Collator Replacement Integratio=
n Team
Schedule Optimizer Module
Final Report
Dr. Thomas Speller
SYST 798/OR 680
Spring 2009=
Contents
Contents<=
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Figures. <=
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Executive Summary. <=
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Introduction. <=
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Project Development Plan. <=
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Team Roles and Responsibilities<=
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Project Intent, Expected Results<=
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Problem Definition, Mission and Goals<=
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Business Strategy / Business Approach<=
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Recommendations. <=
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Conclusions. <=
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Bibliography. <=
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Appendix. <=
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Figures
Figure 1 Production system schematic diagram<=
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Figure 2 Value stream map<=
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Figure 3 Project schedule<=
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Figure 4 top-level functional requirements<=
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Figure 5 detailed functional requirements=
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Figure 6 detailed non-functional requirements<=
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Figure 7 alternative evaluation process<=
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Figure 8 functional decomposition (initial)<=
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Figure 9 functional decomposition (final)=
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Figure 10 Collator Production Mode Options<=
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Figure 11 Algorithm Illustration<=
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Figure 12 Sample Scheduling Results for March 16=
, 2008<=
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Figure 13 Sample Assignment Results for March 16=
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Figure 14 Weekly sales trend<=
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Tables
Table 1 Roles and responsibilities<=
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Table 2 Prioritized stakeholder wants and needs<=
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Table 3 Definition of terms and acronyms<=
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Table 4 List of constraints<=
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Table 5 Hopper Configuration Worksheet<=
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Table 6 Feeder Positions Calculation<=
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Table 7 Cost calculations<=
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Table 8 Financing cost and break even time<=
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Executive Summary
Scheduling, production specification and collat= ion of Sunday newspaper advertisement inserts is manually calculated and produced = with inefficient equipment. The customer needs the programming logic for an automated solution that minimizes total production cost. Our greedy heurist= ic algorithm solution will calculate repeatable schedules and assign advertise= ments to collator hoppers. Cost savings for best, nominal and worst case scenario= s are calculated for new equipment to support an investment decision of several million dollars. The solution is documented with functional decomposition diagrams, functional architecture diagrams, requirements, mathematical notation, operational use diagrams, value stream mapping, and a business ca= se analysis.
Introduction
We are a team of two systems engineeri= ng and two operations research majors in the Master’s degree program at Maso= n. Our capstone course customer is the production department of a major national d= aily newspaper. They currently sell and distribute approximately 920,000 advertisement insert packages with every Sunday edition of the newspaper. Physical collation, bundling and palletizing advertisements for delivery to= as many as 550 zones is accomplished with humans and machinery as shown in REF _Ref229036086 \h Figure 1. The machines have been in continuous operation for thirty years. Scheduling= the sequence of advertisements to be collated into newspaper insert books is currently accomplished manually. The scheduling and hopper assignment proce= sses are based on a penalty matrix of extensive knowledge of what works best. The scheduling subject matter experts have decades of experience with this proc= ess, and replacements will be difficult to train when retirement occurs. In addition, the changing nature of the newspaper advertising business has necessitated increased complexity. The environment has increased from a lim= ited number of large advertisers and wide distribution to greater numbers of sma= ller sales within subdivided distribution areas. Finally, the existing equipment= is reaching the end of its useful service life. The combination of these facto= rs has resulted in reduced margin that should be improved with new technology solutions.
![](3D"CRITFinalReport_files/image002.jpg")
=
Figure 1
The goal of the project is to produce = an algorithm that creates practical schedules and material handling equipment = configurations responsive to physical conditions on the shop floor, advertising and circulation requirements. The primary objectives of this project are to define:
·
An investment decision recommendation suppor=
ted
by business case analysis The project development plan is to define and b=
uild a
system that meets requirements (customer needs) without violating constrain=
ts.
We will use GEIA-632 as an informative standard for systems engineering pro=
cess
management requirements because it provides a balanced mix of the entire
spectrum of management and technical processes. Team roles and responsibili=
ties
as aligned with this standard are defined in Table 1.
A spiral development process of requirements elicitation, definition, model=
ing,
prototyping, and validation will be continuously iterated from start to fin=
ish.
This development model is necessary and appropriate to ensure that we deliv=
er a
useful product that the customer can rely on for production scheduling and a
capital investment decision. 1. &n=
bsp;
Strategy a. &n=
bsp;
Use mind ma=
pping
to brainstorm functional requirements, and a combination of deductive,
inductive and abductive reasoning to identify possible solutions <=
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observations c. &n=
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implementation a. &n=
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Follow a cr=
eative
process of discovery based on application of scientific method-controlled e=
xperiments b. &n=
bsp;
Evaluate
scenarios c. &n=
bsp;
Allocate
functions to forms, identify interface requirements and resolve conflicts d. &n=
bsp;
Aggregate f=
orms
and functions, specify interface requirements and resolve conflicts e. &n=
bsp;
Evaluate sy=
stem
architectures suitability and ability to meet requirements f. &n=
bsp;
Select best=
system
physical architecture utilizing morphological analysis with cross-consisten=
cy
checking to identify best instantiations g. &n=
bsp;
Build proto=
type
of best solution, resolve conflicts h. &n=
bsp;
Test, resol=
ve
conflicts, try a different solution if initial is deemed unsuitable i. &n=
bsp;
Validate
performance against customer requirements; maintain bi-directional requirem=
ents
traceability throughout development process to facilitate stakeholder value
mapping j. &n=
bsp;
Invite cust=
omer
to test the prototype solution, solicit feedback k. &n=
bsp;
Build final=
solution l. &n=
bsp;
Deliver to
customer m. &n=
bsp;
Provide ini=
tial
training 3. &n=
bsp;
Most critic=
al
function identification & risk mitigation a. &n=
bsp;
Prioritizat=
ion of
IPC scheduling and hopper assignment/configuration designation to minimize =
production
time 4. &n=
bsp;
Final
presentation a. &n=
bsp;
Document pr=
ocess,
rationale and results b. &n=
bsp;
Publish doc=
uments
and models on web site =
Team Member & Role Philip Coady Joseph Cremaldi John Deas Steven Escaravage EIA-632 Processes Configuration and data management
Support (S) Lead (L) S S Decision analysis L S S S Design Solution (logical & physi=
cal
architecture form) S L S S Implementation S S S L Integration S S L S Interface management S L S S Logical analysis (functional archite=
cture) S S L S Requirements definition &am=
p;
management S L S S Risk management S S L S Technical assessment L S S S Technical planning L S S S Transition S S S L Verification & Validation S S S L Table 1 The customer is faced with the challenges of
decreasing advertising volume, increasing complexity due to microzoning, an=
d reduced
productivity due to difficult-to-handle materials and aging collator machin=
ery.
In response to these challenges, we were asked to provide recommendations
regarding how to optimize the current Sunday advertising scheduling and
insertion process. In addition, we were asked to prepare a business case for
replacing the current collator with new technology, and optimized schedulin=
g to
eliminate or reduce many of the current constraints. The stakeholders and their prioritized requirem=
ents
are listed in Table 2.
