedence between operations. In other
words, the sequence of operations is constrained
by the colour to be dyed.
▪ Restrictions on the allocation of dyeing machines.
▪ Laid start time to execute the job operation.
▪ Enforced operation duration on the machine
specified.
▪ Resources with limited availabilities. That is, each
machine cannot process more than one operation
at the same time.
▪ Imposed deadline to meet the order delivery.
2.3 The Schedule Objectives
The objectives of the dye house scheduling problem
can be summarized as being geared to meet
customer's requirements, in particular, the on-time
delivery of order and quality of products. Also, from
the maker's standpoint, maximum use of high-valued
dyeing machines is one of the considerable
scheduling goals. The overall quality of products
(socks), as already mentioned, rests heavily on the
colouring of fibres. Thus, the objectives of the target
problem are: (i) to meet due dates and (ii) to
maximise resource utilisation.
3 THE SCHEDULING APPROACH
Constraint logic-based approach adopted by the
proposed scheduling methodology involves: (i)
identifying potentially threatened constraints (i.e.,
colour) associated with the schedule state and
selecting one to address, (ii) taking the decision
clauses to tackle the scheduling constraints and (iii)
propagating the consequences of each decision. The
approach relies on constraint manipulation and
propagation to drive decision making. Each decision
type relates to scheduling constraints. In the dye
house data under consideration, the primary
scheduling constraint types are: (i) the colour
imposed operation sequence, and (ii) the resource
capacity limits. Each of these constraints is
continuously monitored across the full scheduling
horizon.
3.1 The Representation of
Constraints
The scheduling solution must respect a number of
constraints, in particular temporal-capacity
constraints which may be dynamically monitored
throughout the scheduling process. Temporal
capacity constraints refer to colour-dependent order
enforcements that apply over the time available for
processing using a resource. Temporal-capacity
constraints can be monitored in terms of the degree
of threat to their satisfaction, which is a function of
estimated demand and available capacity over time.
These temporal constraints on operations impose a
demand for time at the resource time period. The
proposed constraint logic-based approach takes into
consideration every resource time period of various
durations covering the entire scheduling horizon.
3.2 The Scheduling Method
Scheduling in the constraint logic-based approach
occurs at two levels: constraint solving and schedule
generation. Constraint solving involves two steps of
constraint handling based on temporal relations and
resource capacity constraints. Temporal constraints
can be solved by the successive refinement of
operation time windows. For the dye house problem
under consideration, the colour precedence
constraint L before D, i.e. "operation D with dark
colour can only start after L with light colour has
completed,” is implemented by:
operation (L) + duration (L) ≤ operation (D)
On a machine performing a single operation at a
time, the capacity constraints enforce the mutual
exclusion for each operation pair (L, D) assigned to
the same resource: L before D or D before A. The
implementation uses the constraint clauses as
choices:
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exclusive (L, D):-
operation (L) + duration (L) ≤ operation (D);
operation (D) + duration (D) ≤ operation (L).
Evidently, the constraint solving mechanism in
the proposed approach provides a computational
efficiency that can be expected from the capability
of constraint manipulation to prune the search space
during the computation of a schedule.
Following constraint solving, each operation has
been allocated to a specified resource and its start to
a single time period. No specific operation start time
has been set and operations allocated to the same
resource and time period remain to be sequenced.
This output from the constraint solver serves as the
input to the scheduler. Two approaches have been
developed for schedule generating. One involves a
full search, and other uses a global scheduling
approach. The feasibility of undertaking a full search
depends on the number of allocation alternatives
remaining after constraint solving. This is primarily
determined by the extent to which temporal
refinement is made by the constraint solver. Local
scheduling based on full search proceeds by finding
all possible operation allocations and selecting one
to be allocated to the resource at this time.
Meanwhile, in the case of global scheduling, the
selection of which operation to allocate is made on
the basis of a global constraint, i.e. the operation
with the earliest due date. An ordering of operations
can be inferred where for a pair of operations only
one allocation sequence would allow the due dates
to be met.
4 EXECUTION OF THE
PROPOSED APPROACH
Having described the scheduling approach and
methods used in this dye house implementation, the
computational processes that operate on these
solution methods can be examined in detail.
4.1 Constraint Solving
As stated in the previous section, there are three
major types of constraints in the dye house
scheduling problem. The constraints can be solved
by a linear arithmetic solver. The first type, the
colour precedence constraints state the order within
a set of job operations.
