INT. J. PROD. Rhs.. 2003, VOL. 4 1 , NO. 9, 2021 - 2 0 3 5
_ Taylor & Francis
\^y
Revising the master production schedule in sequence dependent processes
JAMES A. HILLt*, WILLIAM L. BERRYt and DAVID A.
SCHILLINGI
Revising ihe master production schedule (MPS) in a roiling planning horizon
environment to improve plant performance is critical in process industries with
sequence dependeni changeovers. Plant performance is defined in terms of process
changeover time, total shortages, and finished goods inventory. Two heuristics for
revising the MPS are introduced and tested against a rolling horizon MPS thai
does not take sequence dependent changeovers into consideration. These two
heuristics represent two dilTerent approaches to heuristic design: local interchange
(SWAP) and global interchange (3OPT). Simulation experiments are reported
that test the performance of the two different approaches lo revising the MPS
in process industries with sequence dependent changeovers. The MPS designs
were tesled under plant conditions that are frequently encountered in process
industries. The results indicate that revising the MPS in process industries significantly improves plant performance. In addition, 30PT provides a major
improvement in changeover time, while SWAP provides improvement in total
shortages.
1.
Introduction
Changing markets are placing new business reqtiirements on many process industry plants, including the need for greater product variety wilh improved changeover
time and delivery performance (Leschke 1995. Olliff and Burch 1985). Supporting
these requirements is especially difticull in many process industry firms, such as firms
that manufacture chemical products, because such processes frequently involve long
product sequence dependent changeover times. As reported by Leschke (1995) changeover times represent a sizeable proportion of plant capacity, e.g. 47-92%. and are
not easily reduced through conventional changeover time reduction methods. One
means of supporting changeover time and delivery competitiveness in the high variety environment faced by such companies is through the development of improved
master production scheduling. In this paper we focus on improving plant performance by revising the master production schedule (MPS) in a make-to-stock process
industry environment.
The MPS specifies the timing and size of production quantities for each product.
The MPS links the firm's broad strategies, as expressed in the aggregate production
plan, to more specific tactical plans that will enable the firm to balance the product
demands of customers with the supply of products made available by plant schedules
and inventory. Process industry firms generally perform master production schedulRevision received June 2002.
tOwen Graduate School o\' Management. Vanderbilt University. Nashville. TN 37203.
USA.
J Fisher College of Btisiness. The Ohio State University. Columnbus. OH 43210, USA
*To whom correspondence should be addressed, e-maii: james.hill((( owen.vanderbilt.edu
liuenunioiiiil Jmirtiut oj Protluciioii Rt'.u-tmh ISSN 1)020 7543 prinllSSN 1366 5HKX online i; 2003 Taylor & hrancis Lid
http:,''www.landr.Lo.uk'j(.n]rnals
DOI; IO.I0K0/0020754O3IOO0I23BH6
2022
J. A. HilUt al.
ing differently from job shop industries. These firms tend to schedLile capacity first
belbre raw materials because of resource constraints within the chemical blending
and mixing process. If planning for capacity at the chemical mixing and blending
operations indicates potential infeasibilities. the master production schedule shouid
be revised to accommodate these capacity limitations. Most of the previous work on
master production scheduling does not consider process industry firms where changeovers are sequence dependent {Lin and Krajewski 1992. Sridharan et al. 1987. and
Zhao and Lee 1993). In this paper we address the problem of revising a rolling
horizon MPS in process industries with sequence dependent changeovers.
This paper has two objectives: (I) to present computationally efficient methods
to revise the MPS to improve plant performance in sequence dependent processes,
and (2) to determine the sensitivity of these methods to frequently encountered
differences in plant operating conditions. We begin by discussing previous literature
relative to the master production scheduling problem. In the next section, two heuristics are presented to revise the MPS under rolling horizons. Next, we present the
research questions to be examined and the research design used in the simulation
experiments. Finally, computational results are discussed that demonstrate the
improvements in master production scheduling performance.
2.