Level Stakeholder Wants/Needs Value* Primary stakeholders Sponsoring Company Increased profitability 100 Production manager More efficient process, workfor=
ce
savings 75 Data manager Greater automation, less variat=
ion,
workforce savings 85 Schedulers Greater automation, less variat=
ion 70 Workers More efficient work day, Job se=
curity 20 Secondary stakeholders Advertisers Less wait time, increased
opportunities for targeted, smaller purchases 10 Collator manufacturer Proof of design, requirements v=
alidation 90 Trucking companies 70 FSI printers Increased printing time &
customer base 50 GMU SEOR Department Potential for more projects,
educational feedback to the faculty 50 Table <=
/span> * 0 – 100 point scale, 100 being the greatest gain<=
/span> Industry-specific terminology and customer-spec=
ific
acronyms used throughout this report are defined in Table 3. Term Definition<=
o:p> AIMS Accurate Insert Management Syste=
m Book A package of collated and wrappe=
d FSIs
assembled to an IPC specification. Also referred to as a package. Bundle A labeled package of strapped bo=
oks Bundle count The height restriction in MOGS t=
hat
limits the number of products per bundle for the bundler and palletizer BPM Books Per Minute Collator Production system consisting of
hoppers, conveyor belt, controls, meters that collects designated FSIs and
stacks them into books or packages according to IPC specifications Collator state FSI assignments by hopper for an=
IPC Distribution zones Geographic distribution areas wi=
thin
editorial zones (e.g. Dual mode Running two sides of collator
independently (applicable to new equipment only) Editorial zones Broad geographic distribution ar=
eas
(e.g. Feeder The Utility mailer role of loadi=
ng
advertisements into hoppers FSI Free Standing Insert, referred t=
o as
an advertisement Hard changeover (current) Physical movement of an FSI out =
of and
into a hopper at any time. Requires a stoppage in production. Hard changeover (future) Physical movement of an FSI out =
of and
into a hopper with no opportunity for idle time replacement. Requires a
stoppage in production. Head Component of collator where FSIs=
are
laid into the raceway Helper Lowest-skill workers Hopper Component of collator where FSIs=
are
stacked House book A FSI that is used in every IPC =
(i.e.
TV Week, comics, Magazine, Parade) IPC Individual Product Code, referre=
d to
as a job or order IPC Book Individual product code specific=
ation
consisting of designated FSIs in no particular order other than end piece=
s ISS Insert Scheduling System, the sy=
stem
of systems that provides end-to-end sales, production, and delivery of in=
sert
advertisements Mailers Highest-skill workers who operat=
e the
feeders and collator Micro zone Small geographic distribution ar=
eas
within distribution zones MOGS Manufacturing Order Generating S=
ystem;
Specifies the FSI composition of an IPC. Package The book of collated FSIs produc=
ed for
every IPC Penalty Time cost associated with change=
overs PPFM Pages per feeder minute Product run Collation of all required FSIs i=
n an
IPC Production Zone IPC Raceway Collator conveyor belt Ripple start Collator restart after a hard
changeover Ripple stop Hard changeover indication when =
collator
stops for next IPC Sharing opportunity A hopper with more than one FSI
assigned for separate IPCs Single mode Running two sides of collator in
series (applicable to new equipment only) Soft changeover (current) Switch on-off of a FSI within a =
hopper
or insertion of a FSI into an open hopper Soft changeover (future) Current capability plus the abil=
ity to
clear excess FSIs from a hopper while the collator is running (reduces ha=
rd
changeovers) SOM Schedule Optimizer Module TV zone Large geo=
graphic
distribution areas Utility Mailers Moderatel=
y-skilled
workers who feed stacks of FSIs on hoppers and clear excess FSIs from hop=
pers
on completion of product run. May also operate forklifts. Table 3 The problem is that the current system is ineff=
icient,
labor intensive, and does not account for new equipment constraints and
capabilities. The production process value stream is shown in Figure 2. Future production operations will be d=
riven
by the need to serve an increasing number of advertisers in up to 550 micro=
zones.
If ten advertising customers in each microzone placed discrete orders for a
given Sunday edition, the production schedule would increase from the curre=
nt
limit of approximately 300 schedules to over 550, and the average volume of=
a
production run could increase. Scheduling must be accomplished in one =
hour
processing time or less using hardware and software of our design or
specification. Ideally, the solution will run on the customer’s system
under Windows/Office 97. We used a proprietary spreadsheet implementatio=
n of
the QFD House of Quality to prioritize customer needs and wants. Appendix E is the results document (spreadsheets). The current Sunday advertising insert
production operation requires 31 labor shifts of seven hours each on three
collators that produce packages up to 60% of the available time. Hopper
assignments are developed based on experienced scheduler knowledge and a
ShivaSoft™ algorithm [Neiss]. This arrangement=
was acceptable
when hopper assignments remained relatively consistent throughout large wee=
kly
production runs. It is insufficient to meet the challenges of increasing
complexity, materials, and projected sales that will increase the number of
discrete ads and the volume of small orders. The project schedule is shown in Figure 3.
Figure 3 Customer constraints are listed in Table 4. Constraint Impact Solution must be generated in less than one hour Prevents possibility of true optimization by invalidating a solut=
ion Utility mailers will handle 16,000 pages per minute while loading
hoppers Restricts distribution of workload; determines number of workers
required per shift Accuracy must meet or exceed 98.5% Limits solution by restricting losses Pallets of FSIs must not be used in disparate hoppers or collator=
s Limits solution by preventing use of FSIs without regard to hopper
location IPCs within TV zones should be produced contiguously Reduces optimization of production run time by forcing a limited
number of hard changeovers Excess FSIs should not be reloaded onto pallets after placement in
hoppers Requires complete consumption of a pallet, thereby limiting the
number of FSIs available for loading The first and last positions in hopper assignments are reserved
Requires hard coding of designated FSIs to
certain hoppers Physical limit on number of hoppers Cannot avoid single-mode hopper configurat=
ion
for a small number of IPCs with a large number of FSIs Table 4 13.<=
span
style=3D'font:7.0pt "Times New Roman"'> Documentation
was provided electronically and in hard copy formats. The scope of this project is limited to optimiz=
ing
schedules. The input is a list of FSIs that comprise each IPC, and the outp=
ut
is the sequence of IPCs and hopper assignments to be assembled on the colla=
tor.
We recognize that optimizing one part of the production process may result =
in
perturbations in other parts, however, we have attempted to identify and
minimize those effects to the maximum extent possible. The input consists of a database table=
of
IPC specifications of FSIs for the weekly production run. The solution will be used to generate
sequenced hopper assignments for the entire production run. If changes are
required during production, the solution will be able to recalculate the
remaining hopper assignment sequence from within any point in the schedule.
