job grouping in surface mounted component printing

*Corresponding author. Tel.: 358-2-3338671; Fax: 358-2-3338600;E-mail: [email protected]

Robotics and Computer-Integrated Manufacturing 15 (1999) 39—49

Job grouping in surface mounted component printing

Jouni Smed, Mika Johnsson*, Mikko Puranen, Timo Leipala, Olli NevalainenDepartment of Mathematical Sciences and Turku Centre for Computer Science (TUCS), University of Turku, FIN-20014 Turku, Finland

Abstract

The arrangement of operations in a production line for mounting the surface components on a printed circuit board is discussed.The production program includes a wide range of different products, which causes frequent set-up operations. The overall efficiency ofthe production line depends heavily on how the printing operations are organized. Set-ups cause delays which can be cut down byselecting carefully the feeders for the components and by solving a suitable sequence for the products. We describe an integratedproduction management system for job grouping. The system utilizes approximate algorithms for minimizing the number ofcomponent switching instants. A discussion of the exact minimization by using mathematical 0/1 integer programming approach isalso given. The revision of the production management system has had a major impact on the productivity, and an increase of ca. 58%in the number of component insertions per hour is observed. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Printed circuit boards; Group technology; Approximate algorithms

1. Introduction

In flexible manufacturing systems (FMSs) [1] severaldifferent types of products are manufactured by the sameproduction facilities. FMS reduces the machinery invest-ments and widens the product range. However, it alsoprovides us with many challenging production planningand management problems.

We present in this paper a production environmentwhich comprises batches of different products, each de-manding special set-ups, parts, tools and numericallycontrolled execution (NCX) codes. We assume that theset-up times caused by the product changes are non-negligible, and therefore we can decrease the set-up costsby sequencing the products suitably. In addition to thegoal of minimizing the set-up costs, the production mustmeet due dates. The management wants to utilize theproduction facilities maximally and to cope with theshort delivery times. At the same time it is preferable ifthe finished products do not pile up in internal storages.

We can control the finishing times — and in this wayalso the fulfillment of the due dates — by scheduling the

jobs. In many cases the production planner is mainlyconcerned with the due dates, and the minimization ofthe set-up times may sometimes conflict with this goal.The construction of a feasible and, preferably, an efficientschedule is one of the most difficult tasks in productionplanning. It has been shown that the problem is toocomplicated to be solved accurately (even in theory)[2, 3]. Therefore, the problem is usually approached bythe use of approximative algorithms.

In this paper we discuss the organization of an actualproduction plant. Furthermore, we concentrate ona single machine despite the fact that the machine is onlya part of the production process. The reason for thissimplification is the dominating role of this work phasecompared to all other phases in the system. Our researchoriginates from a printed circuit board (PCB) assemblyplant (Teleste Corporation, Nousiainen, Finland) andaims at a solution for everyday use. The productionline considered here is capable of manufacturing a largeselection of different jobs (i.e., batches of PCBs).During the last two years the number of different PCBtypes has been over 350, and their respective annualproduction volumes vary from one to several thousandboards. Because the batch sizes are relatively small,the production is highly flexible and demands severalset-ups daily.

0736-5845/99/$ — see front matter ( 1999 Elsevier Science Ltd. All rights reserved.P I I : S 0 7 3 6 - 5 8 4 5 ( 9 8 ) 0 0 0 3 4 - 9

Research work on PCB assembly has been done bymany authors. Crama et al. [4] divide the problems ofPCB production planning into five categories:

1. partitioning the set of board types into families,2. partitioning the set of component locations for each

board type,3. determining the feeder set-up for each machine,4. assigning a component placement sequence for each

pair consisting of a machine and a board type, and5. assigning a component retrieval plan for each pair of

machine and board type.

Crama et al. focus on problems 2—5, whereas our focus ismainly on problem 1 because we concentrate on one lineand one machine instead of multiple lines, but problems3 (feeder optimization) and 4 (order optimization) arealso taken carefully into account by our system.

Ammons et al. [5] categorize the strategies for set-upmanagement as follows:

1. Single set-up strategy in which a group of machines isconfigured to produce a family of PCBs using a singleset-up:(a) ºnique set-up strategy in which the family con-

tains only one product type (i.e., mass production).(b) Family set-up strategy in which the family com-

prises several product types.2. Multi set-up strategy in which limited component

staging capacity prohibits applying the single set-upstrategy (see also [6]):(a) Decompose and sequence in which the family is

divided into subfamilies which are then sequencedto minimize the incremental set-ups between sub-families.

