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Copyright � 2001 INFORMS0092-2102/01/3101/0007/$05.001526–551X electronic ISSN

INFORMATION SYSTEMS—DECISION SUPPORT SYSTEMSPRODUCTION/SCHEDULING—APPROXIMATIONS/HEURISTICPROGRAMMING—LINEAR

INTERFACES 31: 1 January–February 2001 (pp. 7–29)

Improving Performance and Flexibility atJeppesen: The World’s Leading Aviation-Information CompanyElena Katok Department of Management Science and

Information SystemsPennsylvania State UniversityUniversity Park, Pennsylvania 16802

William Tarantino Center for Army AnalysisFort Belvoir, Virginia 22060

Ralph Tiedeman Jeppesen Sanderson, Inc.55 Inverness Drive EastEngelwood, Colorado 80112

Jeppesen Sanderson, Inc. maintains, manufactures, and dis-tributes flight manuals containing safety information for over300,000 pilots and 400 airlines worldwide. Its service deterio-rated when a growing line of over 100,000 aviation chartsoverwhelmed its production system. We developedoptimization-based decision support tools that improved pro-duction planning. Concurrently, we developed a method forevaluating investments in production technology. Our workreduced lateness and improved production processes, whichled to a decrease in customer complaints, a reduction in costsof nearly 10 percent, an increase in profit of 24 percent, andthe creation of a new OR group. Today, OR-based decisionsupport systems are spreading to all areas of the company.

Jeppesen Sanderson, Inc., the world’sleader in aviation information, main-

tains, manufactures, and distributes flightmanuals containing critical safety informa-tion to over 300,000 pilots and 400 airlinesworldwide from over 80 countries. Over80 percent of pilots rely on Jeppesencharts. Jeppesen’s customers include major

airlines, such as American, Delta, FederalExpress, Japan Airlines, Korean Airlines,Lufthansa, Northwest, Quantas, South-west, United, UPS, US Airways, manysmaller airlines, and many private andcorporate pilots.

Historically Jeppesen has been very in-novative, but in 1997, we found it in trou-

KATOK, TARANTINO, TIEDEMAN

INTERFACES 31:1 8

ble. Jeppesen’s growing product line over-whelmed what had been an efficientproduction system. It could not maintainits once stellar service and was threatenedwith losing a major customer. We devel-oped a suite of optimization-based deci-sion support tools that improved produc-tion planning and revealed the value ofoperations research to Jeppesen managers.Concurrently, we developed a novel and

Some weeks, it revises over1,500 charts.

general method for evaluating investmentsin production technology. With this newmethod, we overcame some difficulties thefirm experienced with previous tech-niques. Our work dramatically reducedlateness, which led to increased customersatisfaction, a reduction in productioncosts of nearly 10 percent, an increase inprofit of 24 percent, and the creation of anew interdisciplinary 14-person OR group.

Jeppesen’s founder, Captain Elrey B.Jeppesen, was one of the aviation indus-try’s early colorful pioneers. In 1927, heearned his pilot’s license, which wassigned by Orville Wright. In 1930, he be-came an airmail pilot with Varney Air-lines, and later with Boeing Air Transport,flying the Salt Lake City-Cheyenne route,the most dangerous route at that time.With no aeronautical charts available,many pilots used road maps for naviga-tion and often followed the railroad tracks.If weather conditions deteriorated toomuch, they made emergency landings infields and waited out the storms. Duringthe winters of 1930 and 1931, several ofJeppesen’s fellow pilots were killed, and

their deaths were partly attributed to thelack of aviation information. These tragiclosses prompted Jeppesen to start makingsystematic notes on issues related to flightsafety. He recorded field lengths, slopes,drainage patterns, and information onlights and obstacles, he made drawingsthat profiled terrain and airport layouts,and he even noted the phone numbers oflocal farmers who could provide weatherreports. On his days off, Jeppesen climbedhills, smokestacks, and water towers, us-ing an altimeter to record accurateelevations.

Pilots started asking Jeppesen for copiesof his notes, and in 1934, the Jeppesencharting business was born. When VarneyAirlines, Boeing Air Transport, and sev-eral other companies merged to formUnited Airlines, United became the firstmajor air carrier to subscribe to Jeppesen’searly Airway Manual Service. In 1961 Jep-pesen became a part of Times Mirror, amajor publisher (which publishes the LosAngeles Times, The Baltimore Sun, and anumber of special interest magazines, suchas Popular Science and Field and Stream). In1995, in recognition of Captain Jeppesen,the Denver International Airport namedits main terminal the Jeppesen Terminal,and it displays a statue of Captain Jeppe-sen there. In October 2000, Jeppesen be-came part of the Boeing Company team.

Today, Jeppesen Sanderson has about1,400 employees (900 in Denver, Colorado,300 in Frankfurt, Germany, and the rest insmall offices around the world). Althoughover 80 percent of pilots worldwide useJeppesen charts, the firm’s competitors in-clude the US and Canadian governments,several airlines, including Swiss Air, and

JEPPESEN

January–February 2001 9

Richel, a European firm. Jeppesen is wellaware that advances in technology aredismantling barriers to entry into theaviation-information market. In fact, thisawareness was one motivation for ourwork. Jeppesen wanted to assure custom-ers that its service and the quality of itsproducts was still unsurpassed.Problem Background: Products

Throughout our work, we concentratedon Jeppesen’s charting products. Jeppesenalso offers flight simulators, training pack-ages, flight planning, and other aviationproducts. The basic building block of allJeppesen’s paper products is the chart orflat (Figure 1). These charts range from 5.5by 8.5 inch black-and-white charts to largemulticolored maps, also called folds.Twenty-five to 36 charts are collated intosections, which are assembled into manu-als, or coverages. A manual is a largeleather loose-leaf ring binder with replace-able charts and folds.

Jeppesen’s primary products include

weekly revisions to which customers sub-scribe and new manuals. The revisions goout to customers who already have Jeppe-sen manuals. A revision is a collection offolds and charts that have been changedor revised during the current productionweek. A pilot subscribing to this servicereceives updated information every week.A customer ordering a manual gets abinder containing all the current folds andcharts for a geographical area.The Processes: The Revision AssemblyProcess

Aviation information changes so oftenthat about 75 percent of all charts are re-vised at least once every year, and a sub-stantial number of charts must be revisedeven more often. Flight manuals are usu-ally configured by geographical areas (forexample, the Western United States, SouthAmerica, or the Pacific Rim). Many pilotssubscribe to these standard coverages. Jep-pesen’s large customers, such as major air-lines, however, often order special sub-

Figure 1: Jeppesen manuals, or coverages, usually contain a set of charts for a geographicalarea, such as the Western United States, Europe, or South America. An average manual containsabout 700 charts. Charts contain safety information, such as approach routes, radio frequencies,and GPS coordinates. Some charts, called folds, are large and printed in color. Most charts,called flats (above), are 5.5 by 8.5 inches in size and are printed in black and white. Manualsare composed of numerous sections, with each section consisting of 25 to 36 flats.