With few exceptions, the production run is to be completed without any hard
changeovers. The output is a set of printable databa=
se
tables of IPC specifications with hopper assignments for each FSI in sequen=
ce. A group mind mapping process was used to decomp=
ose
required functions and performance as shown in Figure 3 top-level functional requirements,
Figure 4 detailed functional requirements
and Figure 5 detailed non-functional requirements Figure 4 top-level functi=
onal
requirements Figure 5 detailed functio=
nal
requirements =
; Figure 6 detailed non-fun=
ctional
requirements Figure 7 Alternative Solution S=
pace
is a factorial combination of potential forms for each function Constraints include
non-functional requirements of the proposed system, operational and
organizational constraints of the client, and operational constraints of th=
e delivery
team In some cases, common sen=
se was
applied to further reduce the alternative space (i.e., unrealistic options -
substantial data entry) An Effectiveness Ratin=
g or
relative evaluation was used to differentiate alternatives in terms of
performance against functional requirements The Preferred Alternat=
ive was
identified through application of an additive value function of the normali=
zed
effectiveness ratings and HOQ weights Throughout the evaluation
process, the resulting alternative instantiations were evaluated against ne=
eds
and wants to mitigate risks Our initial functional decomposition d=
iagram
is shown in Figure 8.
The identified functions were mapped to a number of possible forms. The for=
ms
were considered and analyzed using morphological analysis to determine the =
best
options. As the design matured, functions were reallocated and refined. Figure 8Project Development Plan
Team Roles and Responsibilities
Project Intent, Expected Results
Stakeholder and Needs Identification
Stakeholder Needs Analysis and Value Map
![3D"Sunday-only](3D"CRITFinalReport_files/image004.gif")
Figure 2 Value str=
eam
map
Stakeholder Needs:
Goals:
Design Schedule Optimizer Module:
Secondary goals
Other tasks
Quality Function Deployment (QFD)
Problem Definition,
Problem Definition
![3D"clip_image001"](3D"CRITFinalReport_files/image006.jpg")
Systems Engineering Methodology [Buede]
Scope and Context Definition
Operational Concept
Functional Decomposition
![3D"ISS](3D"CRITFinalReport_files/image008.jpg")
![3D"ISS](3D"CRITFinalReport_files/image010.gif")
![3D"ISS](3D"CRITFinalReport_files/image012.jpg")
Technology Strategy
![](3D"CRITFinalReport_files/image014.gif")
<=
![endif]>Architecture Development
![3D"ISS](3D"CRITFinalReport_files/image016.gif")
The =
as-built
functional decomposition is shown as Figure 9=
, from
which the functional architecture [Appendix B] diagrams were developed. The =
two
best system solutions were selected for prototype development and testing. =
The
two prototype solution models were then tested in simulation against various
problem sets given one year of historic data and our projections of future
sales. The option that met all validated customer requirements was selected=
for
the physical architecture and implementation. Derived requirements were
verified to originating requirements as they were identified.
=
;
![3D"ISS](3D"CRITFinalReport_files/image018.jpg")
Figure 9
Assumptions
Delivery of FSI pallets to the hopper staging area is not a constraint
The new equipment will handle at leas= t 90% of the Sunday workload
Spatial orientation of FSIs in books = is not a requirement
Hard changeovers will take one minute= or less on the new equipment
Utility mailers will work as a team assigned to a group of hoppers vs. individually by specific hoppers
The new equipment will stop and resta= rt without penalty, therefore overlapping shifts are not necessary to optimize production
FSI conditioning is not required on t= he new equipment, thereby freeing workers to load up to 16,000 pages per minute instead of the current standard of 8,000
An arbitrary dispatch schedule is acc= eptable assuming the production run is completed by Friday
MOGS-generated IPCs will be impacted = by incomplete FSI deliveries prior to commencement of production, therefore scheduling module must be responsive to changes
The new equipment will produce 225 pa= ckages per minute and operate at 90% availability
The greatest workload occurs during h= oliday seasons and is used for worst case analysis. The median workload can be accommodated without penalty using the worst case solution provided.
Utility mailer skill level, plus supervision, will suffice as the entire workforce on the new equipment, the= reby reducing the average labor rate.
Utility mailers are multi-skilled and c= an be used to operate forklifts to stage FSIs when hopper feeder demands are redu= ced.
Algorithm Process and Results
The following sections describe the algorithm developed [Albright] to find the IPC sequencing schedule. Individual sections outline the initial data pre-processing steps, the scheduling modules, and the assignment modules.
Data Pre-Processing
The Sunday Edition insert sched=
ule
is impacted by variations in the quantity and make-up of the weekly
advertisement order and the associated collator
configuration and staffing levels to best support those variations. Here, the collator configuration r=
efers
to the number of hoppers positioned on the two raceways (conveyer belts), w=
here
the total on the long side must be less than or equal to 50 hoppers, and the
total on both sides must be less than 80 hoppers. An advantage of the new collator i=
s the
ability to run the machine in dual mode – where the two sides of the
collator operate independently essentially doubling production capacity =
211;
or single mode – where the two sides snake together to increase the
hopper capacity while reducing the total production capacity. These two modes are depicted Figure 10 in below.
![](3D"CRITFinalReport_files/image020.jpg")
Figure 10
To take advantage of this operation mo= de flexibility, the machine must be configured in such a way to approximately minimize total production time by balancing the workload on the short and l= ong sides of the machine, while considering the trade-off of single mode and du= al mode operations. For example,= if the machine were equally balanced with 40 hoppers on both sides, individual jobs with less than 40 FSIs (advertisements) could be produced on either si= de of the machine. Under this configuration, all jobs with more than 40 FSIs would need to be produced in single mode. As an alternative example, if the collator where configured with 50 hoppers on the long side = and 30 hoppers on the short side, the increased capacity of the long side would= reduce the need for single mode operations. However, if less than 50% of the job groupings can be run on the sho= rt side, the total production time will increase due to the unbalanced product= ion load on the long side.
As a result, the proposed algorithmic a= pproach requires the pre-processing of the job make-up for the given week to determ= ine the preferred hopper configuration. The inputs to this pre-processing are the maximum IPC size for each = job grouping, the total packet demand for each job, a target machine speed, and= a target uptime percentage. The inputs are used to determine the total runtime and hopper requirements for = each job group. Then, starting wit= h the extreme configuration case of 30/50 (short side/long side), all hopper configuration possibilities are enumerated to determine the potential production runtime for the short side, long side, and single mode requirements. For cases where= the short side potential runtime is less than 50% of the total runtime, the sho= rt side production time estimate is set equal to the short side potential runtime. If the short side potential runtime exceeds 50% of the total runtime, the short side and long side are set equal to approximately half the total production time estimate excluding any jobs that must be produced in single mode. A sample calculation for editorial= week 3/16/2008 is presented in Table 5 below, with the resulting preferred configuration of 35/45 hoppers.
