Abstract:
Provided is a method for populating printed circuit boards, which includes the steps of acquiring jobs, in each case relating to populating printed circuit boards of a printed circuit board type on the pick-and-place line, and associated probabilities by a job is to be executed in each case, assigning printed circuit board types of the jobs to set-up families, determining for each set-up family the characteristic number which comprises the sum of probabilities of those jobs, the printed circuit board types of which are comprised by the set-up family, optimizing the assignment in such a way that the characteristic numbers of different set-up families are as different as possible, providing a set-up from one of the determined set-up families on the pick-and-place line, and populating printed circuit boards on the pick-and place line.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to PCT Application No. PCT/EP2015/077065, having a filing date of Nov. 19, 2015, based off of German application No. 1020152004 20.1 having a filing date of Jan. 14, 2015, the entire contents both of which are hereby incorporated by reference. 
     
    
     FIELD OF TECHNOLOGY 
       [0002]    The following relates to a method and a system for populating printed circuit boards. To this end, a pick-and-place line is provided, which is designed to populate printed circuit boards with components. 
       BACKGROUND 
       [0003]    An electronic module comprises a printed circuit board and components which are mechanically and electrically attached thereto. To produce the printed circuit board, components are arranged on the printed circuit board using an automatic pick-and-place unit, and thereafter soldered thereto in a reflow oven. A plurality of automatic pick-and-place units can be arranged sequentially on a pick-and-place line. For the production of multiple printed circuit boards, a pick-and-place system can be employed, comprising a plurality of pick-and-place lines. 
         [0004]    A combination of component types on the automatic pick-and-place unit is described as a set-up. Using a set-up, a quantity of different printed circuit boards can be produced, which are described as a set-up family. Customarily, however, printed circuit boards of more different printed circuit board types are to be produced than is possible using a single set-up, thereby necessitating a change of set-up in the course of production. 
         [0005]    A set-up can be accommodated on one or more set-up tables, which can easily be replaced on the automatic pick-and-place unit. However, the equipment of a set-up table with components of predefined component types is complex. Consequently, a distinction is frequently drawn between fixed set-ups and variant set-ups, wherein a fixed set-up table is intended to retain its composition of component types over a predefined planning period, whereas a variant set-up table will foreseeably be refitted within said planning period. 
         [0006]    DE 10 2012 220 904 A1 relates to a method for determining a most advantageous fixed set-up possible for a pick-and-place line. 
       SUMMARY 
       [0007]    An aspect relates to an improved method, a computer program product and a system for populating printed circuit boards which permit a more efficient population of a pick-and-place line. 
         [0008]    For populating printed circuit boards by a pick-and-place line, set-up families having associated set-ups are provided. Each set-up family is assigned at least one printed circuit board type, and each set-up is assigned at least one component type, such that a printed circuit board of a printed circuit board type of a set-up family can be populated by components of the component types of the set-up assigned to the printed circuit board type on the pick-and-place line. A set-up can be implemented in the form of supplies of components of the component types, in order to be fitted on the pick-and-place line. A method for populating printed circuit boards comprises steps of acquiring jobs, in each case relating to the population of printed circuit boards of a printed circuit board type on the pick-and-place line, and associated probabilities with which a job is to be executed in each case, assigning printed circuit board types of the jobs to set-up families, determining, for each set-up family, a characteristic number which comprises the sum of probabilities of those jobs, the printed circuit board types of which are comprised by the set-up family, optimizing the assignment in such a way that the characteristic numbers of different set-up families are as different as possible, providing a set-up from one of the determined set-up families on the pick-and-place line, and populating printed circuit boards on the pick-and-place line. 
         [0009]    Jobs can be associated with practically any time period in the future. Customarily, it is not known—or not exactly known—when a job is actually on hand, and thus when the job is to be executed. The operation of the pick-and-place line customarily follows a predefined rotation wherein, for a given forthcoming period, it is known in each case which jobs are to be processed. The probability of the job indicates how probable it is that a job will need to be executed within any given time period. 
         [0010]    By means of the method, set-ups or set-up families can be constituted in consideration of the knowledge that the population of specific printed circuit board types will recur on a regular basis. The determination of set-ups can thus be improved, such that the change of set-ups during production is reduced. The number of set-ups to be produced can thus be reduced. Preferably, by the method, fixed set-ups are defined which, within a long-term planning period, for example of several days or weeks, are to be fitted to the pick-and-place line in a repeated manner. Jobs which, at the time of execution of the method, are not known, can be processed by variant set-ups, which are only equipped on a one-off basis, then employed on the pick-and-place line on a one-off basis and removed again thereafter. Of the present jobs, not all will need to be considered in the determination of fixed set-ups, as described hereinafter—specifically, jobs with the lowest probabilities can also be ignored in the constitution of fixed set-ups. 
         [0011]    Preferably, optimization is executed such that the number of set-up families is minimized. A number of set-ups can also be reduced accordingly, thereby generating advantages with respect to handling and costs. 
         [0012]    The method can be executed with respect to a predefined time period, wherein the processing time for a job does not exceed said time period. Specifically, the probabilities can relate to the occurrence of a job within the respective time period. This time period is also described as the short-term planning horizon and can, for example, be one day. In other words, it is preferably assumed that each job can be completely processed before the time period has expired. Customarily, predefined jobs to be processed are specified for each time period. 
         [0013]    Probabilities can be determined with reference to previous jobs. For example, experiences obtained from previous production periods can be advantageously employed. Specifically, frequencies of previous jobs can be known, and probabilities determined therefrom. Alternatively or additionally, knowledge of forthcoming jobs can also be employed. In an actual production operation, for example, jobs can be defined for a specific rotation. 
         [0014]    In a first variant, the set-up families are constituted individually in sequence, wherein optimization is executed in each case such that a number of jobs which can be processed using set-ups from the set-up families is maximized. 
         [0015]    In a second variant, the set-up families are constituted individually in sequence, and optimization is executed in each case such that, for the printed circuit board types assigned to a new set-up family, the following characteristic number is minimized: 
         [0000]    log(1−p r ); where p r  is the probability of an occurrence of a job for the population of printed circuit boards of printed circuit board type r. The probability customarily relates to the predefined time period, i.e. the short-term planning horizon. 
         [0016]    Optimization is preferably executed by mixed integer optimization. Effective optimization can thus be achieved in a relatively short processing time; the discrepancy (gap) of optimization from a best possible solution can also be defined. 
         [0017]    A computer program product comprises programming code means or programming code for executing a method, where said computer program product is run on a processing device or is stored on a computer-readable data medium. 
         [0018]    A control unit is designed for acquiring jobs, in each case relating to the population of printed circuit boards of a printed circuit board type on the pick-and-place line, and associated probabilities with which a job is to be executed in each case, assigning printed circuit board types of the jobs to set-up families, determining, for each set-up family, a characteristic number which comprises the sum of probabilities of those jobs, the printed circuit board types of which are comprised by the set-up family, optimizing the assignment in such a way that the characteristic numbers of different set-up families are as different as possible, and controlling the population of printed circuit boards on the pick-and-place line, where a set-up from one of the determined set-up families is fitted on the pick-and-place line. 
     
