EP3485455A1

EP3485455A1 - Method and device for determining optimum batch sizes

Info

Publication number: EP3485455A1
Application number: EP16758139.6A
Authority: EP
Inventors: Alexander Pfaffinger; Christian Royer
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 2016-08-24
Filing date: 2016-08-24
Publication date: 2019-05-22
Also published as: WO2018036622A1; US20190213508A1; US11157840B2; CN109844794A

Abstract

The invention claims a method for determining optimum batch sizes for the placing of components (155) on circuit boards (120) within an assembly line, wherein a set of circuit board types (122) to be produced on the assembly line (110) within a specified planning period is specified; a number of circuit boards to be produced is specified for each circuit board type; the number of circuit boards per circuit board type forms a set that is to be divided into equal-sized subsets, also referred to as batches, which are production orders that are produced at regular intervals during the planning period; the batch size of a circuit board type is equal to the number of circuit boards in a subset; the specified circuit board types are divided into a set of clusters, wherein a cluster (210, 215) and its associated set-up (165, 170) comprises a set of circuit board types which can be produced with the associated set-up, and wherein the method includes the following steps: recording set-up costs that are incurred in setting up the associated set-up of a cluster; determining the time intervals between the production orders per circuit board type as a function of the batch size; determining the set-up costs per cluster during the planning period as a function of the batch sizes of the circuit board types and taking into account the recorded set-up costs; determining the total set-up costs from the sum of the set-up costs per cluster; determining the total storage costs of the circuit boards produced in a time interval within the planning period from the sum of the storage costs per circuit board type as a function of the batch sizes, and optimizing the batch sizes in such a way that the sum of the total set-up costs and the total storage costs is minimized.

Description

description

Method and apparatus for determining optimal lot sizes

The invention relates to a method and a device for determining optimum lot sizes for the assembly of printed circuit boards with components within a placement line. Furthermore, the invention relates to a device for a

Assembly system or a production or assembly line for the assembly of printed circuit boards (assemblies) with components or components. Moreover, the invention relates to a computer program product and a computer readable medium.

Particularly in the field of electronics production, printed circuit boards or subassemblies to be manufactured are produced on SMT assembly lines by surface mounting technology (SMT). A manufacturer of SMT placement machines (pick and place) and systems with the product name SIPLACE is, for example, ASM

(http://www.siplace.com/en/Home).

Several placement machines, which are usually connected by a transport system, and the e.g. for manufacturing

(Electronic) components interact, represent an assembly line.

An armor can be held on one or more armor tables, which can easily be exchanged on the placement machine. However, upgrading a set-up table with components of predetermined types of components is expensive. The armor is therefore often distinguished in hardwares and variant armors, with a hardtable table intended to retain its composition of component types over a predetermined planning period, while a variant armor table is expected to be converted within the planning period. In industrial production plants in the field of electronics production, assemblies (or printed circuit boards) to be manufactured are produced in orders with predefined batch sizes.

The lot sizes implicitly determine how often an assembly is to be produced. The smaller the lot size of an assembly, the more frequently this assembly must be produced and the higher the setup costs.

Assuming a steady demand for an assembly, but with increasing batch sizes also requires an ever-increasing buffer to the SMT line and thus increase the storage costs.

Within the framework of Lean Manufacturing, the goal of minimizing inventories is even aimed at a theoretical lot size of 1, which would, however, lead to immense set-up costs in practice.

The creation of a component armor for a placement line takes about 6-8 hours and thus causes a huge effort. The production of the modules thus takes place in set-up families. A set-up family is a set of construction ^¬ groups that can be produced with a component armor of the placement line.

In other words, a set-up family, also called cluster, comprises a lot of lots that are within one

Armor can be made. All modules of a setup family can therefore be manufactured one after the other without retooling on the line. Static setup groups are setup groups based on medium-term view ^¬ (6-12 months) are formed. Foreseen in this time ^¬ space modules are divided into setup families and formed preconceived armor for it. Is used in a short In the long-term planning period, which can be, for example, a time interval of one day, equipped with a static set-up family, not all assemblies of this set-up family are usually produced, but only those for which orders are currently available. The use of static setup families is common practice in many electronics plants. The arrival of orders is rather random and usually can not be planned. Even if two assemblies always once a week must be manufactured, can not be scheduled in the rule that this is done on the same day of the week and the armor of setup group may thus even less equipped to ^¬ would.