Table 5
![](3D"CRITFinalReport_files/image022.gif")
Similarly, required staffing levels ar= e a function of the product make-up and target machine speed. Staff members responsible for “feeding” the advertisements (FSIs) onto the hoppers are design= ated “Feeders.” For th= is effort, we assumed a single constraint governed the required number of Feed= ers per job, namely the pages per feeder minute constraint. The Sunday Insert Production Job F= oremen target an average of 16,000 pages per Feeder minute (PPFM). Simply stated, a single Feeder sho= uld not be responsible for loading advertisements onto hoppers at a rate of gre= ater than 16,000 pages per minute on average.&n= bsp; Individual advertisements or circulars with a large number of pages,= for example 40 pages, require more frequent Feeder loading into the hoppers giv= en that each packet removes 40 pages from the stack as compared to a two page advertisement, where each packet would only remove 2 pages from the stack.<= span style=3D'mso-spacerun:yes'> In practice, the term “tab pages” is used to represent the number of sides per advertisement (FSI). As a result, the small= est number of pages (“tab pages”) encountered by the algorithm is 2 (for a single sheet of paper). The resulting PPFM constraint is presented below for a single job, although the constraint is traditionally applied as an average across all jobs. Here, the pages collection holds t= he tab page size of each advertisement (FSI); speed indicates the target packets p= er min (e.g., 225); the third condition includes only the advertisements (FSIs) assigned to the Feeder position under interest.
![](3D"CRITFinalReport_files/image024.gif")
The proposed solution, given an aggress= ive schedule, requires the predetermination of the average number of Feeders per shift to provide the assignment algorithm with a non-variable number of Fee= der positions for assignment. Fut= ure iterations of the algorithm might incorporate sensitivity analysis and cost-effectiveness constraints to determine the number of hopper positions = to feed or treat the number of positions as a variable to be determined in-line during execution of the heuristic. Given this limitation, the algorithm uses the integer ceiling (round= up) of the average number of Feeders required per shift. Here, the number of Feeders per sh= ift would be calculated as the production time weighted average of the number of Feeders required per job (IPC)[1]. For jobs that require more than the resulting number of Feeders, the machine speed would be reduced as to not violate the PPFM constraint. = For jobs that require less than the number of Feeders, forecasted changeovers or other activities could be planned to consume the surplus labor. A sample Feeder position calculati= on is provided in the figure below.
Table
6 Feeder Positions Calculation
The objective of the algorithm is to p=
roduce
a feasible job schedule and hopper assignment that minimizes the downtime of
the collating machines due to product change-over. Here, the use of the term “f=
easible
schedule” is to assume the resulting algorithm will not increase over=
all
production time in an attempt to minimize product change-over time (e.g., r=
un
the entire editorial week in single mode on one collator). Given the minimization goal, a num=
ber of
optimization and heuristic approaches were evaluated for a proof of concept
implementation. Exact optimization methods were resea=
rched
to ensure the size of the problem was reasonable in terms of the number of
potential “nodes” in the job “network.” Given the number of jobs per week =
ranges
between a lower bound of 200 and an upper bound potential of 550, all brute
force enumeration and many progressive improvement algorithms were eliminat=
ed
from consideration based simply on size (i.e., many progressive algorithms =
support
up to only 200-225 nodes). Ho=
wever,
some advanced cutting plan solutions were found to easily handle the potent=
ial
network size, and could theoretically handle up to 10,000 node tours. In the end, exact optimization met=
hods
were down-selected due to (1) computational complexity and the lack of
availability of a computational infrastructure to support customer deployme=
nt
testing, (2) the need for the resulting algorithm to be deployed as a module
within the current software environment, and thus be implementable in stand=
ard
software development packages (3) to keep the scope manageable in terms of
constraint derivation and implementation, and (4) realizing that in practic=
e,
the results of the algorithm will be used as a starting point by Client
Experts, and thus transparency outweighs the need to prove optimality. In addition, constructive and improve=
ment
heuristics were evaluated given the relative ease of implementation and
accuracy of results. Construc=
tive
heuristics generate a path through greedy- or insertion- methods (e.g., nea=
rest
neighbor, best insertion) and generally produce fairly good results estimat=
ed
from 1.10x to 2x optimal tours when the problem is structured as a traveling
salesman problem (TSP). In th=
e case
of the Sunday Insert problem, the week can end on any job compared to TSP
constraint of returning home, thus estimates are potentially even larger th=
an
would be found in practice.
However, in some and not necessarily rare cases, constructive heuris=
tics
will produce far from optimal spanning paths (e.g., 2x optimal). Lastly, the improvement heuristics we=
re
researched. Improvement heuri=
stics
start with an initial sequence or schedule developed through a constructive
approach, and attempts to improve the initial schedule through removal or
reconstruction of a subset of transitions.=
For example, k-opt appro=
aches
attempt to improve spanning paths and tours through selection and evaluatio=
n of
k transitions. Other approaches use similar
“swapping” or “switching” approaches paired with ar=
tificial
intelligence components to control the number of improvement attempts (e.g.,
simulated annealing, genetic algorithms).&=
nbsp;
In the end, a greedy constructive heuri=
stic
was selected to ensure prototype testing and analysis would be possible wit=
hin
the provided period of performance.
We elaborate on future considerations and extensions to the algorith=
m in
Recommendations A greedy scheduling and assignment heu=
ristic
was derived and formulated as the key deliverable of the project. The heuristic first iterates throu=
gh the
order detail (Product Table), and at each step determines the next best job=
to
place at the end of the current schedule as to minimize the number of hard
changeovers and soft change-over respectively given the current assignment =
of
the collator. Subsequently, t=
he
algorithm re-orders the initial hopper assignment to balance the workload
across the predetermined number of Feeder positions. Figure 11
presents a high-level overview of the inputs and results of the algorithm,
which will be elaborated in the following sections. Figure 11![](3D"CRITFinalReport_files/image026.gif")
Potential Algorithmic Approaches
Introduction – the Scheduling and Assignment Algorithm
![](3D"CRITFinalReport_files/image028.jpg")
Step 1: Declaration and Initialization
This=
section
defines and initializes the data structures and constants used throughout t=
he
modules in the algorithm. The
following sections will use the actual variables names based on the mapping
below:
Acro=
nym &=
nbsp; Reference
Name &nb=
sp; =
&nb=
sp; Generic
Name
FSI &nbs=
p; &=
nbsp; Free
Standing Insert &nbs=
p; &=
nbsp; Advertis=
ement,
Ad, Insert, Circular
IPC &nbs=
p; &=
nbsp; Integrated
Product Code &=
nbsp; &nbs=
p; Job,
Product
The first set of declarations and initializations
establishes the static values that describe the current configuration of the
new collator, the product make-up in terms of number of FSIs and number of =
IPCs.&nb=
sp;
Throughout the remainder of the formulation, any side specific notat=
ion
will be listed for the long side of the collator only. In actual implementation, two inst=
ances
of the algorithm would be implemented and called as subroutines or procedur=
es on
the remaining set of IPCs to be scheduled.