    
     
       BRIEF DESCRIPTION 
         [0019]    Some of the embodiments will be described in detail, with references to the following figures, wherein like designations denote like members, wherein: 
           [0020]      FIG. 1  shows a pick-and-place system, in accordance with embodiments of the present invention; 
           [0021]      FIG. 2  shows a representation of set-up families on a pick-and-place line according to  FIG. 1 ; 
           [0022]      FIGS. 3-5  show job numbers for various set-up families in different examples; and 
           [0023]      FIG. 6  shows a flow chart of a method for the constitution of fixed set-ups for a pick-and-place system according to  FIG. 1 . 
       
    
    
     DETAILED DESCRIPTION 
       [0024]      FIG. 1  shows an exemplary pick-and-place system  100 . The pick-and-place system  100  comprises one or more pick-and-place lines  110  and a processing or control unit  115 . Each pick-and-place line  110  comprises an optional conveyor system  125  and one or more automatic pick-and-place units  130 . Each automatic pick-and-place unit  130  comprises one or more pick-and-place heads  135 , each of which is designed for the pick-up of components  155  from a set-up table  140  and the placement thereof at a predefined position on the printed circuit board  120 , which is located on the conveyor system  125 . During the population process, the printed circuit board  120  is customarily stationary, in relation to the automatic pick-and-place unit  130 . 
         [0025]    The set-up tables  140  each comprise a plurality of infeed devices  150  of which, in  FIG. 1 , only one is represented for exemplary purposes. Each infeed device  150  holds a stock of components  155  of a predefined component type  160 . For the components  155 , the infeed device  150  customarily has a holding capacity, which can be expressed in terms of tracks. A track is customarily 8 mm wide, and the number of tracks on a set-up table  140  is limited, for example to 40. Components  155  of the same component type  160  are customarily delivered in the form of a belt, on a tablet or in a tube. Each component type  160  requires a predefined number of tracks on the infeed device  150  and on the set-up table  140 , which are customarily mutually adjoining. 
         [0026]    Generally, an infeed device  150  can be configured for the accommodation of components  155  of different component types  160  and, customarily, different infeed devices  150  can be fitted to a set-up table  140 . In the present case, in the interests of simplification, it is assumed that a stock of components  155  of a component type  160  on an infeed device  150  is practically inexhaustible, such that restocking is not required. 
         [0027]    If, on the automatic pick-and-place unit  130 , a component  155  of a component type  160  is required which is not present on one of the set-up tables  140 , customarily, the assignment of components  155  on one of the set-up tables  140  fitted is not altered, but the set-up table  140  is completely replaced with another and appropriately-populated set-up table  140 . The population of a set-up table  140 , which is not fitted to the pick-and-place line  110 , with components  155  is described as prefitting, and can require a processing time of the order of one or more hours, for example approximately 6-10 hours. 
         [0028]    As a change of set-up tables  140  on the pick-and-place line  110 , or so-called set-up change, is customarily associated with an interruption in production, it is endeavored to change the set-up tables  140  as infrequently as possible. Given that, moreover, the set-up tables  140  are expensive, and the changeover of a set-up table  140  can be a complex and lengthy operation, it is moreover endeavored to constitute the smallest possible number of set-ups, in order to manufacture a predefined production volume of printed circuit boards  120  of predefined printed circuit board types  122 . In this case, the production volume comprises a plurality of printed circuit board types  122 , of which in each case a predetermined batch quantity of printed circuit boards  120  is to be populated with components  155  of predefined component types  160 . For example, 300 printed circuit boards  120  of a first printed circuit board type  122 , and 200 printed circuit boards  120  of a second circuit board type  122 , can be populated. 
         [0029]    A set-up  165 ,  170  comprises a quantity of component types  160 , and is comprised of one or more set-up tables  140 , which are equipped with stocks of components  155  of the component types  160  of the set-up  165 ,  170 , and are fitted to the pick-and-place line  110 . 
         [0030]    A set-up family  175  is assigned to the set-up  165 ,  170 , which comprises printed circuit board types  122 , from which printed circuit boards  120  can be populated by components  155  of the component types  160  from the set-up  165 ,  170 . A set-up family  175  is specifically assigned to a set-up  165 ,  170  and vice versa. 
         [0031]    In order to increase capacity utilization on a pick-and-place line  110 , or to reduce a requirement for set-up tables  140 , the constitution of set-up families  175  on the basis of the printed circuit board types  122  to be populated is therefore critical. The constitution of set-ups  165 ,  170  or set-up families  175  can involve the consideration of ancillary conditions, such as compliance with a limited holding capacity of a set-up table  140  for component types  160  or a grouping of predefined printed circuit board types  160  in the same set-up family  175 , for example on the grounds of the use of lead-based or lead-free solder. 
         [0032]    Set-ups can be divided into fixed set-ups  165  and variant set-ups  170 , wherein the fitting of a fixed set-up  165  is intended to remain unchanged on a number of shuttle tables  140  over a predefined planning period, whereas a shuttle table  140  of a variant set-up  170  will foreseeably be refitted with components  155  of different component types  160  within the planning period. The planning period can be, for example, 6-12 months. A variant set-up  165  is customarily present in a predefined configuration for a substantially shorter time than the planning period, for example a number of hours or days, but customarily not more than one week. 