INTERFACES 31:1 10

scription packages or tailored coverages.Tailored coverages contain charts with

customized information, pages speciallyconfigured, and other special features thatcustomers request. Jeppesen maintainsover 500 different standard coverages and2,000 different tailored coverages drawnfrom over 100,000 distinct charts.

A critical change in aviation information(for example, an airport runway is closedor expanded) typically affects one stan-dard chart and several tailored charts.Within one week of modifying a chart,Jeppesen must issue a new manual pageand send it to all those subscribing to cov-erages containing this page. Every weekJeppesen mails between 5 and 30 millionpages of chart revisions to over 200,000customers worldwide. Some weeks, it re-vises over 1,500 charts, affecting over 1,000coverages.

When Jeppesen obtains informationabout a possible change, it decideswhether to alter based on whether thechange is important or permanent. Somechanges, such as a runway closing for 20minutes on one day, do not need to be in-cluded on a chart. If changing a chart isnecessary, the first step of the process is toedit the image file electronically (Figure 2).Simple changes take less than five min-utes, while complex changes can takeeight hours of redrafting. After Jeppesenedits an image file, it prints a new nega-tive and sends it for imaging and printing,where it is stripped onto a plate contain-ing 21 negatives. Jeppesen then prints theplate, cuts the printed sheets into individ-ual charts, then rounds corners and drillsholes into the charts (bindery). It sends thecharts to the machine collating depart-ment, which collates them into sections.

Figure 2: When Jeppesen gets information about a potential change it decides whether thechange requires an alteration of a chart. If so, it edits the image file electronically, prints a newnegative, which goes to imaging and printing, where it is stripped onto a plate containing 21negatives. Jeppesen then prints the plate, cuts it into individual charts, and then rounds cornersand punches holes in the charts in the bindery. After the bindery, the charts go into the ma-chine collating department, where machines collate charts into sections. Each section containsup to 36 charts that will eventually go into the same coverage. These sections and large foldedmaps go to the final assembly department, where employees manually assemble these into cov-erages and stuff them into envelopes. Large boxes of envelopes then go to the shipping depart-ment. Quality control and verification is performed at each step of the process.

JEPPESEN


Figure 3: New-order manuals that are precollated and do not require revision are shipped im-mediately. Otherwise, manuals are hand-assembled or revised and then shipped.

Each section contains up to 36 charts thatwill eventually go into the same coverage.Large maps (folds) are not included in sec-tions because collating machines cannothandle thick folded material. Sections andfolds go to the final-assembly department,where employees manually assemble theminto coverages and stuff them into enve-lopes. Single envelopes addressed to pilotsand large boxes of envelopes for airlinesthen go to the shipping department, whichships by a standard method, if they are onschedule, or by express if they are not.The Processes: Orders for New Manuals

Jeppesen’s marketing department getsabout 1,500 new orders per week, each forvarious quantities of various manuals(Figure 3). For example, an airline runninga class for pilots might order 20 to 30manuals to support this training.

When Jeppesen receives a new order fora manual, it can either ship precollatedmanuals from stock or hand-assemblemanuals to order. About 60 percent of themanuals covered by new orders are pre-collated; the rest are hand-assembled. Or-ders for manuals in stock are shipped im-mediately. However, manuals that areusually precollated can be out of stock orsome of their charts may need replacingbecause of recent revisions. Producing a

new batch of the precollated manuals orhand-assembling a manual may take aslong as a week. When Jeppesen has pre-collated manuals in stock that need revi-sion, it must decide whether to manuallyinsert updated charts or to discard themanuals and build new ones.

For low volume manuals, Jeppesen usesan inefficient build-to-order process. Tobuild a flight manual, an employee mustselect charts from over 250,000 pigeon-holes, arrange them in the correct order,and separate them with the appropriatetabs. Since an average manual has 700charts, this process is extremely time con-suming and prone to errors. To decreaseerrors, Jeppesen subjects each hand-assembled manual to a quality check, inwhich another employee checks each pageagainst a content list and corrects anyerrors.Service Problems

In recent years, the increasing volumeand variety of aviation information threat-ened Jeppesen’s ability to provide promptcustomer service. By the fall of 1997, whenwe began our work at Jeppesen, the num-ber of orders delivered late was growingat an alarming rate. In the early summerof 1998, the Air Transport Association(ATA), the international organization of


INTERFACES 31:1 12

airlines, wrote to Jeppesen’s CEO com-plaining that the timeliness of Jeppesen’sservice “needed improvement and was notmeeting its expanding expectations.” TheATA demanded immediate and dramaticimprovement in the timeliness of both ofJeppesen’s modes of service: its weeklydissemination of updated aviation charts,and its shipment of orders for new flightmanuals. It did not question the accuracyand clarity of Jeppesen’s aviation informa-tion, upon which airline safety depends.

Jeppesen’s customer service had deterio-rated because its existing production andsupporting systems could not keep upwith changing customer demand. In thepast, Jeppesen’s product line had consistedprimarily of standard manuals and a smallnumber of customized manuals. Typically,standard manuals have high subscriptionquantities, and since standard manualshad historically accounted for the bulk ofthe demand, the production system wasgeared to using long production runs.Over the years, demand for customizedmanuals increased, while average sub-scription quantity decreased (Figure 4).While overall production volume in-creased slightly, the number of productsgrew rapidly and the average subscriptionquantity decreased rapidly. The produc-tion process, which relied on a combina-tion of heavy machinery, manual labor,and paper-based planning tools, remainedvirtually unchanged. Jeppesen’s managersrealized the company was in danger oflosing its competitive edge.Project Description and History

In December 1997, Alex Zakroff, a Jep-pesen industrial engineer, asked ProfessorGene Woolsey at the Colorado School of

Mines for help at Jeppesen. Zakroff be-lieved operations research could help Jep-pesen solve some problems at its produc-tion facility. Woolsey took us (fellowprofessor Elena Katok and doctoral stu-dent Bill Tarantino) and several other stu-

Figure 4: Between 1995 and 1997, Jeppesen’scustomer demands changed towards greatercustomization. The number of customers grewmoderately; the number of individual prod-ucts grew quickly, while the quantity per or-der fell rapidly.