(b) Partition and repeat in which the required compo-nents are partitioned into subsets restricted bymachine capacity.

Our approach uses the multi set-up strategy because thenumber of components vastly exceeds the capacity of themachine. We will show later in this paper how to applythe decompose and sequence strategy to the actualproduction process.

Maimon and Shtub [7] present a classification of theapproaches for sequencing PCBs and components on anautomatic assembly line. This classification divides theproblem into four categories according to the number oftimes each PCB is loaded (one or many) and the numberof times each component is loaded (one or many). In ourproblem, the PCBs are loaded only once, whereas thecomponents can be loaded several times. Therefore, wehave three different strategies for the set-up: a staticset-up which is identical for all products, a set-up which isidentical for only a part of the products (family set-up),and every product has its own set-up. The first strategy isstraightforward but, unfortunately, it is not applicable inour case because the total number of different component

types exceeds the feeder capacity. The third strategyresembles the situation before the introduction of thesystem presented in this paper. The second strategy isa compromise: here we form standard set-ups for productgroups (i.e., different products can use the same set-up).Note that in the first strategy we have one single familywhereas in the third strategy each product forms a singu-lar family (or product group). The difficulty with thefamily set-up strategy is that once the families have beenassigned, the jobs should be sequenced on family basis,not independently. Nevertheless, this strategy forms thebasis of the solution presented in this paper: the productsare divided into groups which are then sequenced by theproduction engineer.

Another usual presumption is that the jobs are firstsequenced and after that the set-up is optimized (cf. [8]).In our case optimizing the set-up for a given group is themost important task. Sequencing, which is done later, isleft for the user to decide. Also, the usual optimizationcriterion reported in literature is minimizing the numberof set-up operations (i.e., the total number of loadedcomponents), whereas our goal is to minimize the numberof set-up occasions (i.e., the number of instants the set-upoperations occur). Tang and Denardo [9] present ana-lyses for both minimizing the number of tool switchesand minimizing the number of switching instants (orset-up occasions). In the first case we assume that eachtool switch increases the processing time linearly. In thelatter case we assume that the set-up of the tools for thenext group is parallel to the processing of the previousgroups and, therefore, we should minimize the number ofjob groups.

Crama and van de Klundert [10] define the loadingstrategy as a specification of the contents of the toolmagazine at the beginning of the processing of each joband identifying four basic scheduling problems:

1. ¹ool switching in which we try to find an input se-quence and a loading strategy with a minimum totalset-up time when it depends linearly on the number ofswitches.

2. ¸oading problem in which we try to find a loadingstrategy for a given part input sequence when theminimization criterion is the same as in case 1.

3. Job grouping in which we try to find an input sequencefor the parts and a loading strategy for the tool maga-zine with a minimum total set-up time when it de-pends linearly on the number of switching instants.

4. Batch selection in which we try to find the largestgroup of jobs that can be processed without toolswitches.

Originally, we considered the problem presented in thispaper as an iterative batch selection problem (cf. [11]).However, because minimizing the switching instants (orthe set-up occasions) turns out to be the most importantcriterion, our problem is a variant of the job grouping.

40 J. Smed et al. / Robotics and Computer-Integrated Manufacturing 15 (1999) 39—49

Fig. 1. The production phases of the surface-mounted onsertion. Legend: SMD"surface mounting device, GSM"general surface mounting device,MI"manual insertion.

Carmon et al. [12] divide traditional approaches toreduce set-up times into two categories:

f reducing set-up frequency by enlarging the lot sizes,and

f group technology (GT).

In group technology, efficiencies in manufacturing arerealized by grouping similar tasks and dedicating equip-ment for performing these tasks. GT is often consideredto be a part of medium range planning (cf. [7] for descrip-tions of long-, medium- and short range — or strategical,tactical and operational — production planning in PCBassembly), but in our case the dynamic nature of theproduction environment enforces up to apply GT in theshort-range planning. This feature is contrasted, in addi-tion to those mentioned above, with the works by Bran-deau and Billington [13], Hillier and Brandeau [14] andCarmon et al. [12]: In [14] the component set-up lastsfor 6—12 months, whereas in our case the set-up changesseveral times weekly. In [13] the environment is similarto ours with respect to a wide mix of boards and a lowproduction volume for each board, but the line comprisessemi-automated machines and each board is producedindividually (i.e., there are no batches).

