Vol. 21, No. 2, March–April 2012, pp. 211–223
ISSN 1059-1478|EISSN 1937-5956|12|2102|0211
DOI 10.1111/j.1937-5956.2011.01263.x
© 2011 Production and Operations Management Society
An Application of Master Schedule Smoothing and
Planned Lead Time Control
Chee-Chong Teo
School of Civil & Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, teocc@ntu.edu.sg
Rohit Bhatnagar
Nanyang Business School, Nanyang Technological University, Nanyang Avenue, Singapore 639798, arbhatnagar@ntu.edu.sg
Stephen C. Graves
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA, sgraves@mit.edu
ake-to-order (MTO) manufacturers must ensure concurrent availability of all parts required for production, as any
unavailability may cause a delay in completion time. A major challenge for MTO manufacturers operating under
high demand variability is to produce customized parts in time to meet internal production schedules. We present a case
study of a producer of MTO offshore oil rigs that highlights the key aspects of the problem. The producer was faced with
an increase in both demand and demand variability. Consequently, it had to rely heavily on subcontracting to handle production requirements that were in excess of its capacity. We focused on the manufacture of customized steel panels,
which represent the main sub-assemblies for building an oil rig. We considered two key tactical parameters: the planning
window of the master production schedule and the planned lead time of each workstation. Under the constraint of a fixed
internal delivery lead time, we determined the optimal planning parameters. This improvement effort reduced the subcontracting cost by implementing several actions: the creation of a master schedule for each sub-assembly family of the
steel panels, the smoothing of the master schedule over its planning window, and the controlling of production at each
workstation by its planned lead time. We report our experience in applying the analytical model, the managerial insights
gained, and how the application benefits the oil-rig producer.
M
Key words: make-to-order; production smoothing; master production schedule; planned lead times; oil-rig building
History: Received: April 2009; Accepted: February 2011, after 2 revisions
(IDLT) to downstream internal customers. Violations
of the IDLT for any part would result in a delay in the
completion time of the end item. Increasing the IDLT
can buffer against uncertainties in the parts’s deliveries, but will result in a longer delivery lead time of the
end item, which is detrimental to customer service.
Ensuring availability of customized parts (for which
the manufacturer cannot keep inventories) is a major
challenge to most MTO manufacturers. The manufacturer must produce these customized parts within the
IDLT to meet the production schedule. In the presence of a highly fluctuating demand, the MTO manufacturer must be able to flex its production capability
in periods of high demand, e.g., by overtime or subcontracting, to meet the IDLT.
This article reports an application that addresses
the aforementioned problem, wherein we propose an
improved production planning framework for a producer of MTO offshore oil rigs. At the time of the
application, the company had experienced a sudden
1. Introduction
An important competitive factor for a make-to-order
(MTO) manufacturer is its ability to meet its promised
delivery lead time. To achieve lead time reliability, a
MTO manufacturer must have a reliable production
plan for determining the procurement of raw materials, the production of parts, and the final assembly
and testing of the end item. Typically, this production
planning is based on material requirements planning
(MRP) logic to coordinate the various decisions. For
instance, the requirements schedule for the parts in
the first tier of the bill of material is determined by
offsetting the end-item assembly schedule by the
planned lead time for assembly. The generation of
part requirements continues for all subsequent levels
of the bill of material in a similar fashion, including
the procurement of raw materials.
Thus, for manufactured parts, we can view their
planned lead times as an internal delivery lead time1
211
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surge in demand due to the global increase in
demand for energy. However, given the cyclical nature of the industry, the firm was hesitant to invest
heavily in expanding its capacity because this could
result in over-capacity during the trough of the cycle.
Historically, the firm’s strategy had been to use subcontracting to handle upswings in its production
requirements. This project was part of an initiative to
improve the company’s production planning to
reduce its subcontracting cost. We focus herein on the
production planning of customized steel panels, as
these represent the key sub-assemblies of an oil rig
and their production is on the critical path of oil-rig
building. The panel production had experienced a
highly variable loading on its capacity, resulting in
high subcontracting costs that were incurred to expedite production to meet the IDLT for the steel panels.
In this article, we report our effort to improve the production planning of panel production with the objective of minimizing subcontracting costs. We apply the
model in Teo et al. (2011) in this case study.
We focus on how best to smooth production in the
multi-station steel panel production. We consider two
key planning parameters, namely the planned lead
time at each workstation and the planning window.
The planned lead time at a workstation projects the
planned amount of time each job spends at the station. A longer planned lead time implies more time at
a station, resulting in more work-in-process (WIP) at
the station, but allowing for smoothing of the workload. The planning window is the slack that reflects
how much longer the IDLT is than the total planned
lead time for a job. A longer planning window allows
more smoothing of the master production schedule
(MPS), which results in a less variable work release.
In this project, we first recommended the tactics of
MPS smoothing and the use of planned lead time control for the individual workstations. Subsequently, we
determined the optimal planning windows and
planned lead times that minimize the subcontracting
cost.
There is substantial literature on production
smoothing in make-to-stock production, most of
which focuses on the benefits of a stable capacity
loading. However, there is not much work on production smoothing in the MTO context. Cruickshanks
et al. (1984) consider production smoothing in a single-stage, MTO facility and introduce the concept of
the planning window. Teo et al. (2011) also consider
the planning window in smoothing the MPS, as well
as planned lead time control in a multi-product,
multi-station system. Furthermore, the article considers a production system that quotes a fixed delivery
lead time, which is analogous to the fixed IDLT of the
customized steel panels in this case study. Indeed, the
model employed in this application comes from our
work in Teo et al. The current article complements
Teo et al. in that we show here with a real-life example that MPS smoothing and planned lead time
control are effective tactics to improve production
planning. Furthermore, we discuss the issues of
implementing such tactics and develop managerial
insights on the relationship between the key planning
parameters. We believe this case study is representative of many MTO manufacturers and thus, we expect
the insights derived to be useful for practitioners. This
is especially true in the light of the current trend
toward mass customization, as firms increasingly
need to respond to customer pressure for greater
product variety. This case study is also related to
work on MTO production that quotes a fixed delivery
lead time. So and Song (1998) and Rao et al. (2005)
determine the fixed quoted delivery lead time to maximize profits for a single-stage system that produces
an aggregate product. This article differs from both
these works in that our paper is practice-based and
our analysis encompasses decisions associated with
the MPS and internal lead times in a multi-station,
multi-product environment.