JEPPESEN


dents to tour Jeppesen and found numer-ous opportunities to use OR tools toimprove production planning. Tarantinodecided to tackle Jeppesen’s problems anduse the analysis in his dissertation.Tarantino and Katok worked through theJeppesen plant under Zakroff’s and RalphTiedeman’s guidance in all production ar-eas per Woolsey’s recommendation anddeveloped ideas for the project. We wereactively involved with Jeppesen for thenext two years, developing analyticalmodels for process improvement, and de-cision support tools for production plan-ning and scheduling.

Our project included two parallel efforts(Figure 5). In the first, strategic economicanalysis, we studied how to improve theproduction process by making strategic in-vestments in alternative production tech-nology. We developed a list of technologyalternatives to increase throughput in theproduction areas and a method that com-

bines simulation and optimization to ana-lyze these alternatives and justify invest-ments, and we recommended purchase ofseveral pieces of capital equipment thatcost over $9 million and improved perfor-mance during 1998 and 1999.

In the second effort, we created a suiteof decision-support tools for productionplanning that used all available resourcesefficiently, including newfound capacityfrom additional equipment. We built sev-eral spreadsheet-based and database man-agement tools, which became extremelypopular among planners and have sincepermeated Jeppesen and several of its ma-jor customers, including Delta, United,and US Airways.

Our OR modeling efforts covered sev-eral aspects of production. First, we devel-oped a large-scale linear program, calledthe scheduler, that optimizes productionof the weekly revision. Second, we devel-oped a mixed-integer-programming model

Figure 5: Our project included two parallel efforts: strategic economic analysis and decision-support tools for production planning. Each project had an analysis period, an approval point,and an implementation period. The implementation month listed represents the first month ofimplementation; the implementation period can be as much as six to 12 months.


INTERFACES 31:1 14

that daily optimizes the completion ofnew orders. Third, we developed a sto-chastic dynamic inventory-managementmodel that controls disposal of outdatedcharts that vendors typically print. Finally,we developed an interactive, knowledge-based heuristic based on the approximatesolution of a large-scale nonlinear mixed-integer program to minimize scrap whenmaking plates for offset printing.Models Used in Decision-Support Tools

We used three types of interrelatedmodels in our analysis: spreadsheet-based,optimization, and joint simulation-optimization models (Figure 6, Table 1).

Our first task was to develop accuratecost estimates for the various steps in theproduction process. Jeppesen plannersprovided us with standard rates for someprocesses and average values for perfor-mance data. We tested the data andquickly identified shortcomings, which we

resolved by collecting additional data.What began as data collection to justifythe firm investing in a print-on-demand(POD) digital printing system became acost-planning tool used to make daily pro-duction decisions. To determine the cost ofa particular production step, we collectedempirical data on each process by workingin the area and recording processing timesand product characteristics. For example,to estimate the time it takes to collate acoverage on a tower collator, we recordedthe number of charts in a coverage, the to-tal quantity of the coverage demanded,the setup time for loading and unloading,and the processing times for different cov-erages. We then used regression analysisto fit equations for setup and processingtimes as a function of the number of chartsin a coverage and the quantity demanded.At times, as in the case of tower process-ing times, we observed nonlinear relation-

Figure 6: We used spreadsheet-based models to derive empirically valid time and cost estimatesfor all production areas. We then used these estimates in a variety of optimization models forproduction planning and strategic management.

JEPPESEN


Model Type/Solution Size Implementation Impact

Revisionscheduler

Linear modelcombined withheuristic

250,000variables;40,000–100,000constraints

GAMS with OSLsolver; data anduser interface inAccess

Decreased tardinessin revision by 60%;aided strategicplanning

New-ordersscheduler

Mixed-integer model 1,500variables;1,000constraints

GAMS with OSLsolver; data anduser interface inAccess

Automated thescheduling process;eliminated backlogand tardiness innew orders

Plater Nonlinear mixed-integer problem,solved using aknowledge-basedheuristic

10,000variables;1,500constraints

Algorithmwritten in Perl;data and userinterface inAccess

Automated andshortenedscheduling process;decreased scrap

Inventory-managementtool

Stochastic dynamicprogrammingmodel solved usinga heuristic

Used foralmost 1,000charts

Heuristic solutionimplemented inExcel; data anduser interface inAccess

Automated anordering process;reduced costs ofscrap and reorders

Table 1: We developed four optimization models, each of which improved a different area inJeppesen’s production operations.

ships. We later used these empirically de-rived and validated equations as inputs tooptimization models (Appendix).

Jeppesen’s production group consists ofsix distinctive areas with different pro-cesses, labor requirements, and final prod-ucts. The capacity-planning tools are asuite of spreadsheet and database modelsthat provide these areas with explanatoryreports and daily updates to manage theirweekly and daily workloads.

An important capacity-planning toolthat we developed is the revision-planningtool, a capacity-planning system that de-termines labor and equipment require-ments for the weekly revision. All Jeppe-sen managers use this system to allocatethe work they have for the week. In thepast, the production areas had no way topredict their weekly requirements. As a re-

sult, they could not plan for temporaryhelp or vendor assistance, nor could theytell employees what work to expect. Theresulting lack of efficient planning led tolate revisions, high overtime, and highemployee turnover. The revision-planningtool gave planners flexibility early in theweek to make staffing and outsourcing de-cisions and gave employees forecasts oftheir weekly workloads. In developingthese and other tools, we developed thedata building blocks and equationsneeded for other, more sophisticatedoptimization-based decision-support sys-tems at Jeppesen.

The scheduler is a linear-programmingmodel that minimizes the cost (regularand overtime labor, outsourcing, lateness)of producing the weekly revision subjectto capacity constraints and numerous in-


INTERFACES 31:1 16

ternal business rules (Appendix). Thescheduler also determines the optimal wayto produce coverages (POD, offset, or out-sourcing for printing, different types ofmachines or manual processes in machinecollating and assembly areas). The basicscheduler model has over 250,000 vari-ables and between 40,000 and 100,000constraints.

To be practical, this model must obtainsolutions in minutes on Jeppesen comput-ers. When we first formulated this prob-lem, it took several hours to solve. To im-prove solution times, we took advantageof the problem’s structure and used de-composition to reduce the problem. Wesolve the parts of the problem individuallyand then combine the solutions to con-struct the solution to the whole problem.We implemented this model and the post-processing module in GAMS [Brooke,Kendrick, and Meeraus 1999] and did pre-processing decomposition in Microsoft Ac-cess [Viescas 1999].