O
i
+ d
i
≤ O
j
(1)
Where O
i
(O
j
) denotes the potential start time of
each operation and d
i
indicates the processing time
or duration of operation O
i
. There is therefore colour
precedence between every two adjacent operations
in every job set.
The second type states the exclusively
disjunctive order between each possible pair of
operations within the dye machine. This is in fact the
non-determinism associated with the solution search.
In dye machine Milnor, for example, operation w
(represented by O
W
) can be performed either before
or after operation r (represented by O
R
). In the
proposed scheduling approach, this can be stated as
O
W
+ d
W
≤ O
R
∨ O
R
+ d
R
≤ O
W
(2)
There are a total of three such constraints for dye
machine Milnor. In general, for a machine of n
operations, there are (n
2
- n)/2 such constraints.
The last type of constraints is the bound
constraints which state the bound of the time domain
(values). These variables are key search variables in
the scheduling environment. Under CLP(FD) system,
they can be stated using the constraint X in lower
bound .. upper bound. A procedure to solve the
constraints within the proposed approach is to code
it in the template of Figure 1.
% declare bound
O
W
in StartTime..Deadline,
O
R
in StartTime..Deadline,
O
T
in StartTime..Deadline,
.
.
% precedence constraints
O
W
+ d
W
≤ O
R
,
O
W
+ d
W
≤ O
T
,
O
R
+ d
R
≤ O
T
,
.
.
% disjunctive constraints
(O
R
+ d
R
≤ O
T
; O
T
+ d
T
≤ O
R
),
(O
W
+ d
W
≤ O
R
; O
R
+ d
R
≤ O
W
),
(O
W
+ d
W
≤ O
T
; O
T
+ d
T
≤ O
W
),
.
.
% solution found
show_solution ([O
W
, O
R
, O
T
, ..., O
U
]).
Figure 1: Constraint solving schema in dye house.
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117

4.2 Schedule Generation
From a dye house scheduling perspective, each job
has several different operations to be dyed according
to a given colour sequence. In other words, the socks
should be dyed from light to dark colours in dye
vessels. The dye house has four different dye
machine groups. Each machine required is subject to
the type of fibres such as wool, cotton, and so forth.
The target of dye house scheduling is to produce a
schedule showing the loading of jobs onto machines
and what job order is to be used over a given period
of time. The main task at any particular point in time
is to first determine which machine will be
employed allowing for a particular fibre dyeing, then
jobs that can utilize this equipment are loaded based
on the colour demanded. On the basis of the
algorithmatic scheduling procedure, the solution of
the illustrative example above is given below:
Dye machines Job Operations
Milnor O
EP148264
,O
SP107015
, O
SP132517
Smith Drum O
LP199860
, O
EP180602
Paddle O
LP100173
, O
LP195812
Washex O
SP113831
, O
SP100770
The key to the success of the constraint logic-
based approach in tackling dye house scheduling
problem involving various constraints lies in the
combination of propagation and search. By imposing
the constraints involved in the problem before
commencing search, the size of the domains can be
reduced through the action of consistency check and
propagation. Furthermore, as the search proceeds,
the effects of assignments made to variables are
propagated to the domains of the, as yet unlabelled,
variables, pruning the possibilities that remain open.
Thus, propagation acts to reduce the branching in the
search tree by eliminating paths that do not lead to
solutions in advance.
5 DISCUSSION
The main purpose of this paper has been to
demonstrate that the performance of a scheduling
methodology can be enhanced by preserving and
utilizing the constraints available within the problem
and considering a broad range of perspectives on the
state of problem solving. In this section, the
performance of the proposed scheduling technique
according to both the quality of its schedules and the
computational efficiency of its approach will be
discussed, followed by a summary of the findings on
applying constraint logic-based approach to the dye
house scheduling problem. Three performance
criterions were employed to evaluate the schedule
produced by the proposed approach. These measures
are closely related to the scheduling objectives
described in Section 2.3.
5.1 On-Time Delivery
For the dye house situation, the major concern in
scheduling is to meet the delivery of a customer
order. On-time delivery, which can be measured by
the mean tardiness, is thus considered critical. Table
2 provides the summary of due date related schedule
statistics of the three cases.
Table 2: Due date-related schedule statistic.