This article is organized as follows. In the next section, we review the model in Teo et al. (2011) that was
applied in this case study. In section 3, we describe
the process flow and the problems of planning in the
panel production. We then describe in section 4
the initial study and the plans for improvement. In
section 5, we present the optimization model from
Teo et al. and describe how we validate the underlying model assumptions and parameterize the model
inputs. In section 6, we explain the recommendations
and managerial insights based on the optimization
solution. Subsequently, we validate the model output
in section 7. We conclude in section 8 with a discussion on how the application had influenced the
company.
2. Review of Model
For completeness, we provide a high-level review of
the model in Teo et al. (2011). Teo et al. consider a
MTO, multi-station production system. The system
produces multiple product families, each with a
stochastic demand process and a fixed, guaranteed
delivery lead time. The production schedule is controlled by the MRP-based logic, where the planned
lead time at each workstation controls the production
quantities. We will present the review in the context
of this article, i.e., production planning to meet internal orders. The “fixed guaranteed delivery lead
times” and “product families” in Teo et al. correspond to the IDLT and sub-assembly families, respectively. Note that we will present only the aspects of
the model that are useful to the case discussion.
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
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2.1. Product Planned Lead Time
We begin by defining the product planned lead time
PPLTk as the total planned duration that a job from
sub-assembly family k takes to be completed by the
shop after it is released into the shop. In addition, for
each workstation, we define the station planned lead
time SPLTi as the planned lead time at workstation i; it
is the intended amount of time to complete processing
of each job at the workstation, including both processing and waiting time. We assume each workstation
has the same planned lead time for all sub-assembly
families. We can express PPLTk by:
PPLT k ¼
X
xik SPLTi ;
ð1Þ
i
where xik is the number of times that each job from
sub-assembly family k visits workstation i, assuming
that each sub-assembly family has a pre-determined
job routing.
2.2. MPS Smoothing
The model assumes that orders arrive in each period
according to a random process, with delivery dates
specified by the IDLT. In addition, the MPS dictates
how these orders are met. More specifically, we
equate the MPS with the release schedule to meet the
orders.
Nominally, MRP logic would dictate that an order
with due date t + IDLTk is released at time t +
IDLTk PPLTk. We deviate from this logic to allow
the smoothing of the MPS, and hence, less variable
job releases into the shop. Smoothing of the MPS for
each sub-assembly family k is possible only if its internal delivery lead time IDLTk is longer than its PPLTk.
We define the resulting slack as the planning window
W k:
Wk ¼ IDLTk PPLTk þ 1:
ð2Þ
For orders received at time t, the planning window
spans from t + PPLTk to t + IDLTk. The MPS over the
planning window (i.e., the production quantities to be
completed over t + PPLTk to t + IDLTk) can be leveled, where the extent of leveling depends on Wk; a
larger planning window allows for a more even
spread of the MPS. We note that if IDLTk = PPLTk,
then Wk = 1; this corresponds to no smoothing of the
MPS since the releases in each period t must correspond exactly to the quantities to be completed in
t + PPLTk.
2.3. Workstation Control
Besides the variable MPS, the effective workload at
the workstations fluctuates over time due to varying
job arrivals and production noise, e.g., setups, yields,
and variable processing times. A longer SPLTi permits
a smoother production at the workstation as it has
greater flexibility to level out the variation in workload arrivals over the SPLTi. However, with a longer
SPLTi, jobs stay longer at the workstation, which leads
to a higher WIP inventory.
2.4. Optimization Model
Given that the IDLTk is fixed, the decision variables
are the SPLTi, which would determine the PPLTk
and Wk according to (1) and (2). Increasing the
PPLTk, i.e., allowing for longer SPLTi at the workstations, leads to more smoothing for both job arrivals
and production noise at the stations, but it would
lead to a higher WIP inventory level. A longer
PPLTk also implies a smaller Wk, which causes a less
stable job release and consequently more variable
job arrival at the workstations. In addition, a longer
SPLTi not only smoothes the workload at the workstation, but also smoothes the arrivals to downstream stations.
We now consider how the aforementioned decision variables can affect the relevant production
costs. We let Pit be the random variable denoting the
production requirements in workhours at workstation i in time period t. We interpret Pit as the production quantities required at station i in period
t that assure the work-in-queue meets the SPLTi.
Furthermore, we define Pit as the effective production
output as we assume it includes both scheduled
workload and (unscheduled) production noise. We
let ci be the penalty cost per workhour of capacity
shortfall, which may represent, e.g., subcontracting
cost and overtime cost; mi denotes the nominal
capacity for workstation i in workhours per period;
hik represents the unit WIP inventory holding cost
(per workhour per period) at workstation i for product family k; Qikt denotes the queue length in workhours at start of t for product family k at station i.
We express the expected total cost across all workstations as:
"
#
X
X
þ
ci E½Pit mi þ
hik E½Qikt ð3Þ
i
k
where x = max (x, 0). The term ciE[Pit mi]+ is the
expected penalty cost at workstation i resulting from
capacity shortfall, i.e., if Pit > mi. We assume that
whenever Pit > mi, the station is always able to complete Pit but it incurs ci per hour for all production
in excess of mi. A more variable Pit leads to a higher
expected penalty cost with its variability controlled
by Wk, PPLTk, and SPLTi. The term hiE[Qit] signifies
the expected WIP inventory holding cost at workstation i, where a larger SPLTi yields a higher WIP
inventory level.
+
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Equation (3) forms the objective function of the
optimization program that determines the optimal
SPLTi and Wk. (To achieve a better flow of this article,
we will defer the presentation of the optimization
model to Section 5.) We compute Ri ci E½Pit mi þ by
the linear loss integral, assuming that Pit is normally
distributed. In the rest of this section, we present the
characterization of the first two moments of Pit
required for the computation.