Literature review
Very little work has been reported on master production scheduling methods that
consider changeover time and product sequence restrictions often encountered in the
process industries. Product sequence restrictions and changeover costs were incorporated in a process industry model reported by Oliff and Burch (1985). They present a mixed integer programming model that determines lot sizes, line assignments
and inventory levels for 28 MPS products. However, because of the problem size and
computation requirements, a linear programming approximation that generates
near-optimal solutions is limited to small problem sizes. De Matta and Guignard
(1995) study lot-sizing and changeover decisions in production schedules that are
implemented on a rolling-horizon basis. Their results show that as the planning
horizon lengthens, the changeover and holding costs converge. These authors do
not include re-planning intervals within the planning horizon. Hill et al. (2000)
introduce a two-level approach to master production scheduling. The authors
show that master production scheduling should be done at the bottleneck process
(level two) not the end item (level one) in order to improve plant performance.
Some research has been done on re-planning the MPS under a rolling horizon.
Lin and Krajewski (1992) present a mathematical model for designing a MPS system
in an uncertain environment. The model can be used to estimate the expected cost
per period for any combination of the re-planning interval, the frozen interval and
the forecast window. Venkataraman (1996) addresses the problem of re-planning
frequency for a rolling horizon MPS in a process industry environment. The author
uses actual data from a paint company to determine the appropriate re-planning
frequency. Kern and Wei (1996) evaluate the relative effectiveness of rescheduling
policies in capacity-constrained, just-in-time production environments. The authors
found that higher demand variation, large forecast errors, and tight capacity led to
the degradation of system performance. Yang and Jacobs (1999) examine the use
of both frozen and re-planning intervals for planning the MPS for a capacityconstrained job shop. The results show that forecast error, demand lumpiness, set-up
time, and planned lead time have a greater impact on total inventory and mean total
Revising the master production schedule
2023
backlog than the frozen and re-pkinning intervals. None of these aulhors have
focused on master production scheduling in environments where changeovers are
sequence dependent. In this paper, we examine master production scheduling performance where heuristics are used to revise the MPS within the planning horizon.
We also determine operating conditions that effect MPS performance in a process
industry environment where changeover times are sequence dependent.
In the next section, we demonstrate two approaches to revising the MPS in a
process industry environment where changeovers are sequence dependent. Two
scheduling heuristics. SWAP and 30PT can be used to revise the MPS for maketo-stock sequence dependent products. Since the planning horizon may be sufficiently long to include multiple orders for an individual product, these heuristics
can be used to sequence a series of orders that includes both different products and
repeat orders for the same product. These computationally efficient heuristics, which
represent different approaches to revising the MPS. can be applied to large problems.
3.
Scheduling heuristics
The SWAP heuristic is a simple local search heuristic that has been tested extensively in the scheduling literature (Wilkerson and Irwin 1971. Hill ct al. 2000). It is an
improvement heuristic, which uses a neighbourhood search approach similar to that
used by Gupta and Darrow (1986). The heuristic begins with an initial MPS set of
orders and reduces the changeover time in the MPS through swaps of adjacent
orders until no further improvement is possible. The local switching of orders is
thought to be advantageous in master production scheduling because orders are
not moved far from their original due date generated by the initial MPS. thus
allowing for improvement in both process changeover time and delivery performance,
30PT is an adaptation of Lin and Kernighan's (1973) Three-Opt routine, which
seeks to improve a given MPS by examining interchanges of three orders at a time.
As an illustration, consider a sequence often orders in a master production schedule
(numbered from I to 10)
1.2,3,4,5,6,7,8.9.10.
A possible three-way interchange would be to take the orders and changeovers
represented by 1.2; 5,6; and 8, 9, and create a new sequence where I is followed
by 6; 8 is followed by 2; and 5 is followed by 9. All other changeovers in the original
sequence remain the same. Specifically, the resulting sequence would be:
1,6,7,8,2,3,4,5,9,10.
If the second sequence results in a smaller total changeover time, then it is retained in
place of the first.
There are a number of different ways to perform a three-way interchange. We
have chosen for simplicity to implement solely the swapping approach used in the
illustration above, which maintains the sequence of all orders that were not swapped.
This method provides a counterpoint to the SWAP heuristic.
4.