Let numFSIs &=
nbsp; &nbs=
p; =3D
the total number of FSIs in a given edition week
Let numIPCs &n=
bsp; =
; =3D
the total number of IPCs in given edition week
Let numhopper<=
/a>sLong
=3D the num=
ber of
hoppers on the long side of the new collator
The next declarations establish the primary data structures us=
ed
to store the product and product make-up tables from the Insert Scheduling
System Database. Also, the
following indexing applies to all data structures:
i =3D 1..numIPCs
j =3D 1..numFSIs
k =3D 30…numhoppersLong<=
br>
m =3D 1..numIPCs
n =3D 1..numFSIs
Let IPC
Let FSIj =3D the jth free standing insert for the edi=
tion
week
Let
IPCij &n=
bsp; =
; =3D
![](3D"CRITFinalReport_files/image030.gif")
Let
collatorLongk =
=3D
![](3D"CRITFinalReport_files/image032.gif")
Let
jobLongm =
; =
=3D
![](3D"CRITFinalReport_files/image034.gif")
Let
scheduleLongm,n =3D ![](3D"CRITFinalReport_files/image036.gif")
Let
sizeIPCi =
&nb=
sp; =3D
the number of FSIs in IPCi
Let
productionTimei =
; =3D
the production time in hours at 90% uptime for IPCi
Let
productionLimit =3D
the max runtime for the current side of the collator as determined through
preprocessing
Let
totalProdTime =
=3D
the total production time for all IPCs in the current schedule
The next set of initializations and declarations sets the valu=
es
for known production constraints.
The first statement declares and initializes the set of FSIs referen=
cing
the TV Books. Similarly, the =
FSI
identifiers for the weekly comics, newspaper magazine, and Parade magazine =
are
declared and initialized.
Let tvBooks =
=3D {![](3D"CRITFinalReport_files/image038.gif")
identifies a TV Book}
Let comics &nb=
sp; =
=3D
{![](3D"CRITFinalReport_files/image040.gif")
identifies the Comics}
Let magazine &=
nbsp; =3D
{identifies the Magazine}
Let parade &nb=
sp; =
=3D
{identifies the Parade Magazine}
Lastly, a set or collection is establishe=
d to
store all remaining IPC identifiers that have not been assigned a schedule
sequence, remainingIPCs, and a set to store all IPCs that exceed the side
capacity currently under run that must be reinserted following initial sche=
dule
generation. The final stateme=
nt
removes all IPCs that exceed the current side number of hoppers from the
current scheduling set.
Let remainingIPCs =
=3D
{1, 2 ... numIPCs}
Let
singleModeIPCs =
=3D {![](3D"CRITFinalReport_files/image043.gif")
> the numhoppersLong or numhoppersShort (depend=
ing
on current schedule)}
remainingIPCs =3D remainingIPCs - singleModeIPCs
Step 2: Select Lead IPC and Initialize Hopper Positions Sequentially
Given the dual mode capability of the new collator, and the gr=
eedy
nature of the algorithm, care must be taken to ensure jobs in groupings wit=
h a
relatively large number of FSIs are reserved for the long side of the colla=
tor
while jobs with a relatively small number of FSIs are reserved for the small
side of the collator. As a re=
sult,
we require an initial pre-processing step to determine which side of the
collator to prioritize scheduling of each job.
Let sidePreferencei =3D ![](3D"CRITFinalReport_files/image045.gif")
Given this preference for each job grouping, and ultimately ea=
ch
IPC, we first develop the schedule for the long side of the collator, and t=
hus
prioritize selection to those job groups with large size preference. Within this group, the algorithm
identifies the IPC with the largest sum total of FSI frequencies as the lead
IPC. Stated in another way, t=
he
algorithm looks to identify the IPC with the largest number of frequently u=
sed
FSIs.
For
all IPCs with sidePreferencei =3D 1:
Let freqj =
=
=3D
the frequency with which an FSIj occurs across all IPCs
&nb=
sp; =
&nb=
sp; =
=3D
![](3D"CRITFinalReport_files/image047.gif")
Next
Let jobLong=
1
&=
nbsp; =3D
IPCi with the highest summed total of FSI frequency with sizeIPC=
i
< numHoppersLong + 1
&=
nbsp; &nbs=
p; &=
nbsp; =3D
![](3D"CRITFinalReport_files/image049.gif")
The
algorithm then initializes the long side of the collator and the schedule f=
or
the lead IPC. Here, FSIs are
assigned sequentially to the first j hoppers positions, where j is equal to=
the
number of FSIs in the lead IPC. Lastly, the IPC number of the selected IPC =
is
removed from the remainingIPC set.
Let
collatorLongk =
=3D
sequential order of FSIs in jobLong1 (lead IPC)
=3D ![](3D"CRITFinalReport_files/image051.gif")
Let
scheduleLong1n =
; =3D
collatorLongk =
for n=3Dk, for k =3D 1..numh=
oppersLong
Let
remainingIPCs =
=3D
remainingIPCs – {jobLong1}
Step 3: Iteratively Find the Next Job
The next st=
ep
in the algorithm is to recursively select the next job that introduces the
minimum number of hard and soft changeovers from within the current active =
job
grouping. In the event of a t=
ie break
scenario, the job with the highest summed total within the set with the min=
imum
number of hard and soft change-over is selected. Again, given the first set=
of
schedule assignments is focused on the long side of the hopper, only jobs w=
ith
a large side preference are evaluated.
This module
first sets an index for the current job number to be scheduled, m, and decl=
ares
two arrays to capture the number of hard and soft change-overs required to
transition the collator from the current IPC to the next IPC. Next, the module begins an
iterative “While Loop” that cycles through all IPCs not current=
ly
assigned to a schedule sequence.
The next set of statements determine the set of unassigned IPCs that
should be considered for the next job based on the following priority: (1) =
all
IPCs in the current TV book zone, (2) all IPCs not in the current TV book z=
one
but with a long side preference, (3) all remaining IPCs. The resulting set of IPCs is set e=
qual
to a temporary holding set or collection, potentialIPCs. This process is
terminated if the total production time for the current side schedule excee=
ds
the predetermined runtime upper limit, and all IPCs within the current TV B=
ook
zone are included in the schedule.
Let
m =3D 1
Let
soft_changeoveri =3D the number of soft change-overs required to=
run
IPCi next on collator1
Let
hard_changeoveri =3D the number of hard change-overs required to=
run
IPCi next on collator1
While
![](3D"CRITFinalReport_files/image053.gif")
{
IF (![](3D"CRITFinalReport_files/image055.gif")
)
&=
nbsp; &nbs=
p; Let
potentialIPCs =3D {![](3D"CRITFinalReport_files/image057.gif")
}
Else
IF (![](3D"CRITFinalReport_files/image059.gif")
)
&=
nbsp; remainingIPCs
=3D {null}
Else
IF (![](3D"CRITFinalReport_files/image061.gif")
)
Let
potentialIPCs =3D {![](3D"CRITFinalReport_files/image063.gif")
}
Else
&=
nbsp; &nbs=
p; Let
potentialIPCs =3D remainingIPCs
End
IF
For
the set of IPCs selected for evaluation, the algorithm next loops through a=
ll
potential next jobs and determines the FSIs in the potential next IPC that
would need to be put on the collator (transitionOn), as well as the FSIs on=
the
collator and not in the potential next IPC that could be changed out
(transitionOff). The last sta=
tement
creates a temporary array with the same structure and contents of the colla=
tor
array for use in determination of the number of change-overs that would be
experienced if the IPC under evaluation was sequenced next in the schedule
(tempCollatorLong).