2.5. Characterizing Pit for a Single Sub-Assembly
Family
We first consider a single sub-assembly family and
we drop the subscript k for notational convenience.
We assume that the demand for each sub-assembly
family is independent and identically distributed over
time. For tractability, we introduce a dummy workstation to model the MPS smoothing and work
release. We regard the unreleased orders as a demand
queue at this dummy station, waiting to be released
into the shop. The job arrival to the dummy station
(station 0) in period t is the demand in t and the
production output corresponds to the job release.
We model the MPS smoothing by:
P0t ¼
Q0t
;
W
ð4Þ
where P0t is the production output (job release) in
period t, Q0t is the queue of work at the start of period t and W is the planning window (W 1). In (4),
the shop releases 1/W of the on-hand orders in each
period to approximate the requirement that every
order does not wait more than W periods. Equation
(4) models the smoothing of the release by spreading the on-hand orders evenly over the planning
window.
The model permits the linkage between discrete
time planning and intra-period workflow. In particular, it models the MPS in discrete time buckets and
the arrivals and production at the station are assumed
to occur over smaller time grids to permit multiple
arrivals and production within each time bucket. Specifically, each time period t at station i is sub-divided
into pi equal sub-intervals, each with size Di = 1/pi.
The main assumption here is that the workstation
produces a fixed fraction Di/SPLTi of the work-inqueue at the start of each sub-period. The resulting
production rule is similar to (4) albeit it is a function
of the time grid. Effectively, the workstation i must
not allow work to wait for more than SPLTi periods
and thus it must process close to Di/SPLTi of the
work-in-queue in each sub-period. In addition, to
achieve tractability, the work arrival at the workstation in period t, which we denote as Ait, is assumed to
be uniform within each period t; that is, the arrival
amount at the start of each sub-period is equal to
Ait/p.
Teo et al. derive an expression for Pit, which is
given by:
Pit ¼ bi ði ÞQit þ ci ði ÞAit ;
ð5Þ
where the coefficients b(Di) and c(Di) are expressed
as:
bi ði Þ ¼ 1 ½1 ði =SPLTi Þpi and
1 ði =SPLTi Þ
ci ði Þ ¼ 1 bi ði Þ
:
ð1=SPLTi Þ
ð6Þ
Equation (5) expresses the production in each time
period as a linear function of both the work queue at
the start of the period and the arrivals during the period. The sub-interval Di reflects the size of underlying
time interval for job movements at workstation i,
where Di is set on the order of the average interarrival time. If the workflow is of a high enough
frequency, the workflow can be approximated as a
fluid-like workflow by considering the continuous
time limits for bi(Di) and ci(Di) as Di goes to zero.
The continuous time limits of bi(Di) and ci(Di) are
given by:
bi ð ! 0Þ ¼ 1 e1=SPLTi and
ci ð ! 0Þ ¼ 1 SPLTi bi :
ð7Þ
Teo et al. show by a simulation study that accurate
model output can be achieved if the appropriate coefficients are employed.
2.6. Workflow Model
The workflow model links the MPS smoothing and
the network of workstations so as to capture their interdependencies. We assume that each workhour of
production at station j generates uij workhours of
input to station i on average. We model the work
arrivals to station i by
X
Ait ¼
uij Pjt :
ð8Þ
j
For the dummy station (station 0), we note that ui0
is the average amount of work that starts at workstation i for each new job. Furthermore, we express the
balance equation at workstation i as:
Qit ¼ Qi;t1 Pi;t1 þ Ai;t1 þ fit ;
ð9Þ
where fit denotes the random production noise at
workstation i. By expressing (5), (8), and (9) in matrixvector form, Teo et al. then obtain the vector of expectation of Pit and Qit, and covariance matrix of Pit for all
stations, namely E[P], E[Q], and Var(P), respectively.
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
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Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
To extend the single-family model to accommodate
multiple sub-assembly families, we model each subassembly family the same way as in the single-family
model, i.e., each product family k has an MPS and
each family has its own demand process, routings,
and production noise. The single-family model characterizes the production requirements and WIP
inventory for sub-assembly family k, i.e., E[Pk], Var
(Pk), and E[Qk]. We can obtain the expectation of
the total production requirements and WIP inventory by aggregating
across all sub-assembly
P
P families:
E½Ptotal ¼ k E½Pk and E½Qtotal ¼ k E½Qk . If
demand is independent between the sub-assembly
families, we can obtain the variance of the total production requirements:
VarðPtotal Þ ¼
X
VarðPk Þ:
ð10Þ
k
We can relax the assumption of independent
demand by incorporating demand correlations
between the sub-assemblies into (10) (refer to Teo
[2006] for details).
3. Panel Production: Process Flow and
Challenges
The company is a producer of customized jack-up oil
rigs. Jack-up oil rigs are offshore rigs that are mobile
in water, and can anchor themselves by deploying
jack-like legs. The fundamental structure of the oil rig
is the hull, which is the platform on which most facilities of the rig are built. A typical hull consists of steel
blocks; each steel block is constructed by joining steel
structures called panels. A block commonly consists
of 10 to more than 60 panels. The steel panel represents the most elementary sub-assembly in the hull
construction. A panel is built using one or more steel
plates, with outfitting components welded onto it to
strengthen the structure.
There are three sub-assembly families in the panel
production: Big Panels, Small Panels, and Outfits. Big
Panels are panels built by joining two or more steel
plates, while the Small Panels are built using a single
steel plate. The size of the panels varies widely with
the weight of a panel ranging from 0.5 to 10 tons. The
Outfits are the outfitting components welded onto
the panels. Figure 1 shows the process flow map for
the panel production.
At the Blast station, raw plates are “blasted” by ball
grids to remove surface impurities, followed by the
application of a corrosion preventive coating. The typical raw steel plate is 1.5 m wide, 8 m long, and has a
thickness of ¼–¾ inch. The blasted plates are sent to
the NC Gas Cut or NC Plasma Cut stations to be cut to
the required dimensions. The NC Gas Cut station is
capable of cutting both thin and thick plates, while
the NC Plasma Cut station can only cut thin plates.