Research design
In this section, we present the research design for evaluating master production
scheduling performance under process industry environments. The research questions are provided first. A discussion of the environmental factors that impact
2024
J. A.
performance in process industries is then provided. Next, the experimental design
and performance criteria are described. Finally, the simulation model is outlined.
4.1.
Research questions
Previous research on replanning the master production schedule has not
addressed processes with sequence dependent changeovers. Nor has this research
addressed processes with multiple products. Our research attempts to address
some important issues relative to manufacturing plants that have multiple products
with sequence dependent changeovers. Three questions are examined in this research
to improve master production scheduling performance in process industries with
sequence dependent changeovers. These are:
(1) To what extent can performance he improved hy revising the rolling horizon
MPS with the SWAP and 3OPT scheduling heuristics in sequence dependent
processes?
(2) How is performance of the revised master production schedule affected by
changes in the replanning frequency?
(3) Is the relative performance of the revised master production schedule dependent on the interaction of the independent variables?
4.2. Experimental factors
4.2.1. Coefficient of variation of changeover times
The proportion of plant capacity explained by changeover time can be very large.
When such a large portion of the process capacity is devoted to changeovers. a
relatively small percentage reduction in changeover time can represent an important
improvement in operating performance. Given the sensitivity of many companies in
process industries to improving margins in a high product variety environment, the
design of the master production schedule to incorporate scheduling heuristics that
reduce changeover time can be very important in improving plant performance.
Furthermore, while previous research indicates that scheduling performance is
quite sensitive to changes in the coetticient of variation in changeover times, relatively small values have been used for this factor in evaluating sequence dependent
scheduling heuristics. Previous work by Gavett (1965) and Guinet (1993) report
results covering a range of 0.17-0.57 for the magnitude of changeover time coefficient of variation. While very little has been published concerning the actual magnitude of the changeover time coefficient of variation in plants, our field research
indicates values as large as 0.97. or nearly twice the maximum value studied in
previous research. Understanding plant performance at much higher levels for the
coefficient of variation in changeover times is important in understanding the implications of this factor in master production scheduling. This experimental factor
brings a new dimension to master production scheduling research because, in previous research, changeovers are considered to be either negligible or sequence independent. To understand how the revised MPS performs under different operating
conditions, we varied the changeover matrix to produce two levels of coefficiem of
variation (high = base level of 0.97; low = 0.32 one-third of the hase).
4.2.2. TBO {time between orders)
When scheduling a set of orders, several heuristics have been proposed in previous research to minimize changeover time in sequence dependent scheduling (Clark
Revising the master production seliedide
2025
and Ciark 2000. Haase and Kinims 2000). These authors provide efficient algorithms
10 reduce the amount of CPU lime. However, the rules are tested on relatively small
problem sizes and not under operating conditions outlined in this paper. With the
exception of Guinet (1993). much of the previous research on sequence dependent
single machine processes has been conducted using relatively small problem sizes,
involving 20 orders or fewer.
In master production scheduling the time between orders (TBO) is commonly
used to generate diflerent problem sizes (Sridharan et at. 1987, Sridharan and
LaForge 1994). The TBO is the ratio between the economic order quantity and
the average period demand. If the number of product items is fixed, a plant
having make-to-slock products with predominately small TBO values reflects the
frequent production of small lot sizes and relatively large MPS problem sizes.
Likewise, a plant with products having predominately large TBO values reflects a
situation where products are produced infrequently in large lot sizes, yielding relatively small MPS problem sizes. In our research, we have chosen levels for TBO
(high = 20; low = 4) which generate order sizes ranging from 20 to 100.
4.2.3. MFS method
The experimental factor master production scheduling method was set at three
levels. The first setting represents the results of the initial MPS without using replanning heuristics. The MPS is still updated and rolled forward, although without the
use of scheduling heuristics. From this point further we will refer to the MPS without
scheduling heuristics as the unrevised MPS. The second and third settings represent
results of the revised MPS using SWAP and 30PT respectively.
4.2.4. Demand uncertainty
Past research (Sridharan and Berry 1990. Lin and Krajewski 1992, Zhao and Lee
1993. Kern and Wei 1996. Yang and Jacobs 1999) has shown that demand uncertainty is an important factor affecting master production scheduling performance.