         [0033]    A static set-up can also be constituted, which includes elements of the fixed set-up  165  and the variant set-up  170 . The static set-up, in the same way as the fixed set-up  165 , is constituted for a longer period, during which it customarily remains unchanged. However, a static set-up does not customarily remain fitted, i.e. constituted as a physical set-up on set-up tables  140 , but can also be removed after use. Moreover, a static set-up can also be fitted (i.e. completed) on a partial basis only if, for example, the static set-up comprises a plurality of printed circuit board types  122  and, at a given time point, only jobs for the production of printed circuit boards  120  of some of these printed circuit board types  122  are on hand. In this case, components  155  of such component types  160  which are not required for the population of the printed circuit boards  120  ordered do not need to be fitted. 
         [0034]    Administratively, the static set-up is substantially easier to manage than a fixed set-up  165  or a variant set-up  170 . If the static set-up, further to the use thereof, is not set down, it can also be described as a fixed set-up  165 . Hereinafter, unless indicated otherwise, reference is preferably intended to static set-up families and the static set-ups assigned thereto. 
         [0035]    Set-ups  165 ,  170  can be replaced, as required, on the pick-and-place line  110 . In order to constitute a fixed set-up  165  or a variant set-up  170 , a set-up table  140 , while not fitted to the pick-and-place line  110 , can be equipped with stocks of components  155  of predefined component types  160 . Previously fitted components  155  of component types  160  which are not required can be removed beforehand. This refit can involve a substantial amount of manual labor, and can be time-intensive. 
         [0036]    In order to minimize the complexity associated with a variant set-up  170 , it is endeavored that fixed set-ups  165  should accommodate as many printed circuit board types  122  as possible. In practice, however, a target case involving no variant set-ups  170  is scarcely achievable. 
         [0037]    The control device  115 , in the context of the control of the pick-and-place system  100 , assigns printed circuit board types  122 , the associated printed circuit boards  120  whereof are to be populated on the pick-and-place line  110 , to one set-up family  175  respectively, wherein fixed set-up families  175 , which are assigned respectively to a fixed set-up  165 , and variant set-up families  175 , which are assigned respectively to a variant set-up  170 , can be constituted. 
         [0038]    In practice, for example, for a given production quantity of printed circuit board types  122 , in a first step, a fixed set-up  165  is constituted for a (largest possible) proportion of printed circuit board types  122 , whereafter, in a second step, variant set-ups  170  are constituted for the remaining proportion of printed circuit board types  122 . The quality of these assignment operations dictates, to a substantial degree, the extent of effective capacity utilization of production means of the pick-and-place system  100 , and how efficiently population is executed. 
         [0039]      FIG. 2  shows a representation of exemplary set-up families  175  on a pick-and-place line  110  according to  FIG. 1 . In this case, the set-up families  175  are divided into a fixed set-up family  210 , which is assigned to a fixed set-up  165 , and a variant set-up family  215 , which is assigned to a variant set-up  170 . In the example represented, within a planning period  205 , printed circuit board types  122  of a single fixed set-up family  210  or of a single variant set-up family  215  can be populated on the pick-and-place line  110 . 
         [0040]    It is assumed that, at the start of the planning period  205 , a number of jobs  220  are on hand, which are to be executed as efficiently as possible. The number of jobs is described as the job number. Each job  220  comprises at least one printed circuit board type  122  and one batch quantity  225  of printed circuit boards  120  to be populated. Component types  160  are assigned to the printed circuit board type  122 , components  155  whereof are to be fitted to the individual printed circuit boards  120 . 
         [0041]    Further information can be assigned to a printed circuit board type  122 . For example, a number  230  of component types  160  which are to be fitted to each printed circuit board  120 , a number  235  of population positions on a printed circuit board  120 , or a production time  240  for a printed circuit board  120  of the respective printed circuit board type  122 , can be indicated. The number of population positions corresponds to the number of components  155  which are to be fitted to a printed circuit board  120  of a printed circuit board type  122 , of whatever component type  160 . Moreover, a job number  245  can be indicated, which indicates how many jobs  220  for the population of printed circuit boards  120  of a printed circuit board type  122  are on hand within a predefined planning period  205 . 
         [0042]    By the employment of mathematical methods, significantly superior solutions for the assignment of printed circuit board types  122  to fixed set-up families  175  or to pick-and-place lines  110  can be achieved than by the methods applied previously in practice. For the determination of an optimum assignment of printed circuit board types  122  to a fixed set-up family  175 , automatic optimization can be employed. To this end, different optimization methods can be applied, for example, on the basis of local search methods or metaheuristic algorithms. 
         [0043]    Preferably, however, an IP model (integer programming or an integer program, or a mixed integer optimization model) is employed. One of the principal methods in the field of mathematical optimization is linear optimization, which involves the optimization of linear target functions in respect of a quantity which is restricted by linear equalities and inequalities. Linear optimization forms the basis of the procedural solution of (mixed) integer linear optimization. 
         [0044]    Advantages of linear optimization are as follows:
       A global optimization approach   Easily extendable   Commercial availability of very effective standard solvers (Ilog, Gurobi, Xpress), which are widespread and proven in practice,   For any solution determined, the maximum discrepancy thereof (gap) from the optimum solution is known.       
 