The data requirements for the schedulerare formidable, primarily because each re-vision has its own special business rules.We implemented the scheduler’s data in-terface in Access, which reads a flat filewith all revision requirements, generatesdata-input files for GAMS, initiates GAMSwith a macro button, and reads back theGAMS solution. Afterwards, the schedulergenerates reports for all six production ar-eas. Jeppesen uses this system twice aweek and has used it to identify data er-rors and inefficiencies in past schedulingpractices to improve use of resources andhence to reduce costs. Immediately afterwe introduced this tool, Jeppesen estab-lished a new record for the number of

consecutive weeks with 100 percent on-time revisions. The scheduler decreasedtardiness of revisions from almost ninepercent to three percent, a 60 percent im-provement, avoided expedited-shippingcosts, and dramatically improved cus-tomer satisfaction. However, our main

By working in the plant, weobtained first-handunderstanding.

purpose in developing the scheduler wasto develop a valid optimization model ofthe system for Jeppesen to use in strategiceconomic analysis.

One output of the scheduler model isthe schedule for printing charts. Thescheduler establishes the timing and incor-porates Jeppesen’s business rules, so theinformation on when to print each chartcan go to the interactive plating tool (theplater). Planners use this tool in assigningcharts to printing plates for offset printing.Each plate consists of 21, 16, or eight im-ages of charts with 800 to 1,500 chartsprinted each week in quantities of 100 toover 200,000. When one plate containsmultiple charts, the number of printsmade from the plate determines the num-ber of copies of each chart. A chart can goon a plate multiple times (one to 21), how-ever, and a chart can go on multipleplates. The machine operations area pre-fers to receive charts in close to completecoverages, but printing likes to print eachchart only once. These objectives conflict,which necessitates a systems approach inthe scheduler.

Although we can represent the platingproblem as a nonlinear integer model

JEPPESEN


(Appendix), we suspect that the resultingoptimization model cannot be solved forreal-scaled problems in anything like rea-sonable time. Therefore, we created an al-gorithm for the plater based on the platingrules used by the Jeppesen scheduler. Weimplemented this algorithm in the Perlprogramming language [Schwartz, Olson,and Christiansen 1997] with an Access in-terface that allows users to change inputsand the solution. Jeppesen is using theplater twice a week (Mondays and Thurs-days) to automate scheduling and reduceexcess printing.

The plater solution has a module forscheduling machine collating that deter-mines the first day a coverage can be com-pleted by machine operations. The prob-lem is a mixed integer program withabout 40,000 variables, 30,000 constraints,and about 4,800 binary variables thatchange weekly based on demand andsolves in a few minutes on a Jeppesen PC.

We developed the new orders model asa result of a five-day executive-trainingclass in quantitative methods that we con-ducted at Jeppesen during the fall of 1998.As part of the class, we introduced GAMSand realized that we could use an optimi-zation model to improve the on-time ratefor new orders. Before we developed thismodel, Jeppesen’s on-time rate for 1996through 1998 had averaged 61 percent,and new orders had had a moving-average backlog of about 600 late volumesa week (a volume is 700 charts). We im-plemented the model in the first week ofJanuary 1999. By the end of January, neworders was performing 95 percent on time,and the backlog had nearly disappeared.The new orders on-time rate for the first-

quarter of 2000 was 100 percent.The new-orders group runs the model

every day. The model considers about1,000 outstanding orders, a two-weekplanning horizon, the time required tocomplete an order (empirically estimatedusing a planning tool), production capac-ity, shipping requirements, and differenttypes of lateness. The model minimizescost and penalty functions for lateness thatimplicitly minimize shipping costs. Thegreatest benefits included increased cus-tomer satisfaction, which led to an in-crease in new orders (higher sales); de-creased shipping costs because of a declinein late orders; and decreased productioncosts with reduced overtime.

The new-orders model is a linear pro-gram, and we take advantage of the net-work structure of the formulation to get anearly integral solution (Appendix). Thisproblem is small (about 14,000 variablesand 2,000 constraints) and solves in lessthan a minute on a PC.

After several test runs, we found thatthe new-orders formulation resulted in aninteger solution for approximately 95 per-cent of the orders. Postprocessing similarto the scheduler’s assigns multiple day or-ders to the day in which most of the orderis produced. We enhanced the model’s so-lution with an Access database and userinterfaces. The system provides a dailyschedule that lists the time of day anorder must arrive at the shipping depart-ment to go out that day by the prescribedmethod.

When Jeppesen prints a chart, totalquantity printed is composed of the revi-sion quantity and the bin-stock quantity.The revision quantity goes to current sub-


INTERFACES 31:1 18

scribers as a part of the revision service.The bin-stock quantity is held in anticipa-tion of new orders. Jeppesen uses the in-ventory tool we developed to computebin-stock quantities for the most expensivecharts (enroute, area, and airport qualifica-tion charts).

Since Jeppesen must revise charts at un-predictable times (weeks to months afterthe current version), it cannot use stan-dard inventory-management models. Un-certainties about distribution of demandand the probabilities of revisions affect de-cisions about bin-stock quantity. If Jeppe-sen planners order too few charts, they

The time we invested inworking on the line savedus countless hours in datacollection.

may later incur large fixed costs for neworders, but if they order too many, theyrisk scrapping the bin stock if the chartmust be revised early. We model thisproblem as a periodic-review inventorysystem with random deadline [Katok et al.2000].

The new system includes an Access-based interface that makes it easy for usersto update demand and revision-historydata, to place orders, and to track savings.The system determines savings by calcu-lating the difference in costs between theresults of the old ordering process and thesolutions produced by the new system. Inaddition, we determined reorder costsfrom past invoices and compared them torecent reorder costs. Beginning in August1998, Jeppesen has used the system to con-trol the ordering process for almost 1,000

charts. Between August 1998 and August1999, the system saved over $800,000 in re-duced scrap and reduced reorders.The Sampling Algorithm for FlexibilityPlanning

This project’s most innovative technicalcontribution is a new method for deter-mining the value of equipment that pro-vides manufacturing flexibility, the sam-pling algorithm for flexibility planning.

An investment in new equipment canproduce value in three possible ways. Thenew equipment may be more efficientthan the old equipment—faster, or requirefewer operators—and the added efficiencycan decrease production costs. The newequipment may add capacity at a bottle-neck, increasing the extra capacitythroughput of the entire system and low-ering inventory costs, decreasing leadtimes, and possibly avoiding lost sales.The third way new equipment could cap-ture value is by increasing decision flexi-bility—by allowing managers to postponeproduction decisions until they acquiremore information.