Demand uncertainty was modelled by generating actual demand for multiple
products. The forecast error was modelled using a normal distribution with a
mean of zero and a standard deviation with two experimental settings: I5yo and
30% of mean demand. The forecast requirements used in determining the MPS were
computed by adding the forecast error to the actual demand each period over the
simulation run. A critical assumption is thai the forecast is unbiased. Previous
research has shown that under conditions of demand uncertainty there is no clear
choice of lot-sizing rules (Wemmerlov and Whybark 1984). This .study uses the Fixed
Periodic Requirement (FPR) rule. Wemmerlov (1979) reported that most companies
prefer a FPR lol-sizing rule. The use of the FPR is also supported by Yang and
Jacobs (I999J.
4.2.5. Re-planning frequency
The main objective of this study is to examine the affect of revising the MPS in a
process industry environment. Sridharan and Berry (1990) have shown that the
length of the planning horizon has the least influence on system cost and customer
service. Therefore, it is not our intention to focus on the length of the planning
horizon. We consequently set the re-planning frequency (R) to be a fraction of the
fixed planning horizon (A'). The values of R for our experiments are 0.25, 0.50. 0.75
2026
/ A. ///7/et al.
and 1.0. When R is equal to 0.25, revising is done every 0.25A' periods. These are the
same levels used by Zhao and Lee (1993).
4.3.
Performance criteria
Customer pressure for improved delivery performance makes total shortages an
important measure. Delivery performance is defined as the degree to which manufacturing cannot meet the MPS due dates, i.e. order tardiness. Order tardiness is
measured in terms of the number of scheduling periods each MPS order is delivered
late. This measure is converted into total shortages by multiplying order tardiness by
the average sales forecast per scheduling period. Total inventory is similar to that for
total shortages, and reflects performance frequently reported in process industry
firms.
Changeover time is an important measurement because the MPS is often developed in an uncapacitated environment considering other criteria, such as customer
service inventory investment and instability, leaving changeover time to be considered in shop floor scheduling. Also, additional capacity can be used as a buffer
against demand variability. As a result, this measure reflects the potential improvement in capacity obtained by revising the MPS.
Based on our above discussion, we use three performance criteria to evaluate the
MPS performance; (I) the total amount of shortages in the MPS planning hori/.on.
(2) the total amount of finished goods inventory in the MPS planning horizon, and
(3) ihe total amount of changeover time in the planning horizon.
4.4.
Experimental design
Simulation experiments were conducted to examine the research questions presented earlier. A simulation model was developed using FORTRAN and run on a
Dell OptiPlex GXI desktop system. The SPSS statistical package was used to analyse
the data. A full factorial Analysis of Variance design with 40 replications was used to
examine the research questions.
The replications in these experiments were 40 different product sets. Each product set includes ten products, each having the following data; average period sales
forecast for the next 30 periods (in units), the MPS batch size (in units), the MPS
initial inventory and the run time processing rate (in units/hour). The changeover
time matrix data represent actual operating data collected from a chemical processing firm.
For all 40 replications, the following procedure was used to randomly generate
Ihe product structure data for each of the ten products. The parameter values listed
in this paragraph are representative of actual operating data. First, an average
period demand was randomly generated from a uniform distribution with a mean
of 12000, a lower limit of 4000 and an upper limit of 20000. Second, the experimental factor setting for the time between orders (TBO) value was used as the mean
of a TBO distribution. A TBO value for each product was randomly generated from
a uniform distribution having upper and lower limits of ±50% of the mean value
setting. Third, the formula product batch size was computed to be the average period
demand multiplied by the lime between orders value for each product. Fourth, the
changeover to proce.ssing time ratio value for each product was randomly generated
from a uniform distribution having upper and lower limits set at ±50% of ihe mean
value of 0.25. This setting implies that the average proportion of process capacity
explained by the changeover time is 25%. After the ratio value was set, the run time
Revising the master production schedule
2027
processing rate (in units/hour) was calculated for each product using the fixed value
for the ratio and the average changeover lime from the changeover time matrix.
Finally, the changeover time matrix having the appropriate level for the changeover
time coefficient of variation was used in the MPS.