         [0049]    Hereinafter, examples of IP formulations are provided for the optimization of the described assignment of printed circuit board types  122  to a fixed set-up family  175 . 
         [0050]    A short-term planning period T K  is assumed, for example of several hours or days, and a long-term planning period T L , which is a number of times longer than T K , for example of several days, weeks or months. Fixed set-ups are defined for the pick-and-place line  110 , which are to remain unchanged over the long-term planning period T L , and can be employed a number of times. The definition should proceed such that, in the operation of the pick-and-place line  110 , as few set-up changeovers and as few set-ups as possible are required. To this end, the circumstance is exploited whereby, at the time of definition of fixed set-ups, some information on forthcoming jobs is already known. 
         [0051]    In the operation of the pick-and-place line  110 , it is known which jobs are to be processed in the next respective short-term planning period. If a job cannot be processed using one of the fixed set-ups, a variant set-up must be prepared. The frequency of set-up changeovers, and the frequency of the necessity for the preparation of variant set-ups, is therefore critically dependent upon the quality of the aforementioned assignment of printed circuit board types to fixed set-up families. 
         [0052]    Symbols
   R is the quantity of printed circuit board types   Cl is the quantity of set-up families, consisting of all the printed circuit board types from R   Order r  is the number of jobs for the printed circuit board type   r in the long-term planning period   T L  is the number of days in the long-term planning period   T K  is the number of days in the short-term planning period   
 