From DE 102015200420.1 a method for assembling printed circuit boards is known, comprising the following steps:

the acquisition of orders, each for the assembly of printed circuit boards of a printed circuit board type on the Bestü ^¬ ckungslinie, and assigned probabilities, with which an order is to be executed in each case,

- Assigning PCB types to the jobs

setup groups,

determining, for each setup family, a measure comprising the sum of the probabilities of those jobs whose board types are encompassed by the setup family, optimizing the mapping such,

that the key figures of different set-up families are as different as possible, the provision of armor of one of the specific set-up families at the assembly line and the placement of printed circuit boards on the assembly line.

The orders can relate to virtually any period in the future. It is usually not - or not exactly - known when an order actually exists, so when the job is to be executed. The operation of the assembly plants ^¬ ckungslinie usually follows a predetermined cycle, and it is known in each case for a coming period, wel ^¬ che orders are to be processed. The probability of Order indicates how likely an order should be to run in any period.

By using the method, it is possible, when forming the setup families or armaments, to make use of the knowledge that certain types of printed circuit board are to be regularly re-equipped.

Due to these complex interrelations, the definition of optimal lot sizes in practice represents a very significant problem.

After Wikipedia

(https://de.wikipedia.org/wiki/Klassische_Losformel) is known in German-speaking countries, the classical Losformel or Andler formula (English Economic Order Quantity, EOQ formula) known method for determining the optimal lot size in the context of one-step, unaccepted used industrial manufacturing.

In the Anglo-Saxon area, however, the term dominates

Economic order quantity (EOQ formula), wherein the problem ^{Stel ¬} ment is examined in terms of optimal order quantity. There are similarities between order and production quantity. The determination of optimal order quantities is one of the

Tasks of procurement logistics, whereby the total costs are also composed of depending on the amount of linear La ^¬ gerkosten and ultimately also of the set-up costs in batch production.

In the field of electronics manufacturing lot size determination has not proved by the batch or EOQ formula in practice, since it is not in any way take into ^¬ into account in this formula, that the assemblies are manufactured in setup groups.

It is an object of the present invention to optimize the lot sizes. This object is solved by the independent claims. Advantageous developments are the subject of the dependent claims.

The invention claims a method for determining optimal batch sizes for the assembly of printed circuit boards with components within a placement line,

wherein an amount of printed circuit board types to be manufactured on the placement line within a predetermined

Planning period is given,

wherein a number of printed circuit boards to be produced per circuit board type is specified,

where the number of printed circuit boards per board type forms an amount equal in subsets, too

Loosely called, is to be divided, which are manufactured on the Pla ^¬ planning period distributed as production orders in time evenly,

wherein the lot size of a board type represents the number of boards in a subset,

wherein the predetermined types of printed circuit boards are divided into a set of set-up families,

wherein a setup family with associated armor comprises a set of circuit board types that can be fabricated with the associated armor, the method comprising the steps of:

Acquisition of setup costs spent on setting up the associated armor of a setup family,

Determining the time intervals between the production orders per PCB type depending on the batch size,

Determining the set-up costs per set-up family over the planning period depending on the batch sizes of the PCB types and taking into account the set-up costs,

Determine the total costs of the rescue from the sum of the setup costs per setup family, Determining the total storage costs of the manufactured in a time interval within the planning period Leiter ^¬ plates from the sum of storage costs per board type depending on the lot sizes, and

- Optimize the lot sizes such that the sum of Ge ^¬ samtrüstkosten and total storage costs is minimized.

An essential advantage of the invention is that with the optimized lot sizes an optimal balance between the costs for the setup and storage space or storage costs is created.

According to the optimized lot sizes, armor and storage capacities per time interval can be provided. A time interval corresponds to a short-term planning period and is typically one day. The modules that need to be made in ei ^¬ nem such time interval are produced in the specified setup groups. The armor of a given set-up family is upgraded at most once in a time interval. Eventually such armor will not be fully upgraded. It will be equipped only Bauele ^¬ mente then necessary for fitting in to be produced in this time interval assemblies. The method may additionally include the following steps, which are taken into account for optimizing the lot size:

Determining the probability per board type that a circuit board must be fabricated at a time interval within the planning period, and

Determine Expected values of all setup group, each ^¬ weils express the probability with which a circuit board type from the setup group in ge ^¬ called time interval must be made min ^¬ least.