A group set-up (GSU) method is presented in [12].GSU works through four steps: set up the commoncomponents of the group, print them on the whole group,set up residual components of each PCB, and print themon each PCB separately. Despite the similarities, GSUdiffers from the strategy presented in this paper in thatthe common and residual components — or standardset-up and custom set-up components, as Ammons et al.refer to them in [5] — are printed simultaneously by thesame machine. Because reloading is not allowed, we donot break the families when printing the residual orcustom components, as in GSU.

Crama et al. [2, 10] give a solid theoretical back-ground for the tool management problems and provethat job grouping is NP-hard. They discuss the worstcase of eight known batch selection algorithms and showtheir potential inefficiency. However, we must stress thattheir ‘‘job-sequencing and tool loading’’ problem makesfew assumptions in the theoretical model, and this makesthe problem somewhat different from ours. For example,it is assumed that each tool (or component) fits in one slot

of the magazine; this is not the case in the environmentdescribed in this paper. Also, we must cope with duedates and some production-dependent relations of PCBs(e.g., PCB widths and two-sided boards).

The remainder of this paper is organized as follows.We start by describing the component printing line. Thissection contains some technical details which are neededin order to clarify the aspects of the problem in question.Next, the inefficiencies in the operation and our proposalfor a revised production planning system is described.We also describe a new method for updating the controlprograms of the machine and strategies for filling thefeeders. Next, we study what are the possibilities to im-prove the overall production by grouping the products( job grouping) and present a mathematical model andheuristic algorithms for solving this problem. After thatthe working system is described and an evaluation of theeffects of the new system is given. The paper is closed byconcluding remarks.

2. The production environment

Let us consider a typical assembly line for componentprinting, see Fig. 1. The line comprises several successivework phases. An initially empty PCB passes first a gluedispenser which inserts a glue dot at each onsertionlocus or draws adhesive paste over the whole board inorder to fixate the electric components. The actualprinting is done by two onsertion machines. The firstone, surface mounting device (SMD), is adapted to fastoperation and it is used for the majority of the compon-ent onsertions. Components which require specializedtools are onserted by a more flexible but slower robot,a general surface mounting (GSM) machine. These twoonsertion phases are followed by an oven which heats thePCBs in order to harden the glue/paste. After that thePCBs wait in a buffer storage and finally pass a manualinsertion phase in which some large components areinserted and soldered.

If we look at the different jobs (PCB batches) which areprocessed on the line, we notice that their total number isvery high but the amount of PCBs in a job is usuallysmall. The daily production program includes typically4—10 different products (PCB types). The set-up times

J. Smed et al. / Robotics and Computer-Integrated Manufacturing 15 (1999) 39—49 41

Fig. 2. A schematic view of the SMD printing machine.

form a significant part of the total production time — itcan be as much as 50%. Therefore, our main objective isto minimize the set-up times by arranging the productsefficiently. The due dates are managed by a two-levelpriority classification: products are either urgent or non-urgent. The last feature that affects the overall productiontime is that there are two different widths for the PCBs.Therefore, if the next PCB has a different width than theprevious one, the width of the conveyor must be changed.

Because the set-ups and component printing of theSMD machine [15] consume most of the productiontime, it is the bottleneck of the whole production line.The difficult management of the machine in a multi-modelproduction environment emanates from its flexibility. Themachine gets the surface mounted components from sixcarriage modules, see Fig. 2. The following technical de-tails should be taken into consideration:

1. Each carriage includes 80 linearly arranged feederslots which contain the components. A componenttakes at least two slots giving thus each carriage a the-oretical maximum capacity of 40 components, and240 components for the whole machine. Because thesum of different component types in a PCB is signifi-cantly smaller than the capacity of the machine,we can quite freely choose an appropriate inputorganization.

2. The two outermost carriages can be separated fromthe unit while the machine is operating. The operatorcan carry out the set-up procedure for carriages 1 and2 (or 5 and 6) while carriages 3—6 (or 1—4) are active inthe component printing (configurations shown inFig. 2). While the machine is working, the set-up of themidmost carriages 3 and 4 cannot be changed. There-

fore, they should contain the most commonly usedcomponents.