The Big Panels require thick plates and are therefore
sent to the NC Gas Cut station. The Small Panels
require thin steel plates but are processed at the NC
Gas Cut station to balance the workload between the
two stations. For the same reason, although the Outfits
also require thin plates, a fraction of the Outfits are cut
in the NC Gas Cut station while the rest are processed
at the NC Plasma Cut station. After cutting, the parts
remain joined to the steel plate by connectors called
“bridges,” and these are manually cut at the Bridge
Cut station.
Subsequently, the plates for each sub-assembly
family follow different process routes. The thick
plates for the Big Panels are beveled at the Bevel
station, and then go through a series of welding
processes at the Tack and Join stations to join the
plates to form the basic panel structure. The panels
are then paint-marked at the Mark station to indicate
Figure 1 Process Flow Map for Panel Production
Raw
steel plates
Blast
NC
Plasma
Cut
Blasting
Shop
Outfits
NC
Gas
Cut
Profile
Outfitting
(Small
Panels)
Small Panels
Bridge
Cut
Bevel
Tack
Join
Mark
Outfitting
(Big
Panels)
Panel
Shop
NC
Shop
Big Panels: Blast NC Gas Bridge Cut Bevel Tack Join Mark Outfitting (Big Panels)
Small Panels: Blast
Outfits: Blast
NC Gas
Bridge Cut
NC Plasma or NC Gas
Mark
Outfitting (Small Panels)
Bridge Cut Profile Shop Outfits (both Big and Small Panels)
216
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the positions of the Outfits to be fitted. Eventually, the
Big Panels are moved to the Outfitting (Big Panels) station to weld the Outfits. Since the Small Panels are built
using a single plate, no welding is needed and they
are moved directly to the Mark station and subsequently to the Outfitting (Small Panels) station. The
Outfits are sent to the Profile Shop from the Bridge Cut,
where the cut steel parts undergo some simple metal
forming operations to produce the outfitting components. Finally, the Outfits are transferred to either the
Outfitting (Big Panels) or the Outfitting (Small Panels)
to be fitted onto their corresponding panels. The completed panels are then ready for quality checks before
moving downstream to construct the steel blocks.
The panel production shown in Figure 1 occurs in
three separate shops, namely the Blasting Shop, NC
Shop, and Panel Shop, which are physically located
next to each other. The Blasting Shop consists of the
Blast station, the NC Shop has the two NC cutting
stations, and the Panel Shop includes the rest of the
processing stations. Production control for the panel
production had been based on the planned lead times
at the shop level. The planned lead times for the Blasting Shop, NC Shop, and Panel Shop were 5, 8, and
13 days, respectively, resulting in an IDLT of 26 days
for the panel production; that is, the panel production
facilities need to deliver each internal order of panels
exactly 26 days after receipt of the order.
Any delay in delivering the panels hinders the
downstream assembly for the steel blocks, which
might in turn affect the meeting of the promised oil
rig delivery dates. The progress of jobs is monitored
against the shops’ planned lead times to approximate
whether or not jobs are able to meet the delivery schedule. In times of high capacity loading, jobs are subcontracted to vendors to keep them from falling
behind their planned lead times. Most of these vendors are located close by or within the panel production facility itself. While the production schedule of
the Panel Shop is monitored based on the shop’s
planned lead time, work can be outsourced at each of
its individual workstations. Production planning
relies on a single MPS for all sub-assembly families.
In addition, there is no regulation of the MPS and the
job release, whereby jobs are released once the orders
are received from the downstream internal customers.
With the surge in demand, most workstations in the
production shop experience a heavier and more variable workload, which results in rising subcontracting
costs. The company sought to increase its utilization
of in-house capacity and to reduce subcontracting
costs.
The management identified that one cause of the
variable workload was the highly fluctuating MPS.
The MPS was highly variable for three reasons. First,
the production schedules of panels for the different
oil-rig projects were not well coordinated. As a result,
the total internal demand for panels was quite variable and resulted in variable work release. Second,
raw steel plates of required thickness and grades were
frequently unavailable, and this delayed the release of
some panels. Third, the raw steel plates were stacked
to conserve space and therefore, finding the required
plate often took substantial time; this added considerable variability to the picking time of the raw plates.
In addition to the varying MPS, another cause for the
large workload variability was the diverse processing
requirements at the workstations, due to the different
sizes of plates as well as the different number of
plates and outfitting components required for each
panel. The challenges in the panel production are
illustrated in Figure 2.
The management recognized that addressing these
causes could lead to a reduction in production variability. However, they believed that this would
require a long-term effort and would depend on factors external to the company. Coordination of the
project schedules would involve coordination
Figure 2 Challenges in Panel Production
Highly fluctuating MPS
translates into highly
variable release
High variability leads to
high subcontracting costs
Blasting
Shop
• Project schedules are not well
coordinated
• Raw steel plates are often unavailable
• Much time needed in locating plates
NC
Shop
Panel
Shop
Diverse processing requirements
Many different cut dimensions of
plates, as well as variable number of plates
and outfitting components for each panel
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
between the company’s various departments as well
as with its customers on delivery schedules. Improving availability of raw steel plates would need better
coordination with suppliers and more accurate forecast of global steel supply. Shorter picking times for
steel plates would require considerable capital
investment and time to devise new ways or equipment for material handling. Reducing the diverse
processing requirements would need standardization
of panel types, which would involve setting restrictions on oil-rig customization that might be detrimental to customer satisfaction. The management
decided that to reduce subcontracting cost within the
short term, they should focus on tactical improvements.
The panel production highlights the problems faced
by many MTO manufacturers in producing customized parts to meet a production schedule. The characteristics of the panel production encompass various
operational aspects that can be found in many production systems: a highly variable MPS, multiple
product families and process routes, dissimilar processing requirements, and expediting actions taken to
meet delivery schedules.