The set-up costs per setup group correspond to the expected ^¬ th setup costs per setup group. These may consist of the ermit ^¬ telten expected values, the acquired set-up costs mentioned and the number of time intervals are calculated within the planning time ^¬ space.

A development of the invention provides that every possible starting time interval for the determined time intervals between the production orders of a printed circuit board type within the planning period is equally probable and un ^¬ dependent on other types of printed circuit board. Optimizing the batch sizes can be with an iterative optimization method with a predeterminable initial value Runaway ^¬ leads. The optimization can also or alternatively be done by means of so-called nonlinear optimization. In a further embodiment of the invention, the

Setup costs per setup family always fixed amounts. Koen ^¬ nen also setup group per each equal amounts or having different amounts for each setup group. The total cost of upkeep may be variable by taking into account the cost of equipping one or more required components in an armor in the total cost of the armor. The amount of set-up costs of a set-up family in the named time interval can be dependent on the subset of the component types that are sufficient for the respective production orders.

A further aspect of the invention provides a device for determining optimum lot sizes for the placement of printed circuit boards with components within a placement line,

wherein a quantity of on the assembly line to ferti ^¬ constricting board types within a predetermined planning period is predetermined,

where the number of printed circuit boards per board type forms an amount equal in subsets, too Loosely called, is to be divided, which can be produced evenly distributed in time over the Pla ^¬ planning period under construction contracts

wherein a setup family with associated armor comprises a set of circuit board types that can be fabricated with the associated armor,

comprising:

Means for detecting setup costs spent on setting up the associated armor of a setup family,

Means for determining the time intervals between the production orders per circuit board type as a function of the lot size,

Means for determining the set-up costs per set-up family over the planning period as a function of the lot sizes of the printed circuit board types and taking into account the set-up costs,

Means for determining the total support costs from the sum of the setup costs per setup family,

Means for determining the total storage costs of the goods manufactured in a time interval within the planning period

PCBs from the sum of the storage costs per PCB type depending on the lot sizes, and

Means for optimizing the lot sizes such that the sum of the total costs and the total cost of storage can be minimized.

The apparatus may include means and / or units or devices and / or provide modules for performing the above method which may be marked respectively as hardware and / or firmware moderately and / or software or as Computerpro ^¬ program or computer program product. The device can be developed according to the method described above.

Another aspect of the invention provides an assembly system comprising such a device according to the invention.

This assembly system can be part of a system.

The plant may be characterized among other things by one of the following plant types. Examples for this are:

an automation system,

- a manufacturing or production plant,

- a cleaning system,

- a water treatment plant,

- a device or a machine,

a turbomachine,

- a power generation plant.

Another aspect of the invention is a computer program product or a computer program having means for performing the above method when the program Computerpro ^¬ (-product) is placed in an above-mentioned device or means in the device for execution. The computer program or product can be stored on a computer-readable medium. The computer program or product can be created in a common programming language (eg C ++, yes ^¬ va). The processing device may include a commercially available computer or server with corresponding input, output and storage means. This processing device can be integrated in the device or in its means.

Further advantages, details and developments of the invention will become apparent from the following description of exemplary embodiments in conjunction with the drawings.

Show it: Fig. 1 assembly system ·

2 shows a graph with stock q and setup time ^¬ points when orders arrive every 2 days;

Fig. 3 three graphics with stock q and setup time ^¬ points, if the orders left on the days 1, 4, 7, ..., middle on days 2, 5, 8, or right on days 3, 6 , 9, ... arrive;

Fig. 4 is a graph with stock q and setup time ^¬ points with 2 and 3 day orders in a cluster; and

Fig. 5 diagrammatically various cluster Rüstungskonstel- simulations for a total period length of 6 Ta ^¬ gen.

