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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



efficiently as possible. Two illustrations will be given: for a comparatively 

 low-cost part involving expensive set-up charges and no administrative 

 charges, and for a more costly operation with comparatively inexpensive 

 set-up costs but high administrative costs. For Case I assume a part 

 for which the following constants apply: 



k = 0.15 



N = 2,000,000 



S = $10.00 



In Cast II assume that 



A- = 0.15 



.V = 2,000,000 



S = $2.00 



C\ = so. 10 

 .4=0 



Ci = $1.00 

 A = $100 



The results for these two cases are given in Fig. 4. 



Results such as these are of the utmost value both in manufacturing 

 planning for lowest cost, and in applications planning to show when 

 the lot-size penalties can be tolerated. However, no case is to be expected 

 in practice where optimum conditions can be met more than a part of 

 the time. What with unexpected rush orders, fluctuation of annual de- 

 mands, rescheduling, possible moves, or breakdown of machinery, 

 it is usually impossible to plan production to remain at all times at the 

 optimum value. The variation from optimum cost that results from a 

 departure from optimum lot size is thus of interest; it is readily stated 



10 



1 10 10^ 10^ to'* 10^ 10^ K 



n, ANNUAL DEMAND FOR A GIVEN CODE 



Fig. 4 — Optimum lot sizes and costs. 