&=
nbsp; For
each ![](3D"CRITFinalReport_files/image065.gif")
{
Let i =3D i=
ndex
of next <=
!--[if gte vml 1]>![](3D"CRITFinalReport_files/image067.gif")
potentialIPCs&nbs=
p;
&=
nbsp; &nbs=
p; Let
transitionOn ![](3D"CRITFinalReport_files/image069.gif")
}
Let transit=
ionOff
![](3D"CRITFinalReport_files/image071.gif")
}
Let
tempCollatorLongik =3D collatorLongk
The
next set of statements execute an IPC change-over on the mirror copy of the
collator state (tempCollatorLong) to determine the number of hard and soft
change-overs that would result from this potential IPC sequencing. The order in which FSIs in the tra=
nsitionOff
asset are selected for change-over according to the IF clauses is as follow=
s:
(1) open hoppers are filled first, (2) FSIs in the transitionOff set that a=
re
not used in the previous job, resulting in soft change-over, and (3) FSIs in
the transitionOff set that are used in the previous job, resulting in hard
change-overs. Given a tie bre=
ak
scenario for either hard of soft change-overs, the FSI that is used least
frequently in the unscheduled IPCs is selected for change-over.
&=
nbsp; For
![](3D"CRITFinalReport_files/image073.gif")
transitionOn {
&=
nbsp; &=
nbsp; Let
n =3D index of next ![](3D"CRITFinalReport_files/image075.gif")
transitionOn
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; Let
j =3D index of next transitionOff
&=
nbsp; &nbs=
p; //Replace empty hoppers first
&=
nbsp; &nbs=
p; IF
tempCollatorLongik =3D 0 for some k Then {
&nb=
sp; =
tempCollatorLongik
=3D n <=
/span>//assume
FSIn moves into open hopper
&nb=
sp; =
transitionOn
=3D transitionOn – {FSIn}
&nb=
sp; =
transitionOff
=3D transitionOff – {FSIj}
}//end
If
//If
no hoppers are empty, conduct soft change-over on least used FSI in remaini=
ng
IPCs
Else If ![](3D"CRITFinalReport_files/image078.gif")
{
&nb=
sp; =
Let
tempFSI =3D ![](3D"CRITFinalReport_files/image080.gif")
=
&nb=
sp; =
Find
k![](3D"CRITFinalReport_files/image082.gif")
tempCollatorLongik where { tempCollator=
Longik
=3D tempFSI}
&nb=
sp; =
Let
tempCollatorLongik =3D n =
&nb=
sp; //put
FSIn in hopper k &nbs=
p; &=
nbsp; soft_cha=
ngeoveri
=3D soft_changeoveri + 1 &n=
bsp; //add
one soft changeover for IPCi
&nb=
sp; =
transitionOn
=3D transitionOn - {FSIn=
}
&nb=
sp; =
transitionOff
=3D transitionOff - {FSI=
j}
}=
// end
Else If
Else {&nb=
sp; //only
hard change-overs remaining
&nb=
sp; =
Let
tempFSI =3D ![](3D"CRITFinalReport_files/image084.gif")
&nb=
sp; =
Find
k tempCollatorLongi where {
tempCollatorLongik =3D tempFSI}&=
nbsp;
&nb=
sp; =
Let
tempCollatorLongik =3D n =
&nb=
sp; //put
FSIn in hopper k
&nb=
sp; =
hard_changeoveri
=3D hard_changeoveri + 1 //add one hard changeo=
ver
for IPCi
transitionO=
n =3D
transitionOn - {FSIn}
transitionO=
ff =3D
transitionOff - {FSIj}
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; }//end Else
&nb=
sp; =
&nb=
sp; }//
end For FSI ![](3D"CRITFinalReport_files/image086.gif")
transition=
On
&=
nbsp; }//end
For each IPC potentialI=
PCs
The
algorithm then selects the next IPC for scheduling with the minimum number =
of
hard change-overs, then soft change-overs, and has the largest sum total of=
FSI
frequencies in the remaining unscheduled IPCs.
Let tempIPC=
s =3D ![](3D"CRITFinalReport_files/image088.gif")
Let tempIPC=
s =3D ![](3D"CRITFinalReport_files/image090.gif")
Let![](3D"CRITFinalReport_files/image092.gif")
=
//recal=
culate
FSI frequency
Let nextIPC=
=3D ![](3D"CRITFinalReport_files/image094.gif")
Let jobLongn =3D nextI=
PC &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; =
; //set
the next IPC in the schedule
Let collato=
rLongk
=3D tempCollatorLongik
}//
end For IPC remainingI=
PCs
Step 4: Single Mode IPC Scheduling
Following Step 3,=
all
IPCs within the capacity constraints of the current side of the collator (i=
.e.,
long, short) are included in each side schedule, thus we assume Step 3 has =
been
executed once for each side. =
At
this point, there are a number of options for augmenting the current schedu=
les
with the single mode IPCs stored in the singleModeIPC set. First, the single mode IPCs could =
be
inserted as a set at the front or tail end of the schedule, with the single=
mode
IPCs schedule optimized through the procedures outlined in Step 3. Secondly, the single mode IPCs cou=
ld be
run independently on one of the existing legacy collators with sufficient s=
ize
(e.g., Collator 4). Although =
simple
from a planning perspective, either approach would introduce some complexity
into the delivery process as jobs within given delivery zones could be run =
at
vastly different times in the production week, thus requiring multiple
inventory movements and staging.
Alternatively, the single mode IPCs could be re-inserted into the si=
ngle
side schedules by TV book zone (which would be running on one and only one
side). In this case, the sing=
le
mode collators would be inserted into both side schedules at the point that
resulted in the minimum number of hard and soft change-overs, and also resu=
lted
in the minimum amount of downtime waiting due to the unsynchronized starting
and stopping of previous jobs on the two sides of the collator. Here, the total production time on=
the
collator would be used to determine exactly which IPCs on either side of the
collator would terminate immediately before the insertion point for the sin=
gle
mode IPC.
Due t=
o time
constraints, this insertion module of the scheduling algorithm was not
implemented in the prototype or formulated. As a result, the current algorithm=
only
allows front or backend augmentation of the single mode IPCs. However, the extension described a=
bove
is highly recommended for future iterations and testing.
Step 5: Hopper Assignment=
The first sets of statements declare and initialize the key st=
atic
variables, arrays, and collections for use in the assignment heuristic.