1 shows an exemplary mounting system 100. The mounting system 100 includes one or more pick and place ^¬ lines 110 and a processing or control device 115. Each assembly line 110 comprises an optional Trans ^¬ port system 125 and one or more placement machine 130. Each pick and place machine 130 includes one or a plurality of mounting heads 135, which are each adapted to receive from a setup table 140 components 155 and at a predetermined position on the circuit board 120 to positio ^¬ kidney, which is located on the transport system 125. During the assembly process, the printed circuit board 120 usually stands still with respect to the automatic placement machine 130.

The setup tables 140 each comprise a multiplicity of feed ^devices 150, of which only one is shown by way of example in FIG. Each feeder 150 holds a supply of ready devices 155 of a predetermined type components ^¬ 160th For the components 155, the feed ^¬ device 150 typically has a capacity that can be expressed in trace amounts. A track is usually 8 mm wide and the number of tracks of a Rüsttischs 140 is limited, for example to 40. Components 155 of the moving ^¬ chen type components 160 are usually provided in a belt, on a tray or in a tube. Each type of device 160 requires on the feed device 150 and the set-up table 140 a predetermined number of tracks, the üb ^¬ SHORT- contiguous.

Usually 155 different types of devices, a supply means 150 for processing of devices Bereithal- be configured 160, and usually differed ^¬ Liche supply means can be attached to a set-up table 140,150. In the present case is simplified thereof ^¬ be understood that a stock of components 155 of a type Bauelemente 160 on a feed device 150 is virtually infinite, so retrofitting is not required.

Is the placement machine 130, a component 155 of a component type 160 requires that the Rüstti ^¬ cal 140 is not present on a, it is usually not changed to ^¬ order of components 155 at one of the attached Rüsttische 140, but the set-up table 140 is fully against another, suitably equipped arming table 140 exchanged. The loading of a set-up table 140 with components 155 not mounted on the placement line 110 is called pre-equipment and may require a processing time in the range of one or more hours, for example about 6-8 hours.

Since a change of setting tables 140 on the placement line 110, a so-called set change, is usually associated with a production stoppage, the aim is to perform changing the setting tables 140 as rarely as possible. Furthermore, since the equipment tables 140 are expensive and the conversion of a

Setup table 140 can be complex and tedious, wei ^¬ ter is trying to form as few armor as possible to vorbe a predetermined production amount of printed circuit boards 120 to make certain PCB types 122. The production quantity here comprises a plurality of printed circuit board types 122, of which in each case a predetermined number of printed circuit boards 120 is to be equipped with components 155 of predetermined component types 160. ^{By way of} example, 300 printed circuit boards 120 of a first printed circuit board type 122 and 200 printed circuit boards 120 of a second printed circuit board type 122 can be equipped.

An armor 165, 170 comprises a set of component types 160, and is realized by one or more Rüsttische 140, which are equipped with supplies of components 155 of the component types 160 of the arms 165, 170 and attached to the assembly plants ^¬ ckungslinie 110th

The armor 165, 170 is assigned to a set-up family 175, which comprises printed circuit board types 122, of which printed circuit boards 120 can be equipped by means of components 155 of the component types 160 of the armor 165, 170. A setup group 175 is ge ^¬ precisely an armor 165, assigned to 170 and vice versa.

To increase or decrease the load of a 110 assembly line to reduce a need for Rüsttischen 140, it is crucial, as are formed based on the ladder to be fitted ^¬ plate types 122 setup families 175th In the formation of armor 165, 170 or Rüstfamilien 175 constraints may be observed, such as compliance with a limited capacity of a setup table 140 for component types 160 or a grouping of predetermined types of circuit boards 160 in the same set family 175, for example, for the use of lead-containing or lead-free Soldering tin.

The armor may be differentiated into hardwares 165 and variant armor 170, where a hardshell 165 is intended to remain unaltered on a number of shuttle tables 140 for a predetermined scheduling period, while an upgrade table 140 of an option armor 170 is expected to be shipped within the planning period. elements 155 of other types of components 160 is retrofitted. The planning period can carry, for example, 6 to 12 months be ^¬. In a predetermined constellation, variant armoring 165 usually is considerably shorter than the planning period, for example over several hours or days, but usually not over more than one ^week .