         [0059]    Evaluation Model 
         [0000]    Order r &lt;T L /T K  applies. This condition can be fulfilled, where applicable, by a setting for Order r :=T L /T K .
 
p r  is the probability of the execution of a job for the population of a printed circuit board  120  of a printed circuit board type  122  within the short-term planning period T K , for example 0.08. The probability p r  corresponds to the average relative frequency at which such jobs occur, in the above case, for example, where 8 such jobs are to be executed in the course of 100 short-term planning periods T K . This frequency can be determined, for example, with reference to previous planning periods T K , or with reference to the knowledge of forthcoming jobs.
 
         [0060]    It is assumed that, in each case, jobs are distributed evenly over the short-term planning periods T K . 
         [0000]    
       
         
           
             
               p 
               r 
             
             = 
             
               
                 
                   T 
                   K 
                 
                  
                 
                   Order 
                   r 
                 
               
               
                 T 
                 L 
               
             
           
         
       
     
         [0061]    It is further assumed that the jobs are mutually independent. Within the short-term planning period T K , all jobs on hand can be processed by the fixed set-up and one or more variant set-ups. To this end, each variant set-up required in the short-term planning period T K  is set up only once, all the printed circuit boards of the assigned printed circuit board types which are to be produced are populated, and the variant set-up is set down again thereafter. A further application of the variant set-up on the pick-and-place line  110  is not anticipated. 
         [0062]    The expected value for the required set up of a set-up family clεCl on the pick-and-place line  110  within the short-term planning period is determined as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     EW 
                      
                     
                       ( 
                       cl 
                       ) 
                     
                   
                   = 
                     
                    
                   
                     
                       probability 
                        
                       
                           
                       
                        
                       that 
                        
                       
                           
                       
                        
                       at 
                        
                       
                           
                       
                        
                       least 
                        
                       
                           
                       
                        
                       one 
                        
                       
                           
                       
                        
                       module 
                        
                       
                           
                       
                        
                       r 
                     
                     ∈ 
                     
                       cl 
                        
                       
                           
                       
                        
                       must 
                        
                       
                           
                       
                        
                       be 
                        
                       
                           
                       
                        
                       produced 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       1 
                       - 
                       
                         probability 
                          
                         
                             
                         
                          
                         that 
                          
                         
                             
                         
                          
                         no 
                          
                         
                             
                         
                          
                         module 
                          
                         
                             
                         
                          
                         r 
                       
                     
                     ∈ 
                     
                       cl 
                        
                       
                           
                       
                        
                       must 
                        
                       
                           
                       
                        
                       be 
                        
                       
                           
                       
                        
                       produced 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     1 
                     - 
                     
                       
                         ∏ 
                         
                           r 
                           ∈ 
                           cl 
                         
                       
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             p 
                             r 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
         [0063]    An expected value “EW(Number)” for the number of set-up families to be set up within a short-term planning period is thus given by the following: 
         [0000]    
       