3. The structure of the new system

Before the system described in this paper was introduc-ed, the existing organization of the production lineneeded some refinements. Previously carriages 2—4 werefilled with the standard set-up components. The boardwas then printed with components from carriages 1—4 ifthe required components were contained by the standardset-up carriages 2—4 and the rest could be set up incarriage 1. Otherwise, the board was printed with stan-dard set-up components from carriages 3 and 4 andcustom set-up components from carriages 5 and 6. Thismethod was, however, inefficient because of the followingreasons:

1. The printing program were laborious to update,which caused that the standard set-up componentswere seldomly changed. Therefore, the standard set-up gradually corrupted to contain components whosedemand was not maximal any more. In addition, therewas no efficient method for solving a new standardset-up.

2. Each product required a separate set-up because eachprinting program required a new setting for the cus-tom set-up components. Furthermore, it was seldompossible to print one product during the set-up ofanother.

3. The order of the components in the feeders was notvery efficient, which further reduced the productivity.

4. The printing order was poor.


Fig. 3. The revised update procedure.

The revised production planning system solves theseinefficiencies by introducing the following new features:

1. a method for choosing the standard set-up,2. forming groups of jobs with the same feeder setting,3. feeder optimization for product groups, and4. using an efficient code generator that utilizes the cur-

rent feeder set-up.

However, these features require a flexible and dynamicupdate process for the printing programs which isdiscussed in the next subsection. For the feeder andprinting order optimization we use previously developedmethods [16].

The new system uses a different partition of standardand custom set-up carriages where carriages 3 and 4 con-tain now a standard set of components, thus leaving onboth ends symmetrically two carriages for the customset-up. This layout enables continuous printing: whilePCBs are being printed, the components of the nextset-up can be placed on carriages which, at the time,remain idle on the other end of the machine.

3.1. Updating the printing programs

In the old system the printing program updating wasproblematic. Previously, when there were changes in thePCB or updates to the printing data, the changes weremade directly to the NCX file and not to the CAD file.The NCX files (a file type used by Universal HSP4790/91/92 and Sanyo TCM 1000/1100 SMD printingmachines) contain the feeder set-ups for each PCB. Theprogram which creates them has two inputs: a CAD fileof the PCB and a file containing the standard feederset-up. If the changes were made to the CAD file, theNCX file would have to be recreated by using theCIMBridge-system [17], which takes a long time and isgenerally a laborious task. The minor changes made tothe file continued to add up until it was no longer efficientto use the original source files.

Fig. 3 presents a solution to the problem: The NCXfiles are now updated by using a new program which usesthe old NCX file and a new feeder set-up file as an inputand updates the NCX file accordingly. The updated NCXfile still contains the changes made to the original NCXfile. The revised update procedure enables us to intro-duce new feeder set-ups, which was a troublesome opera-tion in the old system. This is required when we introduce

the concept of product groups. These groups are dy-namic, and therefore every time a product is manufac-tured, it requires an updated NCX file.

3.2. Choosing the standard set-up

By using the production data we have to decide whichcomponents should belong to the standard set-up (i.e., incarriages 3 and 4). In the current system, we pick first themost frequently produced PCBs. From these PCBs weselect 80 most frequently used components (which takethe available 160 feeder slots), omitting wide componentsand components which are slow to print. On the whole,choosing a standard set-up has turned out to be a non-critical factor with respect to the overall operation of theplant.

4. Grouping

In this section we return to the second feature of theplanning system: forming job groups with identical feederset-ups. In the previous section we presented a strategy inwhich a part of the jobs has the same set-up. These jobsform a group [18, 7] and they are printed successively. Inaddition, there is no need for set-up operations betweenjobs belonging to the same group. If the printing ofa group takes a longer time than the set-up of the nextgroup, the group changing does not cause a delay andthe PCBs can be printed continuously. Therefore, theproducts are classified into groups according to theircloseness (i.e., the amount of mutual components).Products belonging to the same group will succeed eachother (if possible). Thus, they use the same carriagesand leave the other end of the carriage unit free for thenext set-up.

Let us give an example of the grouping in which wewant to process jobs A, B,2, J (Fig. 4). Jobs ABC be-long to the same group and use a wide conveyor, whilethe narrow PCBs form groups DE, F and GHIJ. JobD is urgent. Fig. 4b shows a possible sequence forthe groups. The group DE is processed first due to theurgency of job D. The components belonging to thecustom set-up of the group DE are located in carriages1 and 2. The custom set-up of the group GHIJ is incarriages 5 and 6, the next group (F) again in carriages1 and 2 and the last group (ABC) in carriages 5 and 6.