Next, an MPS record v^as established for each product containing a forecast,
projected inventory, and MPS rows. These records were processed to develop a 30
period MPS. At the end of each replanning cycle, the MPS is revised using the
scheduling heuristic and rolled forward through time. This procedure was repeated
until all 30 periods of the requirements were processed. To eliminate the effect of
transient conditions upon the operating performance, the first five periods of operating performance data in each simulation run are discarded. The five-period initialization interval was selected after visual inspection of the inventory level data. In
these experiments, the initial inventory conditions were identical for all product sets.
Therefore, the differences in performance between the replications resulted from
differences in the randomly generated average period forecast, the product ratio
value, TBO values between product structures, and differences in the changeover
time coefficient of variation value.
5.
P.xperimental results and discussion
It is clear from the results in tables 1. 2 and 3 that the MPS scheduling method
and the replanning frequency have a large influence on performance in comparison
with the other parameters studied. In fact, their F-statistic ranks near the top in all
three performance measurements. Therefore the next two sections are focused
around these two parameters. The results showing the effect of experimental factors
F-
Source
MPS
CV
TBO
Demand
Replanning freq
CV X TBO
CV X MPS
TBO X MPS
Repl. X MPS
Repl, X CV
Repl. X TBO
60.2
50.8
108.9
41.3
57.5
31.7
22.9
28.9
20.8
48.1
27.0
Sig.
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
0.00*
* Signilicant al the 0.05 level
Table I.
(a) ANOVA results for total shortages.
Unrevised MPS
MPS-SWAP
MPS-3OPT
Unrevised MPS
MPS-SWAP
MPS-30PT
1.0
0.00*
0.00*
1.0
0.00*
1.0
iU al ihf l).()^ level
Table 1. (b) Tiikey multiple comparisons.
2028
/ . A. /////et al.
Source
F
Sig.
MPS
CV
TBO
187.3
6.3
33.0
46.1
94.2
0.084
0.00*
0.02*
0.00*
0.00*
0.00*
0.77
0.01*
0.00*
0.07
Demand
Replaniiing frcq
CV X TBO
CV X MPS
TBO X MPS
Repl. X MPS
Repl. X CV
Repl. X TBO
7.1
30.7
3.2
10.4
37.2
n.o2*
0.00*
* Sij![iLlic:int al the 0,05 level
Table 2. (a) ANOVA results for total inventory.
Unrevised MPS
MPS-SWAP
MPS-3OPT
Unrevised MPS
MPS-SWAP
MPS-3OPT
1.0
0.931
0.00*
1.0
0.00*
1.0
* Significant al [he 0.05 level
Table 2. (bl Tukev mul
Source
F
Sig.
MPS
CV
TBO
Demand
Replanning freq
CV X TBO
CV X MPS
TBO X MPS
Repi. X MPS
Repl X CV
Repl X TBO
49.3
0.594
3787.5
0.827
1478
0.295
10.4
23.7
18.5
1.8
34.2
0.00*
0.44
0.00*
0.29
0.00*
0.58
0.00*
0.00*
0.00*
0.13
0.00*
* Sijiniticant at the 0.05 level
Table 3. (a) ANOVA results for total changeover time.
Unrevised MPS
MPS-SWAP
MPS-30PT
Unrevised MPS
MPS-SWAP
MPS-3OPT
1.0
0.00*
0.00*
I.O
0.04*
1.0
* Significanl at ihc 0,1)5 level
Table 3. (b) Tukey multiple comparisons.
Revising the master production schedule
2029
on manufacturing performance are presented in three parts. Part I addresses research
question 1, ihc statistical dilTerence in performance between ihe MPS without using
scheduling heuristics and the revised MPS using SWAP and 3OPT respectively. Part
II addresses research question 2. changes in the re-planning frequency and the affect
on performance. Part III addresses research question 3. two-way interactions
between the experimental factors.
5. i.