         
           
             
               
                 
                   
                     EW 
                      
                     
                       ( 
                       Number 
                       ) 
                     
                   
                   = 
                     
                    
                   
                     
                       
                         ∑ 
                         
                           cl 
                           ∈ 
                           Cl 
                         
                       
                        
                       
                           
                       
                        
                       1 
                     
                     - 
                     
                       
                         ∏ 
                         
                           r 
                           ∈ 
                           cl 
                         
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             p 
                             r 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       Number 
                        
                       
                           
                       
                        
                       of 
                        
                       
                           
                       
                        
                       set 
                        
                       
                         - 
                       
                        
                       up 
                        
                       
                           
                       
                        
                       families 
                     
                     - 
                     
                       
                         ∑ 
                         
                           cl 
                           ∈ 
                           Cl 
                         
                       
                        
                       
                         
                           ∏ 
                           
                             r 
                             ∈ 
                             cl 
                           
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               p 
                               r 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0064]    This expected value is an effective quality criterion for a quantity of fixed set-up families Cl. 
       Examples 
       [0065]    In the following examples, the long-term planning period is 100 days and the short-term planning period is 1 day. It has been shown that, with respect to the order number, unbalanced fixed set-up families are tendentially superior to balanced fixed set-up families. 
         [0066]    Modules and their associated job numbers are given by the following: 
         [0000]    
       
         
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Module 
               
             
          
           
               
                   
                 r1 
                 r2 
                 r3 
                 r4 
                 r5 
                 r6 
               
               
                   
                   
               
             
          
           
               
                 Number of jobs 
                 90 
                 70 
                 50 
                 50 
                 30 
                 10 
               
               
                 pr 
                 0.9 
                 0.7 
                 0.5 
                 0.5 
                 0.3 
                 0.1 
               
               
                   
               
             
          
         
       
     
         [0067]    It is assumed that the set-ups, for example by means of the capacities of the set-up tables, are restricted in each case to the accommodation of components of component types for two printed circuit board types only, such that a set-up family can only accommodate two printed circuit board types. 
         [0068]      FIG. 3 a    represents balanced set-up families with respect to absolute job frequencies. A job number is plotted on the vertical axis, while different set-up families are represented on the horizontal axis. The first set-up family can be used to process the jobs r 1 , the second to process the jobs r 2  and r 5 , and the third to process the jobs r 3  and r 4 . 
         [0069]    The expected value EW for the number of set-ups in the short-term planning period is as follows: 
         [0000]    
       
         
           
             
               
                 
                   EW 
                   = 
                     
                    
                   
                     3 
                     - 
                     
                       ( 
                       
                         
                           0.1 
                           * 
                           0.9 
                         
                         + 
                         
                           0.3 
                           * 
                           0.7 
                         
                         + 
                         
                           0.5 
                           * 
                           0.5 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     3 
                     - 
                     
                       ( 
                       
                         0.09 
                         + 
                         0.21 
                         + 
                         0.25 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     3 
                     - 
                     0.55 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   2.45 
                 
               
             
           
         
       
     
         [0070]      FIG. 3 b    represents unbalanced set-up families with respect to absolute job frequencies. The expected value for the number of set-ups is the short-term planning period is now only 2.09 set-ups. Fewer set-up changeovers are therefore required, thereby permitting the efficiency of the pick-and-place line  110  to be improved. 
         [0071]    Improved Solution with an Additional Set-Up Family 
         [0072]    Hereinafter, it is demonstrated that it is not always better to pursue the target of a minimum number of set-up families. Modules and the number of corresponding jobs within the long-term planning horizon are given by the following: 
         [0000]    
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Module 
                 r1 
                 r2 
                 r3 
                 r4 
                 r5 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Number of jobs 
                 90 
                 50 
                 50 
                 10 
                 10 
               
               
                   
                 pr 
                 0.9 
                 0.5 
                 0.5 
                 0.1 
                 0.1 
               
               
                   
                   
               
             
          
         
       
     
         [0073]      FIG. 4 a    shows a breakdown of jobs into three set-up families. The expected value for the number of set-ups in the short-term planning period is 1.76 set-ups. 
         [0074]      FIG. 4 b    shows a breakdown involving four set-up families. The expected value for the number of set-ups in the short-term planning period is 1.65 set-ups: 
         [0000]    
       