It is also possible to form a static armor which carries elements of the festoon 165 and the variant armor 170. Like armor 165, the static armor is formed for a longer period of time, over which it usually remains unchanged. However, the static defense remains common ^¬ not be upgraded, so as armor-Nazi physically 140 to set-up implemented, but can also be downgraded again after use. In addition, a static Rüs ^¬ tion also only partially equipped (= realized), for example, if the static armor several ^{Leiterplattenty ¬} pen 122 includes and at a time only orders for the production of printed circuit boards 120 of some of these types of printed circuit boards 122 are present. Components 155 of such Bauelementty ^¬ pen 160, which are not required for equipping the instructed printed circuit boards 120, then can not be upgraded.

The static armor is administratively often easier to handle than a hard suit 165 or a variant armor 170. If the static armor is not disarmed after its use, can also be spoken of a festive 165. Are where otherwise indicated below, preferably static setup groups and meant to them ^¬ parent static armor.

The armor 165, 170 can be replaced as needed on the assembly line 110. In order to realize a fixed equipment 165 or an alternative equipment 170, a set-up table 140, while it is not mounted on the assembly line 110, is usually prepared with provisions of components 155. certain component types 160 upgraded. Already aufgerüs ^¬ tete components 155 not required types of components 160 may be previously disarmed. This retrofitting can involve a significant amount of manual labor and be time consuming.

In order to minimize the effort associated with variant armor 170, attempts are made to include as many board types 122 as possible in fixtures 165. However, a desired case without variant armatures 170 is hardly achievable in practice.

As part of the control of the placement system 100, the control device 115 assigns each type of printed circuit board 122, whose associated printed circuit boards 120 are to be loaded on the assembly line 110, to a set-up family 175, with sets of arming families 175 each being assigned to a fixed piece of equipment 165. and variant armor setup families 175, each associated with a variant armor 170, may be formed.

In practice, a hard armor may be formed 165 for a (large as possible) of the board types 122, for example, for a given Pro ^¬ production quantity of board types 122 in a first step, whereupon formed in a second step the remaining part of the board types 122 variant armor 170 , The quality of these associations decide to a large extent on how well the means of production of the mounting system 100 may be working at full capacity and how efficiently it stocked who can ^¬.

According to the invention, a mathematical stochastic model for the calculation of optimal batch sizes is presented, in which the production with static set-up families is taken into account. In the following probabilistic model, it is assumed that the orders are based on certain probabilities

arrive. Input parameters:

• Quantity of all module types R.

• The module types of R are divided into a set of setup families Cl.

· The number of days in the year / long-term planning period are T.

• The predicted to be produced quantity of a construction ^¬ group is r D _r. Variables:

• The lot size q _r for the assemblies r. Model:

As classic in the aforementioned EOQ model is ^¬ accepted that demand is constant. Consequently, the orders for ei ^¬ nen module type arrive periodically. In addition, as in the classical EOQ model a unend ^¬ Lich fast production speed, ie a producti ^¬ onszeit of 0 assumed. The same is taken for the set-up time ^¬ . The time interval in which orders for a module r arrive is designated by w _r . The following applies: q _r T

r D _r

The model or the invention is explained below by way of examples, without limiting it to them: Example 1)

The number of days in the planning period is T = 100. If, for a module r, the predicted quantity to be produced D _r = 1000 units and the lot size q _r = 20 units, then w _r = 2, ie the module must be sent every two days to be produced. In Figure 2, a graph shows the situation when orders arrive every two days. The stock q is plotted on the y-axis. The days are plotted with 1 on the x-axis. The intersection between Lagerab ^¬ gangslinie and x-axis is the so-called setup time, with setup time means that the armor (Setup) is prepared for this set-up family (cluster) on this day. Example (2):

W _r = 3, then meet every three days orders for a construction ^¬ r a group. There are different ways to find exactly which days these orders arrive. If w _r = 3, the orders can be a) either on days 1, 4, 7, ...

b) or on days 2, 5, 8, ...

c) or arrive on days 3, 6, 9, .... In FIG. 3, these three possibilities are illustrated on the left a), middle b) and on the right c). It is believed that the various options for the arrival of the orders of a module type, equally true ^¬ scheinlich and are independent of the other module types. The first arrival of a job is Startinter- Vall - called, assuming the case ^¬ play, that a time interval one day be ^¬ bears - more precisely in the example start date.

If an order for the module type of a setup family arrives on one day, the armor for this setup family will be upgraded on that day.

