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Model III: Manufacturing Model without Shortage


Assumptions. Items are manufactured, shortages are not allowed, demand is uniform, lead time is zero, items are produced and used to meet demand simultaneously for a portion of an inventory cycle.


One inventory cycle is illustrated in Fig. 6.4.

Fig. 6.4 Manufacturing model without shortage

In this model,

(i)                 Inventory is building up at a constant rate of (k- r) units per unit time during t1.

(ii)               No production during t2 and the demand is met at the rate of r per unit of time.


The optimal quantities are obtained as given below :

Q*  = EOQ/Economic batch quantity

t1*= period of production as well as consumption

= Q* / k


t2 = penod of consumption only = r

n * = optimum number of production runs per year

= r / Q*

                                 t*= t1* +t2*

Total minimum cost=

Example 4. A contractor has to supply 10000 bolts per day to a customer. He finds that during a production run he can produce 20000 bolts per day. The cost of holding bolt in stock for one year is 3 paise and set up cost of a production nm is Rs. 20. How frequently should production run be made?


Solution.                     r = 10000 bolts/day

k = 20000 bolts/day

c1 = $ 0.03/bolt/year

= $ 0.000082/bolt/day

C5 = $ 20/production run.

= 98772.96 =  98773 bolts.


Length of production cycle= Q*/ k = 4. 94 days.


=> production cycle starts at an interval of 9.88 days and production continues for 4.94 days so that in each cycle a batch of 98773 bolts is produced