Fig. 4. An example of job grouping.

See Fig. 4c for an illustrative Gantt diagram of theprocessing.

The remainder of this section is divided as follows: first,we present a mathematical formulation for the group-ing problem. Secondly, we concentrate on heuristicapproaches. Finally, we give test results for thesealgorithms.

4.1. Mathematical formulations for grouping

We can formulate the job grouping problem as a math-ematical optimization problem [19]. In this section wepresent a model for minimizing the number of groups orequivalently the number of set-up occasions (see [11] fora model which maximizes the size of the group). For thismodel we introduce the following parameters:

f di: the number of feeder slots needed by component i,

f m: the number of different PCBs,f n: the number of different components,f k: the capacity of the carriage,f a

ij: the amount of component i needed by board j.

The set-up occasions are indexed with l wherel"1,2, ¸. Therefore, the carriage is loaded at most¸ times (estimated beforehand).

Let us now denote the decision variables

xil"G

1 if component i is set up in the carriagein the occasion l,

0 otherwise,

yjl"G

1

0

if board j is printed with set-up l,

otherwise,

zl"G

1

0

if set-up l is required,

otherwise.

Then we get the minimal number of groups by solving

1 ) z1#2 ) z

2#2#¸ ) z

L"min! (1)

and

x1l

d1#x

2ld2#2#x

nldn)kz

l, l"1,2, ¸.

yjl4x

il, l"1,2 , ¸; i, jUminM1, a

ijN"1,

(2)yj1#y

j2#2#y

jL"1, j"1,2, m,

xil3M0, 1N, y

jl3M0, 1N, z

lM0, 1N.

This formulation has many equivalent solutions (lJ ! if lJ isthe optimal amount of set-up occasions), and thereforewe can add the restriction

y1, l`1

#2#ym, l`1

4y1l#2#y

ml,

l"1,2, ¸!1. (3)

In this case the size of the first group is the greatest, thesize of the second group the second greatest, etc. Notethat the numbering does not restrict the scheduling of thejob groups at the moment of actual production.

Due to the large size of problems (1)— (3) we will give inthe next section a number of approximative solutionalgorithms for the problem.

4.2. Heuristic methods

Originally, we considered five algorithms based ongreedy selection which try to maximize one group ata time [11]. This problem is called the batch selectionproblem by Crama and van de Klundert [10], and itsrepeated application has commonly been used while


solving the job grouping problem (see [10] for ananalysis of eight batch selection heuristics). The algo-rithms presented in [11] differ in how they construct thenext group. On a coarse level the methods work asfollows:

f Inclusion methods add a new job (or job pair orjob triplet) to the current group so that its inclusioncauses minimal increase in the number of the differentcomponents in the group. This procedure is repeateduntil the capacity of the feeders is exceeded. Thismethod resembles Greedy Board algorithm describedin [13].

f ¼eighting method adds the jobs in decreasing order ofa weighted similarity measure.

f Exclusion method begins with a group containing allPCBs. After that it excludes the PCB which releases thegreatest number of feeder slots, and the same is repeat-ed until the components of the group fit in the car-riages. This method resembles Stingy Componentalgorithm described in [13].

However, the maximal group size turns out be an un-satisfactory criterion because the groups tend to havea highly uneven distribution (i.e., there is one large groupand several small ones). Therefore, we will next give a setof approximative algorithms which try to minimize thetotal number of groups. Thus, we abandon the greedyalgorithm and try to solve the job grouping problemdirectly.

These algorithms begin with an initial solution givenby a clustering method which is related to the clusteringtechniques used in other contexts, cf. PNN algorithm[20]. Among the several possible variations we considerthe following method: Begin with forming singulargroups so that each PCB forms a group of its own.Search for group pairs that can be merged into a singlegroup which does not exceed the feeder capacity. Selectthe pair which gives the greatest benefit among all pos-sible pairs (i.e., if the set R

icontains the components of

the group i, and Rjthe components of the group j, the

pair (i, j) is selected so that *R"DRiD#DR

jD!DR

iXR

jD

is maximal). Merge the groups and repeat the mergingprocedure if possible.

Our algorithms begin with the initial solution and thentry to further improve the grouping. Improvements arelikely since the heuristic merges only two groups at thetime and, therefore, the original grouping is coarse andcontains non-full groups. This free space can be coveredwith components which may make it possible to includea new PCB in the augmented group. We have two localsearch [21] operations to achieve this goal: swap andmerge.