         
           
             
               
                 
                   EW 
                   = 
                     
                    
                   
                     4 
                     - 
                     
                       ( 
                       
                         
                           0.1 
                           * 
                           0.5 
                         
                         + 
                         0.5 
                         + 
                         0.9 
                         + 
                         0.9 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     4 
                     - 
                     2.35 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   1.65 
                 
               
             
           
         
       
     
       Heuristics 
       [0075]    The assignment problem can be formulated as a mixed integer non-linear optimization problem. It is assumed, however, that this problem can only be resolved with difficulty. Consequently, various heuristics are proposed hereinafter, in order to permit the resolution of the problem by means of linear optimization. 
       Heuristic 1 
       [0076]    Using the method described in patent application DE 10 2012 220 904.2, set-ups can be constituted with a maximum number of jobs. Using this method, heuristic 1 involves the constitution of successive fixed set-up families, each with a maximum number of jobs. Accordingly, the set-up families are fully-packed, and the resulting number of set-up families is relatively low. Moreover, the last set-up families to be constituted include only very few jobs, which only increase the anticipated number of set-ups to a limited extent (c.f. the previous example in  FIGS. 3 b  and 3 c   ). 
       Heuristic 2 
       [0077]    In common with heuristic 1, heuristic 2, by the application of the aforementioned method, involves the successive constitution of set-up families cl from the quantity of residual modules. In this case, however, the target criterion: 
         [0000]    
       
         
           
             
               EW 
                
               
                 ( 
                 cl 
                 ) 
               
             
             = 
             
               1 
               - 
               
                 
                   ∏ 
                   
                     r 
                     ∈ 
                     cl 
                   
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     1 
                     - 
                     
                       p 
                       r 
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    assumes a maximum value in each case. To this end, in the method according to application DE 10 2012 220 904.2, the MIP target function is adjusted as follows. 
         [0078]    R′ represents the quantity of residual modules, which are not yet incorporated in fixed set-up families. It is moreover assumed that pr&lt;1 applies to all rεR′. Only one fixed set-up family/static set-up family cl is constituted. The following designation from MIP also applies: 
         [0079]    Assign r,cl : a variable which indicates whether a printed circuit board r is assigned to a fixed set-up family cl. If an assignment exists, this variable assumes a value of 1, or otherwise assumes a value of 0. 
         [0080]    The target function max EW(cl) can be formulated as a non-linear target function with the whole-number variables Assign r,cl : 
         [0000]    
       
         
           
             
               maximize 
                
               
                   
               
                
               1 
             
             - 
             
               
                 ∏ 
                 
                   r 
                   ∈ 
                   
                     R 
                     ′ 
                   
                 
               
                
               
                 
                   ( 
                   
                     1 
                     - 
                     
                       p 
                       r 
                     
                   
                   ) 
                 
                 
                   Assign 
                   
                     r 
                     , 
                     cl 
                   
                 
               
             
           
         
       
     
         [0081]    This is equivalent to: 
         [0000]    
       
         
           
             
               minimize 
                
               
                   
               
                
               1 
             
             - 
             
               
                 ∏ 
                 
                   r 
                   ∈ 
                   
                     R 
                     ′ 
                   
                 
               
                
               
                 
                   ( 
                   
                     1 
                     - 
                     
                       p 
                       r 
                     
                   
                   ) 
                 
                 
                   Assign 
                   
                     r 
                     , 
                     cl 
                   
                 
               
                
               
                 (* 
                 ) 
               
             
           
         
       
     
         [0082]    The following also applies: 
         [0000]    
       
         
           
             
               
                 ∏ 
                 
                   r 
                   ∈ 
                   
                     R 
                     ′ 
                   
                 
               
                
               
                 
                   ( 
                   
                     1 
                     - 
                     
                       p 
                       r 
                     
                   
                   ) 
                 
                 
                   Assign 
                   
                     r 
                     , 
                     cl 
                   
                 
               
             
             = 
             
               e 
               
                 log 
                  
                 
                   ∏ 
                   
                     r 
                     ∈ 
                     
                       
                         
                           R 
                           ′ 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               p 
                               r 
                             
                           
                           ) 
                         
                       
                       
                         Assign 
                         
                           r 
                           , 
                           cl 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0083]    As the exponential function increases in a strictly monotonic manner, and the following applies 
         [0000]    
       
         
           
             
               log 
                
               
                 