For Jeppesen, decision flexibility is veryimportant. Aviation information changesconstantly, so Jeppesen often receives revi-sion or new order information after it hasstarted production. Since the offset processmay take longer than a week, productionmust start well in advance of a due date,usually when demand information is notcomplete. The ability to postpone produc-tion decisions has value.

We can use standard deterministic opti-mization models to capture value from ef-ficiency and capacity, but to capture valuefrom decision flexibility, we must modeluncertainty, which necessitates flexibility.

JEPPESEN


The ability to model uncertainty efficientlyextends our method over prior work. Wemodeled uncertainty by combining the op-timization model of the system with amodel that simulates uncertain parametersin the environment. At each step of the al-gorithm, we simulated a realization of un-certain parameters and optimized the sys-tem given all prior decisions. We thencomputed the new equipment’s value bycomparing the average performance of thesystem with and without the new equip-ment [Katok, Tarantino, and Harrison2000]. This flexibility-planning method isgeneral and can be applied beyond Jeppe-sen. We used this method to justify invest-ments in a new automated collator for theassembly department, in five tower colla-tors for machine-collating and new-orderdepartments, in a new bindery system,and in several presses (Table 2). In theanalysis that had the most revolutionaryimpact on production, we examined the

print-on-demand digital printing system(POD)—a $6.9 million investment thataugments the traditional offset process atJeppesen. This system compresses the pro-duction process of assembling revisionsinto a single operation, shortening leadtimes to hours, and planners can postponeproduction until they have complete infor-mation on demand. Digital images ofcharts are sent to the POD, which pro-duces a collated coverage. IBM custom-built this equipment, overcoming the maintechnical challenge of supporting the thinpaper Jeppesen uses for charts. Increasingits thickness by even a small amountwould increase the weight and size ofmanuals, which would be unacceptable toJeppesen customers.Approach: Active Decision Support

We were not the first analysts at Jeppe-sen to attempt changes in productionplanning or to justify investments in newtechnology, but our effort was the first

Equipment Impact

Two automatedcollators for the finalassembly area

Fewer employees needed to collate folded material. Reduced use oftemporary employees and of vendors for outsourcing foldedmaterials. Decreased costs to complete fold requirements by over$800,000 in 1999.

Two tower collators formachine collating

Improved ability to collate small coverage runs.

Three tower collatorsfor precollating neworders

Improved ability to precollate various coverage types and to precollatefor additional demand.

Bindery Simplified and enhanced bindery operations.Two new printing

pressesImproves ability to do work in house that was formerly done by

vendors.A print-on-demand

(POD) digital printingsystem

Reduced lead times, improved responsiveness, increased productivity,and decreased errors.

Table 2: Based on our analysis using the joint simulation-optimization algorithm for flexibilityplanning (and in the case of new printing presses, Jeppesen’s analysis), Jeppesen bought addi-tional equipment, which greatly improved its production operations.


INTERFACES 31:1 20

successful one in many years. In largepart, we attribute our success to a set ofguiding principles for OR implementationthat we call active decision support. Dur-ing our work at Jeppesen, we found thatthese four guiding principles helped usgain acceptance for OR methods and withsuccessful implementation:(1) Be personally involved throughout theentire process,(2) Use a systems approach to modeling,(3) Start small and build on past success,and(4) Understand and identify explicit risksassociated with change.

We found personal involvement to bethe most important of the four principles.When describing the process of buildingdecision-support systems, most textbookauthors (for example, Turbam andAronson [1998]) talk about a “needs as-sessment” and “identifying basic require-ments” as the first step in constructing aDSS. We often had the most difficulty elic-iting from users precisely what theywanted their system to accomplish. Mostusers are unfamiliar with this concept andtherefore view identifying requirements asan abstract theoretical exercise until theysee a working prototype. After a prototypehas been completed, however, substantialchanges are usually difficult. For this rea-son, we recommend that OR analystsspend time working along side plant em-ployees to fully comprehend all processesbefore starting to build tools to improveperformance [Woolsey 1998]. Many pro-fessionals never work in the areas they aretrying to improve and don’t see doing soas a useful expenditure of their time.However, we found that investing this

time is essential to thorough understand-ing and to accurate definition of systemrequirements. By working in the plant, weobtained first-hand understanding of theproduction processes, we simplified datacollection, and most important, we devel-oped long-lasting personal relationshipsand trust. In the end, the time we investedworking on the line saved us countlesshours in data collection and modeling and

“I didn’t start this company tomake money; I started it tostay alive.”

was crucial in the implementation stages.When it came to implementing thedecision-support tools for productionplanning, we were considered part of theproduction team, because we had takenthe time to participate in the original pro-cess before trying to build tools to im-prove it. Personal involvement shouldcontinue through the system-developmentcycle until full acceptance. We foundthat educating users and passing owner-ship of solutions to users was key toour success.

The second guiding principle is to use asystems approach to all modeling and im-provement efforts. At Jeppesen, each pro-duction area had traditionally operatedautonomously, seeking to maximize itsown productivity and not always consid-ering the effect on other production areas.We demonstrated the benefit of seeking tooptimize the entire production process.Using the systems approach triggered ashift in managers’ thinking about theirproduction processes and methods.

The third principle is to start small and

JEPPESEN


build upon past success. For example, thefirst time we analyzed an investment inequipment, we justified the purchase of anassembly collator, which we thoughtwould quickly improve one of Jeppesen’sproduction bottlenecks. The analysis wasstraightforward because it affected oneproduction area, final assembly, and thecollator was inexpensive given its benefits.Efficient use of the collator started to dissi-pate bottlenecks and reduce costs, ourcredibility increased, and we gained ac-ceptance for several other pieces of pro-duction equipment, each of which im-proved the system’s performance.

The fourth principle is to understandand articulate the risks associated withchange. Whenever a firm embraces a newtechnology, it takes risks. Jeppesen was noexception. These risks fall into four majorareas: technological, financial, implemen-tational, and managerial. Technologicalrisk, whether a system will perform as ex-pected, is always a concern. Financial risksstem from uncertainties about technologi-cal risks, project costs, and benefits. Imple-mentational risks have their roots withintechnical and financial risks, and withinpeople’s natural resistance to change;therefore, any OR tool that requires

change will face resistance during imple-mentation. Finally, managerial risk arisesas managers oversee the project and miti-gate other risks. By understanding therisks and communicating them clearly tomanagement, we controlled their expecta-tions and improved the probability of pro-ject success.Impact on Jeppesen and the AirlineIndustry

Alex Zakroff, the head of planning atJeppesen, compared using OR tools to“turning on the light.” Before the intro-duction of these tools, Jeppesen was un-able to predict future demands, whichforced production to scramble to fill or-ders on time. Planning tools helped Jeppe-sen to see further into the future and toplan accordingly. Also, the planning toolshelped managers to use resources effi-ciently, including the capacity the newequipment added (Table 3).