4. Initial Study and Recommendations
The company learned about the concepts of MPS
smoothing and lead time control from our work in
Teo et al. (2011) and wished to explore if the tactics
would be of help to improve the company’s performance. A team was formed, consisting of the authors
and personnel from the production department. After
a careful study of the model, the production personnel were particularly interested in two potential
improvement areas as follows.
4.1. Smoothing of MPS
The production personnel recognized that a smoother
MPS results in a less variable release and consequently fewer occurrences of “spikes” in capacity
loading. The company became interested in finding
out how the MPS can be smoothed in the panel production. The team recognized that the MPS can be
smoothed over the planning window for each subassembly family if its IDLTk to its internal customer is
longer than its PPLTk.
One seemingly obvious solution was to increase the
IDLTk to allow a longer planning window and PPLTk.
However, the management did not wish to change
the current internal lead time for panel production of
26 days, as the panel production is on the critical path
of oil-rig building and they did not want to affect the
delivery schedule of the oil rigs. Therefore, the team
had to find other ways to smooth production given
the fixed IDLTk.
217
Initial recommendation 1. Upon studying the process
flow, the team identified that the Small Panels and Outfits
require fewer processing steps than the Big Panels. Thus, if
each sub-assembly family has its own MPS and is planned
separately, each of the Small Panels and Outfits would have
a much shorter PPLTk. Hence, given that the IDLTk is the
same for each family, the planning window Wk would be
considerably large for both sub-assembly families to perform
substantial MPS smoothing. Thus, it was recommended
that an MPS is created for each sub-assembly family.
4.2. Smoothing at Stations
The team recognized that the production control in
the Panel Shop had been based on the shop’s planned
lead time, rather than for its individual workstations.
As a result, subcontracting decisions were often
“guesswork” of predicting if a job could be completed
in time to meet its due date. Furthermore, the planned
lead times for the three shops were set based upon
the experience of the production planners without
any analytical basis.
Initial recommendation 2. The team recommended a
station planned lead time SPLTi for each workstation in the
Panel Shop, whereby the progress of jobs could be tracked
more precisely. The team also identified an opportunity to
achieve a smoother workflow by determining the optimal
values of SPLTi.
4.3. Planning Decisions
The team then looked into the planning parameters
and trade-offs in the panel production. We found
that we could omit the holding cost of the WIP
inventories from our analysis. We note that the
exclusion of WIP inventory holding cost differs from
Teo et al. and other earlier work on setting planning
lead times, which consider the trade-off between
capacity requirements and WIP inventory. The primary reason for excluding the WIP inventory is that
the total inventory held by the firm is insensitive to
the planning decisions under consideration. The
majority of raw steel plates required for the entire
oil rig are purchased before the start of each project,
so the material cost of the steel plates represents a
sunk cost, i.e., it is incurred regardless of how we
release work into the production shop. Furthermore,
since the IDLT is fixed, the raw plates stay in the
production system for approximately the same duration no matter how the plates are scheduled. In addition, the team found that the value added to the jobs
through processing (and hence the incremental holding cost) is significantly less than the subcontracting
cost.
The team re-evaluated the key trade-offs and identified the following planning considerations for the
panel production:
218
•
•
•
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
The team needed to set the planning window
Wk and the SPLTi of each workstation (which
determines PPLTk). The planning window
smoothes the MPS (and release) and the PPLTk
(i.e., the sum of SPLTi) smoothes both the arrivals and the noise due to the variable processing
times at the workstations.
Without considering the WIP inventory, the
decision is to allocate SPLTi among the workstations solely to minimize the total subcontracting
cost. The subcontracting cost incurred at each
workstation depends on its unit subcontracting
cost, nominal capacity level, and variability in
job arrival, and processing times.
In this multi-station, multiple-family setting, the
team needed to take into account the interdependence of workflow among the stations as
well as among the sub-assembly families.
The team recognized that the main features of
the panel production could be modeled by Teo
et al.: production control using planned lead times,
influence of MPS smoothing on production workflow, variability at the workstations as well as
subcontracting production to meet the capacity
shortfall. However, before applying the analytical
model, we also considered other simpler alternatives. For example, the team considered setting
the SPLTi of all stations to be proportional to each
station’s utilization rate while satisfying the IDLT
constraints. The rationale behind this method was
that the more heavily utilized stations would need
longer station planned lead times. However, this
method would not be able to account for many
important aspects of the scenario, e.g., the variability of demand and processing requirements, the difference in subcontracting cost between stations and
the interdependencies of workflow between stations. The team also considered the alternative of
using a discrete-event simulation. However, they
found that simulation was not suitable for the
extensive “what-if” analysis they would like to perform, as it would be slow to make the numerous
simulation runs, especially the runs requiring optimization. Furthermore, the management preferred a
method that did not require an extensive learning
process for its personnel. As our model was formulated and solved in MATLAB, the management
thought that the planners and engineers could readily learn how to use it. In addition, the model
parameters, e.g., unit subcontracting cost, workflow,
and capacity levels, could be easily altered according to actual changes. Moreover, MATLAB provided an optimization toolbox that could be used
to find the optimal planning windows and station
planned lead times.
5. Model Application
5.1. Optimization Model
We present the optimization model from Teo et al.
(2011) but our objective in this application differs in
that we minimize just the expected total penalty cost
in (3) (i.e., we exclude the WIP inventory holding
cost). The decision variables are the SPLTi of each
workstation and planning windows Wk of each subassembly family k. The discrete time period t of the
model is one day, which is the time bucket used in
the existing planning system.