Swap operation examines all group pairs and swapsjobs (or PCBs) between the groups if it results a decreasein the feeder demand. In addition to the pair-wise swap-ping, we can try to move a job from one group to

another. The objective is to decrease the total number offeeders required by the group. As a result from the moveand swap operations, we can possibly apply the mergeoperation and, consequently, decrease the number ofgroups.

Merge operation incorporates one group to anothergroup. Normally this operation does not succeed easilyand, as a result, we try to merge two groups applyinga selected rule. In this case we merge a group pair forwhich *C is maximal and the excess of the capacity is lessthan a predetermined limit. The result of this operationmay be — and most probably is — illegal: the new groupviolates the capacity constraint. The violation is thencorrected by moving jobs from the group until the re-quired set of components does not exceed the feedercapacity any more. The superfluous PCBs can be re-moved from the group by applying one of the followingstrategies:

1. Move the PCB that causes minimal increase of thefeeders in the target group.

2. Move the PCB that releases most capacity in itssource group.

3. Move the PCB for which the difference of the twoabove mentioned measures is minimal.

The problem in the first strategy is that it does not takeinto account the amount of released feeder slots in thesource group, and in the extreme case no slots will bereleased. Obviously, this is not desirable since our inten-tion is to make room in the source group. It follows thatthe third strategy suits best for our requirements: it se-lects the source group and the PCB that maximize theamount of released slots and the target group that min-imizes the increase of the feeder load.

In both swap and merge we have intentionally notrestricted the possible operations to those yielding a feas-ible result (i.e., the grouping may still violate capacityconstraints after the operations). This allows us to moveto a different part of the solution space more freely thanwith a sequence of feasible groupings only.

The operations form the basis for the following fiveapproximative algorithms for the PCB grouping.

HK1 (Clustering method): Construct an initial solu-tion with m groups where each group is singular (i.e.,consists of only one PCB). Merge group pairs in a greedyfashion so that *R is maximal and no feeder capacityconstraints are violated. Iterate the merge operation aslong as it is successful.

HK2: In this algorithm we begin with applyingmethod HK1, and after that we try to improve the resultwith a combination of swap and merge operations whichare continued until they do not provide us with animproved grouping. In the merge operation we selecta group pair with the maximal *R value.

HK3: In this algorithm we begin with algorithm HK2and after that try to improve the result with a local search


Table 1The number of different groups produced by the solution

Size HK1 HK2 HK3 HKA1 HKA2 Best Overallmax best

10 1 1 1 1 1 1 115 3 3 3 3 3 3 320 3 3 3 4 3 3 325 4 4 3 4 4 4 330 4 4 3 5 4 4 335 4 4 4 5 5 4 440 7 5 5 6 5 6 545 5 4 4 6 4 4 450 5 5 5 7 5 6 560 7 6 6 8 6 7 670 8 8 8 8 7 8 780 7 7 7 8 8 7 790 9 9 9 10 9 10 9

100 9 9 9 11 8 10 8125 12 10 10 13 11 12 10150 12 11 11 14 11 13 11175 14 12 12 15 12 13 12200 15 13 13 17 13 16 13225 15 15 15 18 14 16 14250 18 15 15 19 16 17 15341 20 16 16 23 19 20 16

Total 182 164 162 205 168 184 159% 14.5 3.1 1.9 29.0 5.7 15.7 0.0

heuristic which uses the swap operation. We decrease thenumber of groups of the initial solution by one andremove the superfluous group by allocating randomlythe jobs of the smallest group to some other group. Afterthis the grouping is likely to be unfeasible because someof the capacity constraints are violated. We solve this bymoving jobs from one group to another and swappingjobs between two groups. Single job moves are used inthe beginning, and when they are no more successful,they are switched to job swap operations. The quality ofthe grouping is evaluated with a cost function H. Minim-izing only the number of groups is too coarse a criterion(i.e., it does not provide us with the indication whetherthe algorithm is moving to the right direction in solutionspace), and therefore the cost function is used to guide thesearch. This function sums the total number of the feederslots H"+L

j/1h ( j)#» )C, where h ( j) stands for the

number of slots required by the group j, ¸ the number ofgroups, » the number of slots exceeding the capacity andC is a penalty constant for the criteria. Hence, the aim isto minimize the value of H. Next, if the result is feasible,we record the solution, decrease the number of groups byone and restart the procedure. If the search was unsuc-cessful, the situation is again randomly initialized and theprocedure restarted. This is repeated until a given timelimit (in our tests 1 minute) has elapsed.