Master production scheduling methods
The results in table 4 show the performance of the MPS without scheduling
heuristics and the two revised MPS solutions with scheduling heuristics for all
criteria (total shortages, total inventory and total changeover time). These results
are averaged across all operating environments. The ANOVA results shown in table
I indicate the main effect MPS method is significant for total shortages. Further, the
Tukey results in table l(a) show there is a significant difference between the unrevised
MPS, revising the MPS with SWAP and revising the MPS with 30PT. The results
for total shortages shown in table 4 indicate the local SWAP method has lower total
shortages averaged across all operating environments than both the global 30PT
method and the revised MPS without scheduling heuristics. Thus, we can conclude
that revising the MPS with the local SWAP heuristic provides the lowest total
shortages when operating in an environment with sequence dependent changeovers.
The ANOVA results shown in table 2 indicate the main effect of the MPS method
is significant for total inventory. The Tukey results in table 2(b) show there is a
significant difference between 30PT with both SWAP and the unrevised MPS.
However, there is no significant difference between SWAP and ihe unrevised
MPS
TBO
CV
Shortage
Inventory
Changeover
CVL
362
8
2151
CVH
987
5
2389
CVL
107
6
420
CVH
292
4
473
CVL
296
316
1675
CVH
573
423
1848
CV[
156
115
334
CVH
200
204
375
CV,
165
13
1805
CVH
253
13
1972
CVL
80
11
364
CVH
149
TBOL
Unrevised
MPS
TBOH
TBO
MPS 30PT
TBOL
MPS
SWAP
TBOH
Table 4.
Average performance at eiich setting.
39?
2030
J. A. /////et al.
MPS. Because 30PT is a global heuristic, orders are potentially moved forward in
the planning horizon causing inventory to build. This result shows that the design of
the scheduling heuristic used to revise the MPS can lead to degradation in MPS
performance when operating under sequence-dependent changeovers. The result
provides partial support to previous research (Yano and Carlson 1987, Sridharan
and Berry 1990) that frequent revising of the MPS can be undesirable under certain
operating environments. However, it is important to note that their measure of
performance was cost while ours is total inventory, and our research is multi
products with sequence dependent changeovers.
The ANOVA results shown in table 3 indicate the main effect MPS method is
significant for changeover time. The Tukey results in table 3(b) show there is a
significant difference between the unrevised MPS versus using SWAP or 3OPT to
revise the MPS- There is also a significant difference between 30PT and SWAP.
Thus., we can conclude that when changeover time is the chosen performance
measurement it is beneficial to revise the MFS to improve performance. We can
also conclude that 30PT outperforms SWAP in reducing changeover time across
the planning horizon. 3OPT"s performance advantage is due lo its ability to hatch
orders together across the planning horizon versus the local SWAP heuristic. Now
that we have concluded that revising the MPS will improve plant performance we
turn our attention to how often the MPS should be revised.
5.2.
Changes in the re-planning frequency
The Tukey procedure was used to test the differences in mean performance
between different MPS replanning frequencies for both heuristics and for all three
performance measurements. It is clear from the Tukey results in tables 5 and 6 that
there is a significant difference in performance between the different levels of replanning frequency. The effect of the replanning frequency on performance is dependent
on the method chosen to revise the MPS and the performance measurement chosen.
The results show that there is a significant difference in changeover time between
all levels of replanning frequency for both 30PT and SWAP. Frequent revision of
the MPS is beneficial when reducing changeover time is the chosen performance
measurement. This result is different from previous research where frequent revision
of the MPS causes degradation in cost and MPS stability (Sridharan and Berry 1990,
Zhao and Lee 1993. and Yang and Jacobs 1999). Frequent replanning of the MPS
leads to more orders open for rescheduling. With more orders open for rescheduling,
more changeover time can be reduced. The results also indicate that there is a
significant difference in total shortages when the replanning frequency is greater
than 0.50 of the planning horizon tor the SWAP heuristic. As replanning becomes
more frequent, more orders in the planning horizon are open for rescheduling. This
leads to an increased probability that more orders will be moved farther away from
their original due date causing an increase in shortages. In contrast, the 3<3PT
heuristic only improves shortage performance when the replanning frequency is
set at 0.75. In this case, only 25% of the planning horizon is open for rescheduling.