Let numHoppersMax =3D numHoppersLong || numHoppersShort based =
on
current side under assignment
Let numFeeders =3D the predetermined number of Feeder positions
allocated to this side of the collator
Let maxHoppPerFeeder =3D the maximum number of hoppers that could be assigned to a
single Feeder
Let virtHoppersk =3D the average FSI tab page count=
in
hopper position k resulting from the scheduling module
Let maxPPFM =3D the maximum number of pages per Feeder minute =
that
could be assigned to a single Feeder
Let machineSpeed =3D the target machine speed in terms of book=
s per
minute
=
//The hopperAssign array is dimensioned for f<=3D numFeeder=
s,
k<=3D maxHoppPerFeeder
=
Let hopperAssignf, k =3D
![](3D"CRITFinalReport_files/image096.gif")
Let hopperMappingk &n=
bsp; =3D ![](3D"CRITFinalReport_files/image098.gif")
Let feederWorkloadf =
&nb=
sp; =3D
the tab pages per book assigned to Feeder position f //running total
Let feederNumHoppersf =3D
the number of hopper assigned to Feeder position f //number of items
The next set of statements introduce hard hopper mapping
constraints for the top of stack and bottom of stack FSIs (i.e., TV book,
Parade are set to the bottom of the pile; magazine and comics are set to the
top of the pile). Here, this =
is a
departure from current operations where TV books are the last item added on=
the
top of the stack. This change=
is to
enable the new collator to operate in single mode while ensuring the TV boo=
k is
inserted on one side of the stack.
'Initialize starting conditions - e.g,. tvbooks, magazine, com=
ics,
and parade
Let hopperMapping1 &=
nbsp; &nbs=
p; =3D {![](3D"CRITFinalReport_files/image100.gif")
mapped to hopper position k by the initial schedul=
e}
Let hopperMapping2 &=
nbsp; &nbs=
p; =3D {![](3D"CRITFinalReport_files/image102.gif")
mapped to hopper position k by the initial schedul=
e}
Let hopperMappingnumHoppersMax=
&n=
bsp; =3D {![](3D"CRITFinalReport_files/image104.gif")
mapped to hopper position k by the initial schedul=
e}
Let hopperMappingnumHoppersMax=
- 1
=3D<=
span
style=3D'font-size:10.0pt;mso-ascii-font-family:Calibri;mso-ascii-theme-fon=
t:
minor-latin;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin'=
> {![](3D"CRITFinalReport_files/image106.gif")
mapped to hopper position k by the initial schedul=
e}
The next section creates a data
structure that will be used to order the greedy assignment process. Here, the data structure,
sortedVirtHoppers, is a set of pairs of elements, where the first element h=
olds
the virtual hopper index from the initial schedule, and second element holds
the average tab page count per virtual hopper position across all IPCs. The data structure must be sorted =
from
largest to smallest value of the second element, and must exclude the virtu=
al
hoppers assigned to the TV Book, Parade, magazine, and comics).
Let sortedVirtHoppersk, n =3D =
{(s,
pages_s), (x, pages_x), (y, pages_y) …} a largest to smallest sorted =
two
dimensional array with the virtual hopper index (s, x, y, z) as the first
element, sorted by the average tab page size in the hopper across all jobs =
in
the initial schedule as the second element. Hopper positions associated with t=
vbook,
parade, magazine, and comics are excluded.=
//Sample sortedVirtHoppersk, n=
=3D
{(2, 48), (9, 40), (3, 36), (18, 32)} where the first element is virtual ho=
pper
2 and //had an average tab page size of 48 pages
The next section executes the initial greedy assignment of vir=
tual
hoppers to Feeder positions based on the current workload assigned to each
feeder and the size of the next virtual hopper in terms of average tab page
count. In each case, the algo=
rithm
attempts to add the next virtual hopper to the Feeder position with the min=
imum
current workload. One special=
case
requires consideration, specifically the case where a single FSI exceeds the
pages per Feeder minute constraint of the Feeders (e.g., 80 pages). These special cases are assigned to
positions on the front of either side of the collator to be post-processed =
by
Client Scheduling Experts as needed.
<=
span
style=3D'font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:115%;mso-as=
cii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin'>For i =3D 1 To numHoppersMax – 4
&nb=
sp; =
min
=3D 999 //initializes a min value holder for the iterations – the min=
imum
workload by feeder
&=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; minIndex
=3D j
&nb=
sp; =
hopperAssignf,
k =3D sortedVirtH=
oppersi,
1 where f =3D minIndex,=
k =3D
feederNumHoppersf + 1
&=
nbsp; feederWorkloadf
&=
nbsp; =3D
feederWorkloadf + sortedVirtHoppersi, 2
&nb=
sp; =
feederNumHoppersf
&=
nbsp; =3D
feederNumHoppersf + 1
Lastly, the assignment algorithm looks to order the hoppers to
centrally concentrate the workload of each Feeder, resulting in larger FSIs
being placed in middle positions and smaller FSIs being placed to the
outside. A new array is intro=
duced,
tempAssign, to hold the sorted array as each Feeder position is processed.<=
span
style=3D'mso-spacerun:yes'> This array is eventually used to r=
ecord
the final virtual hopper to physical hopper mapping.
Let tempAssignz =3D s if hoppe=
r s is
assigned to hopper position z
n =3D 3 //index for final physical hopper
mapping, four hoppers already reserved for TV Book, parade, …
For i =3D 1 To numFeeders
&nb=
sp; =
Let
midposition =3D Int(feederNumHoppersi / 2) + 1
&nb=
sp; =
tempAssignmidposition
=3D hopperAssigni, 1
&nb=
sp; =
j
=3D 1
&nb=
sp; =
Do
While (j <=3D Int(feederNumHoppersi))
&=
nbsp; &nbs=
p; If
(midposition - j > 0) Then
=
=
&nb=
sp; =
tempAssignmidposition
- j =3D hopperAssigni, 2*j
=
=
&nb=
sp; End
If
=
=
&nb=
sp; If (midposition + j <=3D feederN=
umHoppersi)
Then
=
&nb=
sp; &=
nbsp; tempAssign
=
=
&nb=
sp; End
If
=
=
&nb=
sp; j
=3D j + 1
Loop
//end while loop
&nb=
sp; =
'Reset
the hopper Assignment with the sorted values
&nb=
sp; =
For
k =3D 1 To feederNumHoppersi
&nb=
sp; =
&nb=
sp; hopperAssigni,
k =3D tempAssignk
&nb=
sp; =
&nb=
sp; hopperMappingn
=3D tempAssignk
=
=
&nb=
sp; n
=3D n + 1
Next
Next
The resulting hopper assignment capturing the final mapping fr=
om
virtual hoppers output in the initial schedule to physical hoppers is store=
d in
the hopperMapping array. This=
array
is then post-processed against to restructure the initial schedule with the
balanced workload assignment.
Sample Results
The =
graphic
below presents a snapshot of the results of the initial scheduling and assignment
heuristic for the first 20 jobs and first 20 hoppers of the March 16, 2008
edition week. Here, the green
shading indicates an FSI is included in the current job, gray shading indic=
ates
an FSI is loaded on the collator in that hopper position but not used in the
current job, and a maroon border identifies a soft change-over (note: no ha=
rd
change-overs are depicted in this sample).