Performance Index 3-Day 2-Day 1 -Day
Mean Earliness 2.12 2.54 2.15
Mean Tardiness 0 0 0
Mean Lateness -2.12 -2.54 -2.15
Average WIP 17.67 11.58 7.67
Average Inventory 18.67 12.75 8.83
Table 2 contains the indices of due date related
statistics in three dye house cases. It is worth noting
from the schedule statistics that, as would be
expected, the mean tardiness of each schedule in the
dye house is zero. This confirms the results of three
dye house scheduling cases. Indeed, by
incorporating the time bound of each job order over
a computation domain before schedule generation,
the scheduling window can be reserved by the bound
constraints imposed. As a consequence, the
constraint based scheduler always produces an
excellent solution as far as job tardiness is concerned.
5.2 Resource Utilisation
Another measure of the performance in the dye
house is maximum use of highly expensive facilities.
Table 3 summarizes the results of three cases of dye
house scheduling. Each case presented here indicates
the average utilisation of four different dye machines
- Washex, Paddle, Milnor, and Smith Drum. It can
be seen from the results of Table 3 that daily
scheduling produces better performance on machine
utilisation, compared with that of the other two cases.
This might be, along with idle time, caused by the
size of manufacturing orders to be scheduled. In
general the machine utilisation has an immediate
relationship to the amount of orders to be performed.
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However, the job order in this case is subjected to
the influence of the state of front and rear
manufacturing processes. Accordingly, the
utilisation of dye house affects the situation of other
shop floors.
Table 3: Time-related schedule statistic.
Performance Index 3-Day 2-Day 1-Day
Total Flow Time 1272 556 184
Av. Flow Time 37.41 25.27 14.15
Av. Processing Time 5.88 5.82 5.23
Av. Idle Time 2.58 2.91 2.15
M/C Utilisation 17.67 11.58 7.67
5.3 Computational Efficiency
The proposed scheduling scheme was programmed
in CLP(FD) and CLP(R) and run on an IBM
Pentium system. One issue to be dealt with, however,
is the management of the additional data structures
used to control constraints which are permutated and
propagated in the process of scheduling. Indeed,
these data structures may be more costly to maintain
in terms of memory consumption and in terms of
computation.
Table 4: Computer process time of dye house scheduling.
Dye house Manual Proposed Approach
*
Scheduling Method Local Global
1-Day 45 min 50 ms 30 ms
2-Day 100 min 70 ms 60 ms
3-Day 240 min 160 ms 140 ms
Table 4 exhibits the results of the computation
times for the three dye house scheduling cases.
Based on the scheduling method and procedure,
three different computation times are compared. The
first one records the average scheduling time taken
by the human scheduler under existing conditions.
Obviously, the time required depends on the size of
job orders to be scheduled. The second uses the local
constraints only for the dye house scheduling
without satisfying the global constraints, and in the
third one the scheduling objective as a global
constraint is given to the scheduler to optimize the
solution. The results of constraint logic-based
scheduling reflects that the more constraints, the
faster schedule generation. Finally, it is worth noting
from Table 4 that, unlike manual scheduling, the
number of job orders has less influence on CPU time
as far as the dye house scheduling is concerned.
6 CONCLUSIONS
With some notable exceptions (e.g., ISIS - Fox &
Smith, 1984), most of the scheduling research
discussed so far have concentrated on oversimplified
and abstract target applications. Such abstract
applications provide a means of focusing on key
aspects of the scheduling problem and establish a
good platform for controlled experimentation, but
their practical viability and adaptability are limited.
This paper addresses the specific scheduling context
to which constraint logic-based approach has been
applied, and attempts to achieve some level of
validity by focusing on the modelling and solving of
realistic scheduling problems. In this paper the main
characteristics of the dye house problem were tested
using the constraint logic-based approach. This
paper has also presented a view of constraint
manipulation as a solution procedure, and has
attempted to place the constraint behaviours to
solving mechanisms of the proposed scheduler.
From the point of view of a practical application,
this case study has demonstrated the potential
capability of applying the constraint logic-based
scheduling technique in practice. The objective of
constraint-based approach is to provide reliable,
realistic, and computationally efficient schedules. In
consequence, the application of constraint logic-
based approach to the dye house scheduling problem
has demonstrated that a schedule can be obtained
within seconds.
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