Our work at Jeppesen dramatically de-creased lateness in both new orders andrevision assembly (Figure 7). In 1998, morethan a third of new orders were late. Thiswas unacceptable, because airlines dependon Jeppesen’s products for safe operationof their flights. Through May 2000, neworders were running at 100 percent on

1998 Jan–May 2000

New orders 35% late 0% lateRevisions 8.8% late 3.3% lateCustomer complaints Increasing DecreasingThreat of lost customers Yes NoProduction cost (1998 to 1999, 1999 to 2000) �7% �10%Gross profits — �24%OR group No YesNew equipment (1999 and 2000) None $9 million

Table 3: OR had a significant impact on the performance of Jeppesen’s production and distribu-tion division that controls the revision and new-orders processes between 1998 and May 2000.


INTERFACES 31:1 22

Figure 7: As a result of using OR methods, Jeppesen’s performance has improved. Between1996 and 1999, it nearly eliminated lateness in new orders, while average daily demand in vol-umes (one volume is 700 sheets) grew by 65 percent. In revision assembly, lateness decreasedby 60 percent while total yearly volume increased by 25 percent.

time, even as demand grew. Revisions’lateness has decreased by 60 percent whilethe volume of revisions has increased by30 percent, or a quarter of a billion charts.With improved performance, Jeppesen re-ported that customer complaints and thethreat of losing major customers haddecreased.

Using Jeppesen’s financial records,which include all costs for producingflight manuals, we calculated that produc-tion costs decreased by almost 10 percent(Figure 8) and profits increased by 24 per-cent, as demand increased. The newequipment provided additional produc-tion capacity, and the planning tools and

models enabled Jeppesen to improve itsuse of all resources.

The OR methods we introduced to Jep-pesen served as catalysts for new ideasand encouraged out-of-the-box thinking.Most important, by increasing on-time de-liveries to Jeppesen’s customers, our workhas improved safety in the airline indus-try. We made improvements in four areas:—We isolated and analyzed six technolo-gies that when used efficiently in produc-tion increased the flexibility of Jeppesen’sproduction system enough that it couldprovide acceptable customer service.Based on our analysis and recommenda-tions, Jeppesen bought $9 million worth of

JEPPESEN


Figure 8: As a result of introducing OR, thegrowth trend in production costs was re-versed. While in 1997 and 1998 costs grew byalmost seven percent, in 1999 costs decreasedby almost 10 percent.

new equipment.—We developed a suite of decision-support tools for planning and sched-uling revisions that improved Jeppesen’sproduction performance. The decision-support system (DSS) combines a rela-tional database model of the revision-assembly process with a flexiblelarge-scale optimization model. Thismodel determines resource requirementsfor assembling the week’s revisions andprovides information needed to optimizethe week’s revision process. After we de-veloped the first module of the DSS, weimplemented the revision-planning tool inthe summer of 1998, and from then untilthe spring of 1999, Jeppesen deliveredonly two revisions late. It made similarimprovements in new orders increasingon-time orders from a low of 65 percent in1998, the year prior to our work, to 100percent in 2000.—We introduced OR to Jeppesen and,during two years, substantially changedits operations.

—We believe we succeeded because weused active decision support, starting byphysically working through the produc-tion process from start to finish. By doingthis, we gained understanding of the pro-cess and credibility with employees andmanagers on the production floor, withoutwhose support change would not havetaken place.—Our work introduced Jeppesen to opera-tions research methods, highlighting theusefulness of applied OR for manufactur-ing and technology management. NowOR-based decision support systems arespreading throughout the company, andin its 1999 organizational restructuring,Jeppesen created an autonomous, interdis-ciplinary operations research and planninggroup at the director level. This group of14 people consists of OR analysts, indus-trial engineers, production planners, andmanagement-information-systems profes-sionals, who are charged with using ORapproaches to improve efficiency through-out the company.—We improved the safety of the airline in-dustry. Jeppesen products are essential tothe airlines and their safe operation. Al-though the benefits are difficult to quan-tify, the reliable, on-time delivery avoidsdisruption to airline services (with possi-ble losses in revenue and even in terms ofloss of human life). Many customer testi-monials concerning Jeppesen’s charts’ im-pact on the safe operation of various air-lines and private pilots are on file at themarketing department. As Captain ElreyJeppesen said, “I didn’t start this companyto make money; I started it to stay alive”[Opening ceremonies at Denver Interna-tional Airport, February 21, 1995].


INTERFACES 31:1 24

Contributions to Operations ResearchProfession

Our work at Jeppesen demonstrated thevalue of OR analysis in a company that in-fluences the safety of millions of airlinepassengers and pilots every week. It alsochanged every facet of Jeppesen’s produc-tion process. Indeed, Jeppesen demon-strated that it realized the value of thiswork by creating its OR group. Jeppesen’sthen parent company, Times Mirror,awarded Jeppesen the 2000 Times MirrorInnovation Prize in recognition of itsrevitalization.Acknowledgments

We thank Gene Woolsey for his adviceand support throughout this effort. Hiscommon sense approach to the practice ofOR greatly contributed to our success andto the acceptance of the OR tools andideas at Jeppesen.

Our heartfelt thanks go to RickRosenthal, who was our coach for theEdelman competition. Rick’s insightfulsuggestions improved our presentationand this paper. He was extremely gener-ous with his time and went beyond thecall of duty in coaching us—thanks, Rick!

We thank Gerry Brown, Rob Dell, andKevin Wood of the Naval PostgraduateSchool, and Terry Harrison and GaryLilien of Penn State University for com-ments on our presentations and for pro-viding extremely valuable feedback.

We are also grateful to our spouses,Gary Bolton, Arleen Tarantino, and SandyTiedeman for their feedback and their con-tinuous support, not to mention theirgreat patience during the last two weeksbefore the Salt Lake City INFORMSconference.

To the team at Jeppesen, who incurredrisks and assisted us in our attempts—abig thank you! A special thanks to HorstBergmann, Tim Bolton, Dominic Custodio,Gary Ferris, Hans-Peter Gantz, BruceGustafson, Cindy Pakiz, Tim Sukle, MarkVan Tine, Paul Vaughn, Alex Zakroff, andall the other Jeppesen staff who assisted uswith data collection, model development,and implementation.APPENDIX

We used the following mathematicalmodels at Jeppesen Sanderson, Inc.The Production Scheduling Model(Scheduler)Indicest days of the week, e.g., Monday.r production resources, e.g. machine

tower, ditte collator, and insertercollators.s production stages, e.g. printing (PR),

machine collating (MC), assembly (FA).c, c� coverages.p charts, or pages in a coverage.