HKA1: In this algorithm the grouping order is con-trolled by defining a group similarity measure s

jfor all

groups j :

sj"

k+i/0

i )Ni

k#1,

where k stands for the number of different components inthe group j, and N

iis the number of components of the

group j that are used in i other groups besides the group j.In other words, a group with a high similarity measurecontains a lot of components which are used also in someother groups, and therefore its merging should not be toocostly.

The algorithm sorts the groups into a decreasing orderaccording to the similarity measures. The first group isthen merged with some other group if possible; if not, thesecond group is merged with some other group, etc. Afterthe merge operation the similarity measures are updatedand the groups sorted. The procedure is repeated untilthere is no improvement.

HKA2: Similar to HKA1 but the result is improved byapplying method HK2 which performs the swap andmerge operations.

4.3. Test results

In Table 1 we present results for the improved heuristicmethods presented in the previous section. The test prob-lems were constructed by sampling random PCB types

from the actual production data. We can conclude fromthese results that methods HK2, HK3 and HKA2 givequite similar results. HK3 turns out to be the bestmethod giving results which on average are 1.9% fromthe optimum. In the best maximal grouping method (Bestmax) column the best result from the previous methods isduplicated (more detailed results appear in [11]). Theimproved methods were able to outdo the previous resultin 15 cases out of 21 and by 15.7%.

The structure of the method HK3 is demanding and,consequently, it requires more time than the othermethods. The benefits of the method HKA1 are its speedand good efficiency throughout different problem sizes.However, all the methods are quick enough for problemsizes found in actual situations.

In Table 2 a summary of results from another test ispresented. In this case each grouping problem comprised30 randomly chosen PCBs (this problem size representsthe average weekly production size). The test wasrepeated 30 times for each heuristic method. Also, in thiscase method HK3 gives the best results. Additionally,we solved the optimal result for the same problems,and for all tested cases HK3 gave the optimal result.Method HKA1 gives the worst result, and its group sizeis over 20% from the best result. The running time forall heuristics, excluding HK3, is ca. 1—2 s; becauseof the time limit, method HK3 requires one minute ofrunning time.


Table 2Results from 30 cases of problem size 30

Method Averagegroup size

Excess overoptimum (%)

HK1 4.30 11.2HK2 4.13 6.9HK3 3.87 0.0HKA1 4.77 23.3HKA2 4.30 11.2

Best 3.87 0.0

Table 3An analysis of a sample schedule for a period of one week. Legend:Old"production time in the old system (min), New"production timein the revised system, Improvement"difference between Old and New,%"difference in percents, Group"group to which the productbelongs

PCB pcs. Old New Improvement % Group

D2284A1 200 48.61 32.64 15.97 32.9 1CRT212 30 96.62 70.90 25.71 26.6 1D5250A 100 55.06 40.73 14.34 26.0 1D5450B1 210 42.87 34.13 8.75 20.4 2CRR212C 35 103.16 83.70 19.47 18.9 1D2187B1 31 33.15 27.05 6.09 18.4 1D2161A1 79 31.77 26.21 5.56 17.5 1D2481A 100 37.42 30.92 6.50 17.4 1D2281A 200 38.95 32.45 6.50 16.7 1DXA821RE 52 37.52 31.78 5.74 15.3 1S2203 30 47.46 41.20 6.26 13.2 1M3151EC2 30 105.90 93.49 12.41 11.7 3AXP2011 50 39.19 35.10 4.09 10.4 2MHE6107 47 78.28 70.47 7.80 10.0 2DXO802 200 37.10 33.48 3.62 9.8 1A80430B1 30 62.06 57.42 4.64 7.5 2DTU082B1 31 30.78 28.73 2.06 6.7 1AXF246D 30 22.52 21.96 0.56 2.5 1AXA860 56 36.73 36.73 0.00 0.0 1M3153CC2 10 104.30 104.53 !0.24 !0.2 1DTU121B1 31 27.63 29.70 !2.07 !7.5 1

Total 1,117.07 963.31 153.76 13.8

5. System description

The system depicted here includes tools for groupingthe jobs of the production plan and optimizing the set-upfor each group [22]. When using the system, the produc-tion engineer can

f choose the products from a product list,f choose which heuristic method is applied to form the

groups,f assign the standard set-up,f assign the custom set-up for a given group and carriers

(1, 2 or 5, 6),f produce optimized NCX codes for a whole group or

for some jobs within a group,f compare two groups in order to discern mutual com-

ponents and their respective locations,f view the current groups by listing the jobs, the compo-

nents or the feeder set-up,f remove groups,f move jobs between groups,f get graphical and numerical information of the groups

and the jobs,f inspect whether a new job can be inserted to some

existing group, andf edit the component library.