Frequent revision of the MPS using the 3OPT heuristic can cause degradation in
total shortages. This result occurs because 30PT is a more global heuristic ihan
SWAP and, as more of the planning horizon is open for rescheduling. 30PT
moves orders further away from iheir original due date thus increasing the likelihood
of increased shortages. As far as inventory is concerned, there is a significant difference in performance between all levels of the replanning frequency for 3OPT. More
Revising the master production schedule
2031
SWAP
Changeover Time
Replanning
frequency
0. 25
0.50
0.25
0.50
0.75
1.0
LO
0.03*
0.00*
0.00*
LO
0.02*
0.00*
0.75
LO
0.00*
Short ages
LO 0.25
1.0
1.0
0.40
0.01*
0.00*
0.50
1.0
0.08
0.02*
0.75
LO
0.03*
Inventory
LO 0.25
0.5
1.0
0.34
1.0
0.06
0.02*
0.70
0.16
0.75
LO
1.0
0.99
1.0
* Sigiiificanl at p •= 0.1)5
Table 5. Tukey results for replanning frequency.
30PT
Replanning
frequency
0.25
0.50
0.75
LO
Changeover Time
0.25
0.50
0.75
1.0
0.00* 1.0
0.00* 0.00* LO
0.00* 0.00* 0.00*
Shortages
LO 0.25
0.50
0.75
1.0
0.12
LO
0.04* 0.13
1.0
LO 0.00* 0.00* 0.04*
Inventory
1.0 0.25
0.5
0.75
LO
0.00* LO
0.00* 0.00
1.0
1.0 0.00* 0.00* 0.00*
1.0
LO
* Signilkanl al p = 0,05
Table 6. Tukey resuit.s for replanning frequency.
changeover time is taken out of the schedule as the frequency of replanning
increases. As more changeover time is taken out of the schedule, inventory starts
to build. For the SWAP heuristic there is no significant difference in inventory until
frequent replanning occurs at 0.25 of the planning horizon. The Tukey results for the
MPS where scheduling heuristics arc not used were nol conclusive. In fact, the results
of a full factorial ANOVA indicated that the re-planning frequency is not as
significant a factor in comparison with other environmental factors. This is consistent with previous research (Sridharan and Berry 1990, Zhao and Lee 1993, and
Yang and Jacobs 1999).
5.3.
Two way interactions
Many of the two-way interaction effects in tables 1, 2 and 3 are significant. The
results indicate the MPS x CV interaction is significant for all three performance
measurements. This result indicates Ihe effect of CV on total shortages is not
the same for the unrevised MPS and the two revised master production schedules.
The interaction is shown in figure I. Total shortages degrades in the unrevised MPS
and in ihe revised MPS using 3OPT as CV increases versus the revised MPS using
SWAP, where total shortages is relatively constant across both levels of CV. The
MPS X CV interaction can also be seen under total changeover time in figure 2. An
increase in CV causes more changeover time in the unrevised MPS versus the revised
MPS solutions. The results in tables 1, 2 and 3 also indicate that the MPS x TBO
interaction is significant for all performance measurements.
J. A. Hlllet al.
2032
700
600
g 500
• mps/3opt
Io 400
mps/swap
« 300 n
•un-revised mps
o 200
100
0
low
high
CV
Figure L
MPS method versus
1600 J
a, 1400 --
I 1200 I
1000 -
• mps/3opt
800
mps/swap
600 -
•un-revised mps
400 200 0
low
high
ev
Figure 2. MFS method versus cv.
Many of the two-way interactions involving the replanning frequency with other
operating factors are significant in tables I. 2 and 3. A summary of the replanning
frequency x CV interaction on shortages, inventory and changeover time is shown in
table 7 for the 30PT heuristic. The data indicate that the replanning frequency
produces a greater eft'ect on inventory and shortages when the coefficient of variation
is high and the 3OPT heuristic is used to revise the MPS. A similar eftect is also
3OPT
Changeover Time Reduction
Total Shortages
Total Inventory
Replanning
frequency
CV
(low)
CV
(high)
CV
(low)
CV
(high)
CV
(low)
CV
(high)
0.25
0.50
0.75
LO
1649
1043
716
60S
1907
1091
802
646
2%
241
183
214
522
401
277
346
328
250
183
101
421
Table 7.
Results of replanning frequency interaction with CV (in units).