Example (3): A setup family consists of two module types, a 2-day and a 3-day module type. FIG. 4 shows possible setup times for the armor of the setup family. In the example according to FIG. 4, the set-up family is upgraded on days 2, 3, 5 and 7.

If, as in this example, the period lengths or time intervals are integral, the total period length for the modules is the lowest common multiple (kgV) of the individual period lengths. For the two module types in the example, it is 6. The resulting cluster armor for the 6 different constellations on the 6 days in the overall period are shown in FIG. The expected number of clusters for the 6 days is therefore 4. On one day, the expected number of clusters is therefore 1.5.

However, integerity of the period ^lengths is not assumed. For example, it is permissible to produce a module type r twice in the (working) week, ie every 2.5 days.

As expected setup costs for the setup family cl you get:

Setup costs (cl) = K _cl T 1

The total setup costs are thus:

Setup costs

Storage costs:

For an assembly type r, the expected annual storage costs, as in the classic EOQ model, are Tq _r / 2. The storage costs total thus

Z h _r q _r T

2

The total costs result from the sum of the total set-up costs and the total storage costs.

Extensions:

(1) Consideration of upgrades of individual component types

If the armor of a static set-up family is upgraded, not all of the component types of the armor are upgraded, but only those that are necessary for the production of the jobs to be produced. In other words, the set-up costs of a set-up family in the mentioned time tervall, in the example a day, depending on the subset of device types that are sufficient for the respective (manufacturing) jobs. In the model, this can be taken into account and the setup effort can be determined in even greater detail.

Additional parameters: C _c i Device types of the module types recl.

cl _c Module types in the setup family cl that contain the

Component type c included,

k Cost of upgrading a component in

an armor.

The expectation that a component type ceC _c i must be equipped for one day in the armor of the setup family c1 is

1-] ^ [(l - p _r )

reclr

The expected number of component upgrades for cluster cl in one day is therefore

CE _{C (} rec _c / The total setup costs are thus

Setup costs

c Σl eCl-

(2) Consideration of fixed and variable setup costs

The setup cost K _ci that were initially Darge ^¬ provides in this section could be used as fixed costs of armaments and consider setup costs from enhancement (1) as variable setup costs. The cost of equipping one or more required components in an armor is then included in the total cost of the armor. Combinations of both (fixed and variable setup costs) are also conceivable.

With the presented model, comparisons and evaluations can be made between different lot size variants, in which the production with set-up families is considered.

Using iterative optimization methods, it is possible to determine lot sizes with which a total cost minimum is achieved.

It is assumed D _r > l. Thus the following lower and upper bounds are assumed for q _r : l <q _r ^ D _r

Iterative optimization methods can be characterized by the following (iterative) steps:

a) determining a starting solution or first current solution from a (user) specifiable initial value. For example, you can start with an initial value of a lot size = 1 and determine the start or current total costs (total costs + total storage costs).

b) calculating a new lot size by means of an optimization program or standard solver (see below), whereby the total cost of support and the total cost of storage are gradually minimized,

c) repetition of b) until a sufficient balance between the largest possible lot size (consequently: minimal set-up costs) and minimum storage costs is achieved.

Accordingly, the steps can be carried out iteratively and a program abort occurs when a previously determined te time limit or result quality (see, for example, the above balance ^{¬ unit} ) is achieved.

A special case of optimization methods is linear optimization. It deals with the optimization of linear

Objective functions over a set constrained by linear equations and inequalities. It is the basis of the solution method of (mixed) integer linear optimization. A so-called solver is a collective term for special mathematical computer programs that can numerically solve mathematical problems. In the context of mixed integer linear programming (MIP), for small IP programs (integer optimization models) standard solvers such as e.g. CPLEX, Scip, Gurobi, Xpress can be used.

More difficult than the linear optimization is the case of non-linear integer optimization (MINLP), where the objective function, the constraints (NB), or both may be present. The solution is achieved by using suitable linear ^{approximations} , so that standard solvers can be used directly. In addition, the standard solver mentioned above can already solve certain types of nonlinear problems. There are also additional solvers that specialize in solving nonlinear problems (eg ANTIGONE, BARON).