                   ∏ 
                   
                     r 
                     ∈ 
                     
                       R 
                       ′ 
                     
                   
                 
                  
                 
                   
                     ( 
                     
                       1 
                       - 
                       
                         p 
                         r 
                       
                     
                     ) 
                   
                   
                     Assign 
                     
                       r 
                       , 
                       cl 
                     
                   
                 
               
             
             = 
             
               
                 ∑ 
                 
                   r 
                   ∈ 
                   
                     R 
                     ′ 
                   
                 
               
                
               
                   
               
                
               
                 
                   log 
                    
                   
                     ( 
                     
                       1 
                       - 
                       
                         p 
                         r 
                       
                     
                     ) 
                   
                 
                  
                 
                   Assign 
                   
                     r 
                     , 
                     cl 
                   
                 
               
             
           
         
       
     
         [0000]    the target function (*) is equivalent to: 
         [0000]    
       
         
           
             minimize 
              
             
                 
             
              
             
               
                 ∑ 
                 
                   r 
                   ∈ 
                   
                     R 
                     ′ 
                   
                 
               
                
               
                 
                   log 
                    
                   
                     ( 
                     
                       1 
                       - 
                       
                         p 
                         r 
                       
                     
                     ) 
                   
                 
                  
                 
                   Assign 
                   
                     r 
                     , 
                     cl 
                   
                 
               
             
           
         
       
     
         [0084]    This target function is linear, and can thus be employed in MIP as a new target function. In one example, in which heuristic 2 is superior to heuristic 1, the modules and job numbers considered are as follows: 
         [0000]    
       
         
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Module 
                 r1 
                 r2 
                 r3 
                 r4 
               
               
                   
                   
               
             
             
               
                   
                 Number of jobs 
                 90 
                 50 
                 50 
                 50 
               
               
                   
                   
               
             
          
         
       
     
         [0085]    It is assumed that r 1  is appropriate to only one further printed circuit board type in a set-up family, and that r 2 -r 4  are appropriate to a common set-up family. 
         [0086]      FIG. 5 a    shows the result of heuristic 1. The expected value for the number of set-ups in the short-term planning period is 1.775 set-ups. 
         [0087]      FIG. 5 b    shows the result of heuristic 2. The expected value for the number of set-ups in the short-term planning period is 1.7 set-ups. 
       Heuristic 3 
       [0088]    If, by the application of heuristics 1 and 2 respectively, the minimum number of set-up families is exceeded, a further heuristic 3 is proposed. 
         [0089]      FIG. 6  shows a flow diagram of a method  300  for heuristic 3. The method  300  commences with a step  305 , in which the quantity of printed circuit board types R′ yet to be assigned is equal to the original quantity of printed circuit board types R to be assigned. The present set-up family cl opt  is blank in the first instance. 
         [0090]    Thereafter, in a step  310 , the remaining modules from R′ are divided into set-up families, for example using the “method for constituting set-up families on pick-and-place lines” described in patent application DE 201 213 064, such that, in each iteration, a further alternative solution cl min  is obtained respectively. 
         [0091]    The combination of the solutions cl opt  and cl min  is evaluated in a step  315  with respect to the expected value for the number of set-ups in the short-term planning horizon, and the best solution is selected. 
         [0092]    In a step  320 , it is decided whether further printed circuit board types are present in R′. If this is not the case, the method  300  terminates at step  325 . Otherwise, the method proceeds directly to a step  330 . Alternative or additional interruption criteria, such as the achievement of a maximum execution time or the constitution of a predefined number of fixed set-ups, are also possible. 
         [0093]    In step  330 , again as in the case of heuristics 1 and 2, for example by the method described in DE 10 2012 220 904.2, a set-up family cl opt  is constituted successively with respect to a maximum job number or a maximum expected value. 
         [0094]    In a subsequent step  325 , cl opt  is added to the set-up family quantity Cl opt . The printed circuit boards of cl opt  are removed from R′. Thereafter, the method  300  continues with the aforementioned step  310 . 
         [0095]    Although the invention has been illustrated and described in greater detail with reference to the preferred exemplary embodiment, the invention is not limited to the examples disclosed, and further variations can be inferred by a person skilled in the art, without departing from the scope of protection of the invention. 
         [0096]    For the sake of clarity, it is to be understood that the use of “a” or “an” throughout this application does not exclude a plurality, and “comprising” does not exclude other steps or elements.