ECONOMICS OF TKLKl'llONK Ki;i,AY A I'l'LICA'l'lON'S 245 



needed cost. The problem is how l)est to combine these opposing fac- 

 tors. 



In iUust ration, consider a relay which is to be ecjuipped with molded 

 spring arrangements, capable of providing any number of "transfers" 

 from 1 to 12, each of which is used in approximately equal numbers in 

 the system. At the one extreme, only one molding might be provided, 

 always equipped with 12 transfers. At the other extreme 12 different 

 moldings might be provided, co\'ering each individually needed quantity 

 of "transfers." In the case of the single molding there is no lot-size 

 penalty at all, but on the a\'erage a large penalty in surplus contacts; 

 while for the tweh-e kinds of moldings, lot-size penalties corresponding 

 to one-twelfth of the possible annual output are incurred, but no spare 

 parts at all will be needed. Such a problem may be treated as given 

 below. 



Let the number of kinds of spring sets chosen be designated by v. 

 Then the annual output of each kind is the total output N divided by 

 V, or 



N 

 n= -. (25) 



V 



Now it was shown in Section 1 .2 that the cost penalty for making things 

 in lots is given by equation (12). For the present problem, this may be 

 expressed in terms of v, by substituting equation (25) into equation (12). 

 The resulting lot-size cost penalty is then 



V 



n — 



_VW(H)i^)^'^ 



+ A 



(26) 



The penalt}' due to pro\-iding unneeded springs is the dollar value of 

 the average number of spare springs. The average number of spares is 

 approximately 



2v 



Thus for only one kind furnished, always 12 transfers, the number of 

 spares can vary between and 11, an average of 5.5, as given by the 

 equation. If there were eight kinds, consisting possibly of moldings of 

 1, 3, 5, 6, 7, 8, 10 and 12 sets of transfers, the average number of extras 

 would be 0.25. The dollar penalty compared to no extras ever needed is 