With the aid of non-linear integer optimization methods, it is possible to determine lot sizes that achieve a total cost minimum. If the integrality of w _r not be assumed, then the optimization problem is reduced to a simple problem to be solved purely nonlinear optimization ^problem-¬. In this case, total cost-minimum lot sizes can be determined using pure nonlinear optimization methods. For this purpose, for example, the software known as "Matlab", which is suitable for solving ^mathematical problems and numerical calculations, may be used, although the invention has been illustrated and described in detail by the preferred embodiment disclosed examples be ^¬ limited and other variations can be derived therefrom by the skilled artisan without departing from the scope of the invention.

The implementation of the processes and procedures described above may be based on instructions SUC ^¬ gen, which (collectively referred to as computer readable storage) on computer readable storage media or volatile computer memories gen. Computer-readable memory, for example, volatile storage such as caches, buffers, or RAM and non-volatile memory as Wechselda ^¬ pinion carrier, hard disks, etc.

The functions or steps described above may be in the form of at least one instruction set in / on a computer-readable memory. The functions or steps are not tied to a particular instruction set or to a particular form of instruction sets, or to a particular storage medium or to a particular processor or to specific design schemes and can by software, firmware, microcode, hardware, Prozes ^¬ sors, integrated circuits, etc. are carried out alone or in any combination. A variety of processing strategies can be used, such as serial processing by a single program. processor or multiprocessing or multitasking or parallel processing etc.

The instructions may be stored in local memories, but it is also possible to store the instructions on a remote system and access them via network.

The term "processor", "central signal processing",

"Control unit" or "data evaluation means" as here USAGE ^¬ det, processing means includes in the broad sense, that is, for example, servers, general purpose processors, Grafikprozesso ^¬ ren, digital signal processors, application specific inte ^¬ grated circuits (ASICs), programmable logic circuits, such as FPGAs, discrete analog or digital circuits and be ^¬ undesirables combinations thereof, and any other processing means known in the art or developed in the future. Processors can consist of one or more devices or devices or units. If a processor consists of several devices, these can be designed or configured for the parallel or sequential processing or execution of instructions.

Claims

claims

1. A method for determining optimum lot sizes for the assembly of printed circuit boards (120) with components (155) within a placement line (110),

wherein a quantity of on the assembly line to ferti ^¬ constricting types of boards (122) is set within a predetermined planning period,

wherein the number of circuit boards each board type is an amount which called into equal-sized subsets, also lots, is to be divided, which are manufactured evenly distributed in time over the Pla ^¬ planning period as production orders,

- wherein a set-up family (210, 215) with associated armor (165, 170) comprises a set of circuit board types (122) that can be manufactured with the associated armor,

the method comprising the steps of:

- recording setup costs that are spent on setting up the corresponding armor of a setup family,

Determining the time intervals between the production orders per PCB type depending on the lot size,

Determining the set-up costs per set-up family over the planning period depending on the lot sizes of the PCB types and taking into account the set-up costs,

Determining the total costs of the installation from the sum of the set-up costs per set-up family,

Determining the total storage costs of the ladders manufactured in a time interval within the planning period plates from the sum of the storage costs per PCB type depending on the lot sizes, and

Optimizing the batch sizes such that the sum of Ge ^¬ samtrüstkosten and total storage cost is minimized.

2. Method according to the preceding claim, characterized in that the method additionally comprises the following steps that take into account for optimizing the batch size of the ^¬:

Determine Expected values of all setup group, each ^¬ weils express the probability that a min- board type from the setup group in ge ^¬ called time interval must be manufactured least.

3. Method according to the preceding claim, characterized in that the set-up costs per set-up family are represented by the expected set-up costs per set-up family, which are calculated from the determined expected values, the mentioned set-up costs and the number of time intervals within the planning period.

4. The method according to any one of the preceding claims, characterized in that armaments and storage capacities per time ^¬ interval provided according to the optimized lot sizes who ^¬ the.

5. The method according to any one of the preceding claims, characterized in that each possible start time interval for the determined time intervals between the production orders of a printed circuit board type (122) within the Pla ^¬ tion period is likely and independent of other PCB types.

6. The method according to any one of the preceding claims, characterized in that the optimization of the lot sizes is carried out with an iterative optimization method with a predetermined initial ^¬ value.

7. The method according to any one of the preceding claims, characterized in that the optimization by means of so-called

Nonlinear optimization done.