Coverage and Chart Index SetsC all coverages.P all charts.CAW� C airway coverages.CAC � C air-carrier coverages.PAW � P airway charts.PAC � P air-carrier charts.The two groups of charts and coverages,

airway and air carrier, are mostly pro-duced separately, although one group ofair-carrier coverages contains only airwaycharts. Airway coverages never containany air-carrier charts and are shipped toall categories of customers. Air-carrier cov-erages are generally shipped to airlinecustomers.Time Index SetsT all days of the week.TAW � T days for producing airway

coverages, beginning of the week.TAC � T days for producing air-carrier

coverages, end of the week.

JEPPESEN


Resources Index SetsR all production resources.RPR printing resources.RMC machine-collating resources.RFA final-assembly resources.

Given Data on Coveragesdemandc subscription quantity of cover-

age c.foldc number of folds in coverage c.flatc number of flats in coverage c.maxdist maximum difference in content

of two coverages to be produced simulta-neously in machine collating.Given Data on Chartstotqp total print quantity for chart p.bstockp bin stock quantity for chart p.

Given Capacity and Production Dataregprinttr number of hours of capacity

available in printing area on day t onresource r � RPR.regcollatert number of hours in machine

collating available on day t on resource r� RMC.regassemrt number of hours in assembly

available on day t on resource r � RFA.otpintt number of overtime hours of ca-

pacity available in printing area on day t.otcollatet number of overtime hours in

machine collating available on day t.otassemt number of overtime hours in as-

sembly available on day t.secr number of charts in a section built

using resource r.opersr number of operators needed to

run resource r.tempcapt maximum number of tempo-

rary hours available on day t.Given Revision Characteristicscontentcp 1 if coverage c contains chart p

and 0 otherwise.ucovboundct the upper bound on produc-

tion of coverage c on day t. Generally ucov-boundct � demandc ∀ c � CAW, t � TAW or c� CAC, t � TAC and 0 otherwise, but thereare some exceptions.uchartboundpt the upper bound on pro-

duction of chart p on day t. Generally

uchartboundpt � totqp ∀ p � PAW, t � TAWor p � PAC, t � TAC and 0 otherwise butthere are some exceptions.Given Cost Datareginwages regular hourly wage in pro-

duction stage s � {PR, MC, FA}.otinwages overtime hourly wage in pro-

duction stage s � {PR, MC, FA}.outprcost cost to print one chart using an

outside vendor.outassemcost hourly cost for outside as-

sembly vendor.lcostc penalty cost if coverage c is late.invpenalty small inventory penalty to

prevent unnecessary inventory.tempcost hourly cost for temporary em-

ployee in assembly.Derived Datadistc,c� � �p |contentcp � contentc�p| the

difference between coverage c and c�.sectionscr � [flatc/secr] if flatc � 0, 0 oth-

erwise; number of sections in coverage c ifit is collated using tower.sqtyp � �c contentpc � demandc amount

of chart p needed to produce the entiresubscription quantity of all coverages thatcontain it.sfactorp � 1 � totqp � sqtyp/sqtyp scrap

factor for charts printed.Empirically Derived Datamsetupcr time (in minutes) it takes to set

up coverage c in machine collating area tobe processed on resource r � RMC.mprocesscr time (in minutes) it takes to

process one unit of coverage c in machinecollating area on resource r � RMC.asetupcr time (in minutes) it takes to set

up coverage c in final assembly area to beprocessed on resource r � RFA.aprocesscr time (in minutes) it takes to

process one unit of coverage c in final as-sembly area on resource r � RFA.pprocess time (in minutes) to print one

chart, approximated by allocating thefixed setup time over the average runquantity for a plate of 21 charts.tprocesscr time (in minutes) for a tempo-


INTERFACES 31:1 26

rary worker to process one unit of cover-age c in the final-assembly area on re-source r � RFA.

We empirically derived setup and pro-cessing times for using different resourcesat different production stages by collectingthis data and then fitting regressionequations.Decision Variables for Production/FlowPAPERPRODprt number of charts p pro-

duced in printing using resource r � RRPon day t.COVERPRODcrt number of coverages c

produced in machine collating using re-source r � RMC on day t.ASSEMPRODcrt number of coverages c

produced in final assembly using resourcer � RFA on day t.SHIPct number of coverages c shipped

on day t.LATEc number of coverages c late.

Decision Variables for InventoryPAPERINVpt number of charts p avail-

able at the end of day t.COVERINVct number of coverages c that

passed machine collating available at theend of day t.ASSEMINVct number of coverages c that

passed final assembly available at the endof day t.Decision Variables for Overtime, TemporaryEmployees, and OutsourcingOUTPRNpt quantity of charts p out-

sourced for printing on day t.OUTASSEMct quantity of coverages c

outsourced for assembly on day t.OTPRNtr number of overtime hours

used in printing on day t on resource r �RPR.OTMCtr number of overtime hours used

in machine collating on day t on resourcer � RMC.OTFAtr number of overtime hours used

in final assembly on day t on resource r �RFA.TEMPASSEMtr number of temporary

hours used in final assembly on day t on

resource r � RFA.ObjectiveMinimize

�c (lcostc � LATEc � outassemcost �OUTASSEMc) � outprcost � �p OUTPRNp� �rt (otinwagePR � OTPRNtr �otinwageMC � OTMCrt � otinwageFA �OTASSEMtr) � �prt (reginwagePR � ppro-cess � opersr � PAPERPRODprt) � tcr�Rmc(reginwageMC � opersr � msetupcr/demandcmprocesscr COVERPRODcrt) � �cr�R tFA

(reginwageFA � opersr � asetupcr/demandcaprocesscr ASSEMPRODcrt) � invpenalty �ct(COVERINVct � ASSEMINVct) � invpen-alty �pt PAPERINVct � tempcost � tcr�RFA(opersr � tsetupcr/demandc tprocesscrTEMPASSEMrt).