379
300
LS4
Revisini; the master production schedule
2033
observed when TBO is low. Therefore, the conditions under which the decision is
made as to when replanning the MPS is beneficial can have an important influence
on performance.
6.
Summary
These experiments show how master production scheduling performance in process industries with sequence dependent changeovers can be significantly improved
through revising the MPS. These experiments show manufacturing performance can
be improved by adjusting the timing of production orders in sequence dependent
processes through the use of scheduling heuristics such as 3OPT and SWAP. This is
especially important in plants having a high coefficient of variation of changeover
times.
6.1.
Improvement against MPS without revision
Using the results in table 4 it is apparent that the two heuristics used to revise
the MPS, 3OPT and SWAP are superior to the unrevised MPS when considering
changeover time and shortage performance. Total changeover time was reduced by
15% over all experimental settings using SWAP, and by 21% using 3OPT to revise
the MPS. In the case of total shortages, SWAP has a 50.7% reduction against the
unrevised MPS versus 11.5% reduction for 30PT. It is apparent that revising
the MPS can be critical in improving both changeover time and total shortages in
sequetice dependent processes. From these results, we can conclude that iho local
SWAP heuristic provides lower shortages while 30PT provides lower changeover
time. The design of the local SWAP heuristic is more advantageous in reducing
shortages because the MPS is already in the earliest due date sequence and the
local SWAP heuristic improves performance by adjusting orders to decrease changeover time without moving orders too far away from their original due date. It is also
important for managers to consider the trade-off of changeover time and inventory
when revising the MPS. This is especially true with 30PT. The more often the MPS
is revised the larger the trade-off between inventory and changeover time reduction.
Managers should pay close attention to the frequency of the replanning cycles, as
this will have an etTect on the size of the trade-off.
6.2.
Scheduling environment impact
The experimental results indicate the nature of the scheduling environment
(measured in terms of TBO, changeover time coefficient of variation, replanning
frequency and the choice of scheduling heuristics) can affect plant performatice.
Replanning frequency and TBO were significant under all criteria studied. These
results indicate plants having a large number of MPS orders can expect improvement
in performance measured in terms of total changeover time, and total shortages by
revising the MPS. It is also true that frequent revision of the MPS is beneficial for
changeover time reduction. However, it is also critical to revise only a portion of the
MPS when TBO is low because frequent revision will cause too many open orders to
be moved away from their original due date, which will cause degradation in shortage performance.
It is clear that CV plays an important role in plant performance. An increase in
CV does not alTect changeover time as it does shortages. An increase in CV leads to
more shortages in the planning horizon, although total changeover time remains
relatively constant. An increase in CV allows more chances for the scheduling
2034
J. A. Millet al.
heuristic to reduce changeover time, which could lead to more orders being moved
far away from their due date. Under low CV changeover time can be reduced with
far less movement of orders, thus reducing the effect on shortages. Thus process
industry environments characterized by high CV and low TBO indicate potential for
significant improvement in changeover time and shortage performance through
revising the MPS. The frequency of revision is dependent on the scheduling heuristic
used to revise the MPS. Therefore, to improve overall plant performance, managers
should look to decrease the variability in changeovers between products through
improvements in product and process design. If further improvement cannot be
made in this area, then using scheduling heuristics to revise the MPS is another
alternative.
6.3.
Conclusions
These experiments demonstrate the importance of revising the MPS in process
industry environments with sequence dependent changeovers. These results represent
significant improvements against the unrevised MPS. The results are especially
significant since they were achieved under operating conditions not considered in
master production scheduling literature where changeovers were assumed to be
either negligible or sequence independent. Previous authors (Sridharan and Berry
1990, Zhao and Lee 1993, and Yang and Jacobs 1999) have found replanning not to
be as significant a factor as we have and their results were not as conclusive.
This study is an exploratory examination of revising the MPS in process industries with sequence-dependent changeovers. The paper also builds on previous
research by explicitly studying the combined effects of revising the MPS with processes that have multiple products with sequence dependent changeovers. Further
work should investigate the design of the master production schedule in process
industries with sequence dependent changeovers, and the sensitivity of scheduling
methods to changes in operating conditions.
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