X
Min
ci E½Pit mi þ
i
s:t:
X
SPLTi þ Wk 1 ¼ IDLTk ; 8k
ð11Þ
i
W k a k ; 8k
ð12Þ
SPLTi bi ; 8i
ð13Þ
To evaluate the objective function, we need to
determine the variances of the random variables Pit;
these depend on the workstation’s SPLTi (5 and 6),
the SPLTi of its upstream workstations and the planning windows Wk. Constraint (11) combines (1) and
(2), which defines the relationship between Wk, SPLTi,
and IDLTk, where IDLTk are fixed at 26 days for all
sub-assembly families. We note that in (11), xik = 1
for all i and k since every job visits each workstation
once. Constraints (12) and (13) assure a lower bound
of at least ak and bi on the Wk and the SPLTi, respectively. Lower bounds of SPLTi and planning windows
are needed to avoid excessively frequent monitoring
to track the job progress and the MPS. We set both ak
and bi to be 1 day, as the planning time bucket of
1 day was the minimum duration that the management perceived to be suitable for planning within this
highly dynamic system. The decision variables were
not restricted to be integers, as non-integer values
were acceptable for production control. The team set
the SPLTi s of the Profile Shop which produces the Outfits, to be fixed at 2 days, as the station’s processing
time is relatively stable and reasonably independent
of the workload.
As reported in Teo et al., we have not been able to
determine whether or not the objective function is
convex. Therefore, we cannot assert that the solutions
are global optimal. In this exercise, we solved each
test problem using many different starting points. We
attained the same solution for each test problem,
which increased our confidence that we had obtained
a global optimum.
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
5.2. Validation of Model Assumptions
The team validated the following assumptions in Teo
et al. for the current study.
5.2.1. Capacity Assumptions. Equation (3) assumes
that every workstation is always able to meet the
production requirements, although it incurs additional cost per workhour of capacity shortfall. In the
panel production, subcontracting is routinely used
to expedite work to meet the production requirements. Since the subcontracting is performed in
nearby shops and by on-site contract workers, relatively little time is wasted in transporting the jobs.
Furthermore, from the management’s experience,
there are very few occurrences where the subcontractors failed to produce the outsourced demand
within the SPLTi. The team also examined the
assumptions for the nominal capacity mi. To apply
(3), mi must be measurable and its value assumed to
be constant. It is straightforward to measure mi for
NC Gas Cut and NC Plasma Cut stations as both are
machine constrained. We observed that the other
stations operate with skilled workers, some of whom
are cross trained to work at more than one station.
Thus, there is some flexibility in allocating workers
to the heavily loaded stations, which somehow disagrees with the assumption of constant nominal
capacity. However, the team found that such redeployment of workers was infrequent after the
company experienced the high capacity loading
due to the demand increase. This is because the
stations with cross-trained workers become heavily
loaded at the same time, thus preventing labor
re-allocation.
5.2.2. Workflow Assumption. In deriving (5), the
arrival to the workstation is assumed to be uniform
within each time period t. However, in the panel
production, jobs start to move to the next station
upon completion and therefore the arrival at the
downstream station is not exactly uniform within
each period. Teo et al. validate this assumption via
a simulation model wherein jobs move to the next
station immediately after completion. The study
shows that the simulation results are close to the
model output despite relaxing the uniform flow
assumption; the errors are small provided that the
appropriate production function (i.e., either the subinterval function (6) or the continuous-time function
(7)) is chosen at each workstation according to the
average flow rate. The average percentage difference between the simulation results and the model
output is 2.3% for all test problems and the maximum error is 6.5%. The study also establishes the
range of average flow rates that (6) or (7) should be
219
selected. The team observed that the arrival rates
are low at Join, Mark and both the Outfitting
stations, as these stations assemble or process panels rather than plates and Outfits. As a result, the
arrival rates at these stations fall within the range
of flow rates found in the simulation study that
necessitates the use of the sub-interval function (6).
Thus, we employed the sub-interval function for
these stations. The other stations have sufficiently
high flow rate to justify the continuous-time
assumption and hence the continuous-time function
(6) was utilized.
5.2.3. Production Assumption. The development
of (5) assumes that the workstation is regulated to
produce a fixed fraction of the work-in-queue to satisfy its SPLTi, even if capacity is available to produce
the entire work-in-queue. In the panel production, the
job start times at NC Plasma, NC Gas, Tack, and Join
stations are scheduled to coordinate with the receipts
of engineering drawings for cutting and welding
(which is similar to the synchronization of part
requirements in MRP logic). Furthermore, due to the
large physical size of the jobs and the space constraints in the facilities, the stations usually produce
just to meet the SPLTi, so as to avoid taking up the
downstream shop space unnecessarily. To compute
the total penalty cost in (3) (that forms the objective
function) using the normal linear loss integral, Pit is
assumed to be normally distributed. To validate this
assumption, we constructed normal probability plots
for the daily production output from a 2-month data
and the plots showed that this assumption is reasonable.
5.2.4. Demand Assumption. In contrast to the
assumption of stationary demand, the observed
demand for each sub-assembly family is generally
non-stationary. However, if the time horizon is
considered as successive time segments, with each
segment representing a constant number of oil rigs in
production in their respective stable project phase, we
observed that the demand is stationary within each
time segment. Each time segment typically ranges
from about 15 to 45 days. In addition, the daily
demand data showed a fairly constant coefficient of
variation (standard deviation mean) of demand
within each segment. We show the demand data for
the Big Panels over a 3-month period in Figure 3.
To test the sensitivity of our solution to the nonstationary demand, the mean demand for each
sub-assembly family was set to be either 100% or
125% of the original mean demand while keeping the
demand coefficient of variation constant. The analysis
showed that for all eight test scenarios, the subcontracting cost resulting from the original demand’s
220
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
Figure 3 Demand for Big Panels over 3-Month Period
optimal station planned lead times is no more than
4% higher than the test scenarios’ minimum subcontracting cost.
correlation coefficients at more than 0.70. We modeled
correlated demands between product families for (10)
by incorporating the demand correlations.
5.3. Data Collection
We discuss the data required for the model inputs,
and how we obtain and parameterize the relevant
data.
5.3.4. Effective Processing Times. We acquired
the mean and variance of the effective processing
times (in hours) at each station from data collected in
a 2-month period. We needed the mean processing
times to define the workflow matrix consisting of uij,
which defines the average amount of work that each
unit of production at a station generated for each
downstream station. The variance of the processing
time at each station is required to calculate the zeromean noise term nit at each station. We computed the
noise due to the variability of processing time by:
5.3.1. Capacity. To measure the nominal capacity
levels mi, we observed the throughput rate in periods
of high demand, when most stations were operating
at full capacity. We approximate mi by the mean
throughput (in hours) per day observed in these
periods.