In the current system (see Fig. 5) the production engineercan freely re-sequence the groups and the jobs withina group. The latter does not affect the set-up times sinceno set-up is needed for jobs in the same group. The duedate, the batch size, the conveyor width and the avail-ability of required components are the most importantfactors when the production engineer is constructinga feasible schedule.

6. Experiences

In order to demonstrate the performance of the newsystem we present an actual production plan for a periodof one week, see Table 3. The production schedule iscreated by using both the old system and the new system.

We can calculate the number of required componentchanges, component change operations (i.e., set-ups) andthe expected printing time for each board by usinga simulator presented in [16]. From this data we cancalculate the total time required to produce the wholeproduction program in both systems.

The benefits of the new system are obvious (seeTable 4). In the old system we have to do 21 set-ups,one for each product, while in the new system productsare divided into three groups, each requiring a singleset-up. Also, the printing time is vastly reduced;in this case the reduction is ca. 18%. It must be noted thatwe have included only the times which differ in the newand the old system. However, there is a lot of processing(program loading, line changing, coping with break-downs and other problems) which is not affectedby the change of the system, and therefore this analysisis not complete. We believe that the decreased numberof set-ups will increase the production much morethan these estimates suggest, the reason being that whenthere are only few set-ups, the whole organization ofother tasks works more efficiently because of less inter-ruptions.

The new system has been in production use sinceMay 1997. The manufacturer has collected statisticaldata from the production. We compared the firstten-week period after the change with the preceding


Fig. 5. Main window of the grouping system and information windows for feeders, boards, components and groups.

twenty-week period and observed the followingimprovements:

f The average number of component placements perhour (of total time) has increased by 57.6%.

f The average number of component placements perhour (of the actual printing time) has increased by 16%which is in accord with the results of Table 3. The mainreason for this is the improvements in printing andfeeder optimization (cf. [16]).

f The average number of completed jobs in a week hasincreased from 22 to 28.

f The average time to change from one job to another

(including machine set-up and other delays) on thewhole line has decreased from an hour and a half toone hour (35.5%).

We realize that there has been minor changes inthe product assortment during the test period. Theaverage size of a batch has slightly increased whichcauses that the number of placements per hour (of totaltime) given here is somewhat optimistic. On the otherhand, the number of completed jobs per week suffersfrom the growing batch sizes. Also, a slight improvementis due to purchasing new feeder reels which speeds up theset-up.


Table 4Comparing the old and new system

Number of Number of Total set-up Total onsertion Total productionset-up occasions feeder changes time (s) time (s) time (s)

Old 21 294 30,240 72,868 103,108New 3 246 16,560 60,067 76,627

Improvement 18 48 13,680 12,801 26,481% 85.7 16.3 45.2 17.6 25.7

7. Concluding remarks

We discussed the production planning in a flexiblemanufacturing line. The situation was abstracted as themanagement of a single machine. Even with this simplifi-cation we were confronted by a number of hardoptimization problems. We solved the grouping problemand the code generation problem separately. These solu-tions formed the basis for the new system which intro-duced new ways to solve the scheduling problems in theproduction plant. The system described in this paper is indaily use and has decreased the average change time ofa job by 35%. The number of component placements perhour has increased by 58% due to the new system andcode optimization.

There remains yet a number of open research ques-tions we would like to solve, for example, how to se-quence the groups efficiently. The division between theSMD and GSM machines should be reconsidered inorder to gain a better balance for the load of the wholeproduction line. We presented algorithms which groupthe products heuristically. The algorithms use the sameframework: construction of initial groups and improve-ment of the grouping. We used the clustering techniquefor the initial grouping and local search methods forimproving. Because there are several conflicting goalswhen forming the groups, we are currently developingnew objective functions which are based on the fuzzymultiple criteria optimization.

Acknowledgements

The authors wish to thank Mr. Jouni Lehtinen fromTeleste Corporation for his time and cooperation.

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