8. The method according to any one of the preceding claims, characterized in that the setup costs per setter family each have fixed amounts.

9. The method according to any one of the preceding claims, characterized in that the set-up costs per scaffolding family each have the same amounts.

10. The method according to any one of the preceding claims, characterized in that the set-up costs per Rüstfamilie each have different amounts.

11. The method according to the preceding claim 9 or 10, characterized in that the total cost of support are variable in that the cost of equipping one or more required components in an armor are taken into account in the total cost of the structure.

12. The method according to any one of the preceding claims, characterized in that the amount of setup costs of a setup family in said time interval depends on the subset of the component types (160), which are sufficient for the respective production orders.

13. The method according to any one of the preceding claims, data characterized by, that a time interval one day repre sented ^¬.

14. The method according to any one of the preceding claims, characterized in that the time interval between the incoming production orders for a printed circuit board type is integer.

15. An apparatus for determining optimum lot sizes for the assembly of printed circuit boards (120) with components (155) within a placement line (110),

wherein a set of printed circuit board types (122) to be produced on the assembly line is specified within a predetermined planning period,

Loosely called, is to be divided, which can be produced evenly distributed in time over the Pla ^¬ planning period under construction contracts

wherein a set-up family (210, 215) with associated armor (165, 170) comprises a set of circuit board types (122) that can be fabricated with the associated armor,

comprising:

Means for determining the set-up costs per set-up family over the planning period as a function of the lot sizes of the printed circuit board types and taking into account the set-up costs, Means for determining the total support costs from the sum of the setup costs per setup family,

Means for determining the total storage costs of the printed circuit boards manufactured in a time interval within the planning period from the sum of the storage costs per circuit board type depending on the lot sizes, and

16. Device according to the preceding claim, characterized in that the device additionally comprises the following means which are suitable for optimizing the lot size:

Means for determining the probability per board type that a board must be fabricated at a time interval within the planning period, and

Means for determining the expectation values per set-up family, each of which express the probability with which at least one printed circuit board type must be produced from the set-up family in the specified time interval.

17. Device according to the preceding claim, characterized in that the set-up costs per set-up family are represented by the expected set-up costs per set-up family, which can be calculated from the determined expected values, the aforementioned set-up costs and the number of time intervals within the planning period.

18. Device according to one of the preceding device claims, characterized in that armor and Lagerka ^¬ capacities per time interval according to the optimized lot sizes can be provided.

19. Device according to one of the preceding device claims, characterized in that each possible start ^¬ time interval for the determined time intervals between the production orders of a printed circuit board type (122) within the planning period is likely and un ^¬ dependent on other types of printed circuit boards.

20. Device according to one of the preceding device claims, characterized in that the optimizing of the lot sizes can be carried out with an iterative optimization method with a predetermined initial value.

21. Device according to one of the preceding device claims, characterized in that the optimization is carried out by means of so-called non-linear optimization.

22. Device according to one of the preceding device claims, characterized in that the setup costs per setter family each have fixed amounts.

23. Device according to one of the preceding device claims, characterized in that the setup costs per scaffolding family each have the same amounts.

24. Device according to one of the preceding device claims, characterized in that the setup costs per setter family each have different amounts.

25. Device according to the preceding claim 23 or 24, characterized in that the total support costs are variable in that the cost of equipping one or more ^¬ required components in an armor can be taken into account in the total costs.

26. Device according to one of the preceding device claims, characterized in that the amount of Rüstkos ^¬ th a setter family in said time interval is dependent of the subset of device types (160) that are sufficient for the respective manufacturing jobs.

27. Device according to one of the preceding device claims, characterized in that a time interval represents a day.

28. Device according to one of the preceding device claims, characterized in that the time interval between the incoming production orders for a printed circuit board type is integer.

29, assembly system (100) comprising a device according to one of the preceding device claims.

30. Computer program having means for carrying out the method according to one of the aforementioned method claims when the computer program is executed on a device or in a unit or by means of the device according to one of the aforementioned device claims.

A computer-readable medium comprising instructions which, when executed on a suitable processing device or device or in one or more means of the device of any preceding device claim, cause the computer or device or unit or means to perform the ^Execute method according to ei ^¬ nem of the preceding method claims.