5.3.2. Subcontracting Cost. The vendors quote
the subcontracting costs in terms of cost per metric
ton. Since workload in our model is measured in
hours, we had to convert the subcontracting cost at
each station into average subcontracting cost per
workhour ci. We approximated the average subcontracting cost based on the average weight of the jobs
at the station (in metric tons) and the mean processing
time of the jobs (in hours).
5.3.3. Demand. We obtained the mean and standard deviation of the internal demand for each subassembly family from an 8-month demand record.
We found a low correlation coefficient of 0.13 between
the demands of Big Panels and Small Panels. However,
the correlations between Big Panels and Outfits as well
as between Small Panels and Outfits, are high with
Varðnit Þ ¼ Expected number of jobs at station i
Variance of processing time
6. Results and Insights
We report the optimization results as well as the corresponding expected subcontracting work and costs
in Table 1. The subcontracting costs presented herein
have been scaled to protect the company’s confidential data, but the insights drawn are identical to the
conclusions based on the actual data.
With a separate MPS for each sub-assembly family, there is a greater flexibility to adjust the planning
windows of each sub-assembly family for a
smoother release. The solution suggests that there
should be substantial smoothing for the release of
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
221
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
Table 1 Optimization Results
Planning window for Big Panels
Planning window for Small Panels
Planning window for Outfits
Blast
NC Gas Cut
NC Plasma Cut
Bridge
Bevel
Tack
Join
Mark
Original Wk or SPLTi
Optimal Wk or SPLTi
Expected subcontracting
work (hours/day)
Expected subcontracting
cost ($/day)
1.0
1.0
1.0
5.0
8.0
8.0
1.0
10.8
9.8
1.0
4.4
4.4
3.1
1.0
1.0
7.8
1.0
–
–
–
0.13
0.37
0.12
0.12
<0.01
<0.01
5.96
<0.01
–
–
–
73
155
60
143
<1
<1
775
<1
6.6
5.83
874
6.6
4.39
351
m
Panel Shop
13:0
Station
Outfitting (Big Panels)
Outfitting (Small Panels)
.
Small Panels and Outfits, with planning windows
equal to 10.8 and 9.8 days, respectively. The planning window for Big Panel is 1 day, meaning no
smoothing of its MPS.
The solution suggests that the SPLTi of Blast should
be reduced from 5.0 to 1.0 day, and NC Gas Cut and
NC Plasma Cut from 8.0 to 4.4 days. A proportion of
the original SPLTi at these stations acts as safety time
to buffer against the uncertainties of unavailable steel
plates and the long picking times. For the Small Panels and Outfits, most of the excess days from this
reduction are reallocated to their planning windows.
Here, the planning windows would not just smooth
the MPS but also act as the safety times for acquiring
steel plates. For the Big Panels, the SPLTi of the Blast
station is mainly reallocated to the other workstations.
The optimal SPLTi at the Join station is the largest
among the workstations at 7.8 days. We observed that
the utilization rate at the Join station is more than
90%; its processing time is also highly variable, with a
coefficient of variation of 0.76. The optimal SPLTis of
Outfitting (Big Panels) and Outfitting (Small Panels) are
also high at 6.6 days, but still lower than Join, despite
both stations having higher utilization rates and coefficient of variation for their processing time. The
reason is that the larger SPLTi at the Join station
would smooth the production output, which in turn
would lead to smoother arrival at the downstream
Outfitting (Big Panels) and Outfitting (Small Panels).
The solution also suggests that Bevel, Tack, and Mark
stations have the shortest station planned lead times
of 1.0 day due to their comparatively lower utilization. Even with a station planned lead times of
1.0 day, the expected subcontracting costs are low at
these stations.
By exercising the model for different what-if scenarios, the team developed the following insights for
setting the planning windows and station planned
lead times:
•
•
•
The team gained insights on the interaction
between the planning windows and the station
planned lead times. A longer planning window
is preferred if a sub-assembly family faces a
highly variable demand and relatively lower
workload variability at the stations. On the other
hand, if the variability of processing time at the
stations is relatively larger, longer station
planned lead times are preferred to smooth production at the workstations.
A workstation would require a longer SPLTi if it
faces greater variability in processing requirements, has higher utilization rate and/or unit
subcontracting cost. The management had previously thought that the SPLTi should be based
only on the utilization rate.
Smoothing at an upstream station has the added
advantage of smoothing the arrivals to downstream stations. The management learned that
looking at each individual station in isolation is
suboptimal.
We note that in situations where the WIP holding
cost is significant, one also has to consider that longer
SPLTis lead to higher WIP inventory levels. The above
insights are useful for understanding the trade-offs
among capacity, lead time, and production smoothness.
7. Validation
The team attempted to validate the predictive capability of the model, i.e., the accuracy of the model in
characterizing the panel production. The most useful
validation would be to compare the actual amount
of work subcontracted out with that predicted by the
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
222
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
model. However, the subcontracting decisions in the
Panel Shop were based on the aggregate planned lead
time of the shop. In our model, production control is
set based on the SPLTi of individual stations. Thus,
the above comparison could not be made for the
Panel Shop and unfortunately, this is where most of
the workstations are located. For the Blasting Shop
and NC Shop, we found that the amount of subcontracted work predicted by the model is about 26%
and 21%, respectively, lesser than the actual data for
the two stations. The team viewed this as a reasonable validation given the presence of high variability
in the system and the somewhat incomplete subcontracting data, since the company did not keep an
organized record of subcontracting cost incurred at
Adjusted subcontracting cost ¼ 100%
Computed subcontracting cost
100% þ Percentage error
each workstation. After the recommendation to
assign the SPLTi to individual stations was implemented, new and more comprehensive data on subcontracting costs became available. We re-validated
the predictive capability of the model and found that
the model output is about 9% lower than the actual
costs; this error is significantly lower than the initial
limited validation using data only from the Blasting
Shop and NC Shop. The corresponding percentage
difference at each workstation is shown in Table 2.