Figure 12 Sample Scheduling Results for March 1=
6,
2008
|
# |
1 |
88 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
0 |
75 |
||
|
2 |
63 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
3 |
69 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
4 |
70 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
5 |
71 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
6 |
75 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
7 |
73 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
0 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
8 |
74 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
9 |
76 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
10 |
77 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
0 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
11 |
67 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
12 |
68 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
13 |
72 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
14 |
85 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
15 |
65 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
16 |
80 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
17 |
86 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
18 |
89 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
19 |
94 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
|||
|
20 |
101 |
104 |
52 |
0 |
0 |
47 |
32 |
91 |
0 |
24 |
0 |
135 |
0 |
94 |
65 |
46 |
95 |
14 |
0 |
76 |
75 |
The resulting scheduled provides t=
he
Sunday Insert Scheduling division with a feasible schedule that can be used=
to
plan the sequencing of FSI (advertisements) onto the mailroom production fl=
oor
from the warehouse, as well as to inform the collating machines as to which
hoppers need to be active for each production job. Lastly, the resulting visualization
provides the mailroom Foreman with a visualization of upcoming forecasts to
enable ad hoc change-over forecasting.
A second key output is depicted in=
the
table below, which presents the average workload per physical hopper positi=
ons
calculated in terms of average tab pages per book. Ideally, the resulting hopper assi=
gnment
would provide discrete Feeder position workloads that are equally balanced =
and
equally distributed across the physical hoppers barring constraints. The sample data below for the Marc=
h 16,
2008 edition week presents a properly assigned and balanced assignment as
confirmed by client experts.
Figure 13 Sample Assignment Results for March 1=
6,
2008
![](3D"CRITFinalReport_files/image108.gif")
Business Strategy / Business Approach
The decision to invest several million dollars for = new equipment must be based on sound financial analysis in addition to the appa= rent requirement to replace aging equipment. Our approach is based on the calcul= ated production times, notional labor costs fully burdened with overhead, and la= bor productivity rates as specified by contract. Sales trends are shown in Figure 12 and used for projections.
1. Current cost calculation
Existing equipment, run times, availability rates a= nd labor skill mix are used to calculate current production costs for a single week.
·
Identify number of shifts worked per week
·
Identify number of workers per shift
·
Estimate average fully burdened labor rate
·
Identify hours worked per shift
·
Calculate the weekly operating cost
2. Simple projection cost calculation
This projection uses promised (manufacturer cla= imed) run times, feeder capacity and equipment availability rates with the current labor skill mix to determine expected costs to operate the new collator.
·
Use the estimated number of shifts to be worked per week
·
Estimate the number of workers required per shift
·
Reuse average fully burdened labor rate
·
Reuse hours worked per shift
·
Calculate the simple weekly operating cost
·
Calculate the simple weekly operating cost savings
![](3D"CRITFinalReport_files/image110.gif")
<=
![endif]>
Figure 14
3. Optimistic (best case)= projection cost calculation
Decreased labor costs due to lower required ski= ll levels are combined with minimum calculated production times (at maximum ra= te and availability) to determine the best case scenario. This calculation does not consider the effects of worker learning.
·
Lowest calculation of number of shifts to be worked per week
·
Identify number of workers needed per shift
·
Constant fully burdened labor rate to reflect lower average required
skill mix under higher demand
·
Reuse hours worked per shift
·
Calculate the minimum weekly operating cost
·
Calculate the maximum weekly operating cost savings
4. Pessimistic (conservat= ive) projection cost calculation
This calculation provides a cost projection bas= ed on production run time least improvement and worst-case labor cost, and assumes there will be a 90% learning curve with the new, more automated equipment.<= /p>
·
High estimate of number of shifts worked per week
·
Identify number of workers per shift
·
Constant fully burdened labor rate to reflect lower average required
skill mix under higher demand
·
Reuse hours worked per shift
·
Calculate the maximum weekly operating cost
·
Calculate the minimum weekly operating cost savings
=
=
|
|
Collator shifts/ |
Workers/ collator shift |
Fully-burdened $/ |
Hours/ |
Operating cost $/ |
Savings/ week |
|
|
Current conditions |
31<= o:p> |
10<= o:p> |
|
||||
|
Simple projection |
15<= o:p> |
10<= o:p> |
$45.00 |
7 |
$47,250 |
||
|
Conservative projection |
20<= o:p> |
10<= o:p> |
7 |
$63,000 |
|||
|
Best-case projection |
12<= o:p> |
10<= o:p> |
7 |
$37,800 |
Table 7 Cost calculations
*Simple projection - no change to current labor =
cost,
lower bound of required shifts per week
**Optimistic Projection - increased labor costs,=
lower
bound of required shifts per week
***Pessimistic Projection - increased labor cost,
upper bound of required shifts per week
5. Calculate financing co= st and payback time
This calculation determines the amount of time = to realize a return on investment for each projection without financing. If the purchased were financed, at a 3.3 million dollar cost (given a nominal principal amount of ten million dollars to be financed at six percent for t= en years) the return on investment is calculated for the pessimistic projectio= n.
·
Estimate capital investment cost
·
Estimate financing rate and term
·
Calculate monthly payment
·
Calculate cost of capital (total payment over full term)
·
Calculate break even time for each operating cost calculation
![](3D"CRITFinalReport_files/image112.jpg")
Table 8 Financing cost and break even time
Recommendations
Future project possibilities include l= eaning the entire production and distribution process. Opportunities identified du= ring this project are:
·
C=
alculate
effects of new sales model. What happens to the business case if:
·
Advertising sales increase or decline?
·
Number of customers increases or declines?
·
If more cus=
tomers
buy smaller orders?
Conclusions
The proof of concept was confirmed thr= ough implementation of a prototype algorithm that will increase automation of the planning process. The result of our analysis indicates that the best hopper configuration would be to run the new machine 100% in dual mode, and the existing collator #4 only to cover those IPCs too large for one side of the= new machine. This solution assume= s that TV book zones will govern production scheduling. Under this model, the enti= re average production run could be completed in a little as 12 shifts (worst case using 3/12/08 data is 13.5 shifts). With increased automation of the new equipmen= t, an optimal operating labor cost savings of 61% will result. At this savings= , a $10 million investment break even time is only three years two months.
We verified that the new equipment sh= ould consist of 80 hoppers to achieve optimal results.
We verified that the best hopper configuration consists of approximately 35 hoppers on one side and 45 on the other. An exact balance by run time is achieved with a 36/44 split. This ve= rification was tested using a calculation of balancing the opportunity for hopper load= ing in comparison of single and dual modes to minimize the total run time.
The solution is sub optimized to allo= w for TV zone, pallet splitting & distribution constraints.
We used a weighted average of workers n= eeded per shift given a target line speed of 225 books per minute and a physical constraint of 16,000 pages per feeder minute. Ideally, the resulting schedu= le would optimize production time for maximum line speed for a minimum number = of workers.
Bibliography
GEIA-632, Processes for Engineering a =
System,
Information Technology Association of
Albright, S. C=
hristian,
VBA for Modelers : Developing Decision Support Systems Using Microsoft®
Excel,
Buede, Dennis, The Engineering Design of Systems: Models and Methods, Wiley, 2000
Neiss, Alan M., Ins= ert Scheduling System synopsis, January 20, 2009
Appendix
=
A.
<=
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D.
G.
[1] Alternatively, if under staffing or overstaffing concerns question the use = of the weighted average, the use of weighted percentile is recommend (e.g., nu= mber feeder positions =3D 85th percentile of job requirements)