The objective function minimizes the to-tal weighted sum of lateness penalty, out-sourcing cost, overtime-labor cost, andregular-labor cost. We approximate theimpact of setup costs in the machine-collating and assembly areas by calculat-ing the per-unit setup costs by dividingthe total setup cost by the demand (lines 4and 5). This approach has been shown towork well in a wide variety of lot-sizingproblems [Katok, Lewis, and Harrison1998].Production Flow ConstraintsFlow constraint for printingPAPERINVp(t�1)

� PAPERPROD �OUTPRN� prt ptr�RPR

� content COVERPROD� pc � crtc r�RMC

�PAPERINV �0 ∀ p, t.pt

(1.1)Flow constraint for machine collatingCOVERINV � COVERRODc(t�1) � crt

r�RPR

� ASSEMPROD� crtr�RFA

� OUTASSEM � COVERINVct ct

� 0 ∀ c,t.(1.2)

JEPPESEN


Flow constraint for final assembly

ASSEMINV � ASSEMRODc(t�1) � crtr�RFA

� OUTASSEM � SHIPct ct

� ASSEMINV � 0 ∀ c, t.ct

(1.3)

Every coverage demanded is eithershipped or is late

SHIP �LATE �demand ∀ c. (1.4)� ct c ct

Capacity ConstraintsCapacity in printing

pprocess � sfactor� pp

� PAPERPROD � regprintprt rt

� OTPRN ∀ t, r � R . (1.5)rt PR

Capacity in machine collatingWe approximate the impact of setups on

capacity by allocating the setup time on aper-unit basis.

((msetup /demand � mprocess )� cr c crc

� (COVERPROD ) � regcollatecrt rt

� OTMC ∀ t, r � R . (1.6)rt MC

Capacity in final assemblyNote that since setups in assembly are

external, they do not affect capacity.

aprocess � ASSEMPROD� cr crtc

� regassem � OTFArt rt

� TEMPASSEM ∀ t, r � R . (1.7)rt FA

Overtime capacity in printing

ORPRN � otprint ∀ t. (1.8)� rt tr�RPR

Overtime capacity in machine collating

OTMC � otcollate ∀ t. (1.9)� rt tr�RMC

Overtime capacity in final assembly

OTFA � otassem ∀ t. (1.10)� rt tr�RFA

Temporary employee hours capacity

TEMPASSEM� rtr�RFA

� maxtemp ∀ t. (1.11)t

Business Rules ConstraintsThis constraint insures that similar cov-

erages are produced at the same time onthe same resource in machine collating.Note that this constraint fulfills its intentwhen coverages c and c� are each pro-duced on a single day using a single re-source. This is the case with over 95 per-cent of coverages. For the other fivepercent, we use a postprocessing moduleto move production to the resource andday where the largest quantity isproduced.

COVERPROD COVERPRODcrt c�rt�

demand demandc c

∀ r and c, c� where dist � maxdist.cc�

(1.12)

Insures that business rules on chart pro-duction are respected

PAPERPROD� prtr�PPR

� unchartbound ∀ p, t. (1.13)pt

Insures that business rules on coverageproduction are respected.

COVERPROD� crtr�RMC

� ucovbound ∀ c, t. (1.14)ct

New-Orders ModelIndicest the next 14 work days.p order number.c coverage.r resources (30-bin tower, 60-bin tower,

by hand).Index SetsCp � C coverages in order p.

Given Datacapacityt available hours for a day t.otval overtime limit for any week (usu-


INTERFACES 31:1 28

ally 20 percent).capval limit on the amount of available

time that can be used for orders.flatc number of flats in coverage c.infoldc number of folds that must be

placed inside coverage c.endfoldc number of folds that go on the

bottom of coverage c.sectionscr number of resource r sections

in coverage c.wage hourly regular-time wage.otwage hourly overtime wage.

Empirically Derived Dataptimep time required to complete an

order.duep,t penalty cost if order p is shipped

on date t. (Penalty factors are based on thenumber of days an order is late andwhether the order is late in shipping orlate to the customer. An order late to ship-ping can reach the customer on time bypremium shipping method. The highestpenalty is lateness to the customer.)caprealt the real capacity for any day t,

where caprealt � capacityt(1 - capval).msetupcr time (in minutes) to set up cov-

erage c in order p in the new-orders areato be processed on resource r.mprocesscr time (in minutes) to process

coverage c in order p in the new-ordersarea on resource r.asetupcr time (in minutes) to set up a

coverage c in order p in the new-ordersarea to be assembled on resource r.aprocesscr time (in minutes) to assemble

coverage c in order p in new orders on re-source r.

We empirically derived setup and pro-cessing times for each coverage in an or-der using different resources at differentproduction stages by collecting requireddata and then fitting regression equations.Derived Dataptimepr total time to complete order p us-

ing resource r.ptimepr � (msetupcr � mprocesscr�c�C ,rp

� asetupcr � aprocesscr).

Decision VariablesXprt production of order p on resource r

day t.OTIMEt overtime on day t.

Objective FunctionMinimize �prt dueptXprt � wage �prt

ptimeprXprt � otwage �t OTIMEt.Minimizes the sum of total labor cost

and total late penalty cost associated withproducing all the orders.ConstraintsCapacity constraint

ptime X � capreal� pr prt tpr

� OTIME ∀ t. (1.15)t

Ensures that the entire order is processedon one day t

X � 1 ∀ p. (1.16)� prtrt

0 � Xprt � 1 ∀ p, r, t.OTIMEt � 0 ∀ t.

Interactive Plating ModelIndicesc all charts in the revision.p all plates in the revision.

Given Datafcostp the fixed cost of using plate p.vcostp the variable cost pf printing one

copy of plate p.demandc number of copies of chart c

needed in the revision.csizec the size of chart c.psizep the size of plate p in terms of the

number of size-1 charts it can hold.Decision VariablesXcp the number of times chart c is put on

plate p.Yp is 1 if plate p is used and 0 otherwise.Qp the number of impressions of plate p

printed.For each plate p, we can compute the

upper bound on print quantity Q̄p as afunction of what is on the plate:

demandcQ̄ � max .p � �Xc cp

JEPPESEN


Objective FunctionMinimize �p vcostpQp � fcostpYp. Mini-

mizes the total plating and printing cost.Constraints

Ensures that we print sufficient numberof each chart c

X Q � demand ∀ c. (1.17)� cp p cp

Links the Qp and the Yp variables

¯Q � Q Y ∀ p. (1.18)p p p

Ensures that we do not put more chartsc on a plate p than the room on the plateallows

csize X � psize . (1.19)� c cp pc

Yp�(0, 1) ∀ p, Xcp integer ∀ c, p,Qp � 0 ∀ p.

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Katok, E.; Lewis, H.; and Harrison, T. P. 1998,“Lot sizing in general assembly systems withsetup costs, setup times and multiple con-strained resources,” Management Science, Vol44, No. 6, pp. 859–877.

Katok, E.; Tarantino, W.; and Harrison, T. P.2000, “Investment in production resourceflexibility: An empirical investigation ofmethods for planning under uncertainty,”Working paper, Pennsylvania State Univer-sity, University Park, Pennsylvania.

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