In the same table, we also present the actual cost at
each workstation as a percentage of the total actual
cost to show the relative significance in cost at each
workstation.
Table 2 Percentage Differences Between Actual Cost and Computed
Cost Per Day (After Adopting SPLTi at Individual Workstations)
Cost of subcontracting
as percentage of total
subcontracting
cost
Actual cost
100% Total
actual cost
Blast
NC gas station
NC plasma
Bridge
Bevel
Tack
Join
Mark
Outfitting
(Big Panels)
Outfitting
(Small Panels)
Before implementing the recommendations, the
management needed to gain confidence in the
results. Given the incomplete subcontracting data at
the time, the team first attempted to determine
rough-cut potential savings that would result from
these changes. The team attempted to compare the
actual subcontracting cost with that computed by the
model. To accommodate the model’s predictive
error, we adjusted the computed subcontracting
costs for the Blasting Shop and NC Shop. Specifically,
we modified the computed subcontracting cost by
the percentage error determined through our
validation of the model’s predictive capability (i.e.,
the aforementioned errors of 26% and 21%,
respectively) by:
Percentage
difference
ComputedActual cost
100% Actual cost
3.0
6.4
2.5
5.9
<1.0
<1.0
30.9
<1.0
11.3
12.5
9.9
3.4
12.7
2.5
10.9
6.6
34.9
9.4
14.4
9.0
As stated earlier, we could not determine the
computation error at the Panel Shop. We use the percentage errors at the Blasting Shop and NC Shop as a
guide and set the Panel Shop’s percentage errors to
be in the range 18–30%. Comparing the resulting
adjusted optimal total subcontracting costs with the
actual average historical cost, we estimated that the
recommendations would result in a 20–30% cost
reduction, which is acceptable to the management.
In another effort to estimate the potential cost savings, the team input the current SPLTis into the model
and compared the resulting total subcontracting cost
with the optimal cost. However, the individual stations in the Panel Shop had not been assigned SPLTi.
To overcome this, the current cost was estimated by
setting the SPLTi of the stations in the Panel Shop proportional to the station’s utilization rate while satisfying the Panel Shop’s planned lead time of 13 days. The
results from this comparison showed that the optimal
solution would reduce the cost by about 21.8%. We
also compared the optimal cost with that of another
alternative in which the SPLTis of all stations were set
proportional to each station’s utilization rate while
satisfying the IDLT constraint. By inputting the SPLTi
based on this alternative into the MATLAB program,
we found that the total expected subcontracting cost
for this alternative is 14.4% higher than that of the
optimal expected cost. We regard the abovementioned comparisons as conservative estimates of the
true savings. This is because the actual production
control of the Panel Shop was based on the shop’s
planned lead time, rather than the more accurate control using the SPLTis of individual stations as
assumed in the comparison.
Teo, Bhatnagar, and Graves: Master Schedule Smoothing and Planned Lead Time Control
Production and Operations Management 21(2), pp. 211–223, © 2011 Production and Operations Management Society
The major limitation of our model is that it does not
account for rush orders of urgent panels. These panels
are crucial components for the downstream steel
blocks and their late completion would lead to serious
delays in the steel block production. These orders are
processed immediately upon arrival and are frequently subcontracted to expedite their completion.
Typically, each order is subcontracted at some
selected stations depending on the order’s processing
requirement; therefore the rush orders do not have
distinct flow paths but have numerous processing
routes. Hence, even though we had explored overcoming this limitation by defining the rush orders as
separate product families, we faced difficulties in
accurately capturing the rush orders with our existing
shop data. Nevertheless, the management concluded
that the collected data, model assumptions, and
results were reasonable and that our model serves
well for tactical planning since it is able to capture the
core features of the problem.
8. Influences on Company
The company adopted the recommendations of creating a MPS for each sub-assembly family and individual planned lead times for each station. In particular,
each MPS is smoothed over the planning window
with the job releases leveled, and the company uses
the station planned lead time to monitor the progress
of jobs at each workstation to determine whether or
not a job should be subcontracted. More specifically,
the shop managers monitor the job progress by
approximating completion time of newly arrived jobs
at each workstation based on estimation of total processing times of the jobs in queue.
Before implementing the recommendations for the
values of the planning windows and SPLTis, the company decided to add production capacity as it
observed a continuous growth in oil-rig demand and
projected that the growth was sustainable. However,
the company did not acquire excessive amount of
capacity to buffer against demand variability but
chose to maintain the strategy of subcontracting.
Therefore, instead of implementing the precise recommendations for the values of planning windows and
SPLTis as a static solution, the company utilized the
model to support the monthly updating of the values
in response to the continual changes in production
capacity. Furthermore, since the model requires large
amounts of data as inputs, the use of the model is
helped by the company’s new initiative to regularly
update shop data.
The company also employs the model for what-if
analysis to support planning; for instance, the model
223
is used by the company to determine how capacity
addition affects subcontracting cost. In addition, the
model is also used as a guide for focusing improvement efforts. The model helped to identify steel availability and production scheduling as two potential
areas in which subcontracting cost could be reduced;
consequently, there were projects carried out to
address these issues (see Huang [2006] and Tan [2006]
for details of these projects). Another significant result
is that the project has led to greater awareness of
the importance of considering the interrelationship
among lead time, capacity, and production smoothness. Furthermore, there is now a greater emphasis on
reducing variability of production. However, we were
not able to quantify the resulting savings in subcontracting cost because of the ongoing changes in the
production shop and oil-rig demand, as well as fluctuations in global steel supply, and subcontracting
charges.
Acknowledgments
This research has been supported by the Singapore-MIT
Alliance (SMA) program. The authors thank the Departmental Editor, Senior Editor, and two anonymous referees
for their valuable comments, which greatly improved the
article.
Note
1
Note that we use the term internal delivery lead time
(IDLT) to represent the total planned lead time of producing
a part or sub-assembly needed for downstream processes.
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