A beer distributor incurs a penalty cost of $ 2.00 per case of shortage and $ 1.

Question

A beer distributor incurs a penalty cost of $ 2.00 per case of shortage and $ 1.00 charge per case left over in inventory at the end of the week. Assume that the demand ( in number of cases ordered) follows the decrete distribution given in the table below.

demand    and      probability

10                           .2

20                           .3

30                           .3

40                           .1

50                           .1

a) what is the optimal number of cases to have on hand to minimize expected total costs in a single week? show your calculations.

b) what is the expected cost?

Explanation / Answer

a) expected demand = 10*0.2+20*.3+30*0.340*0.1+50*0.1 = 26

also for shortage optimal quantity = sqrt((2*A*D/H)(H+K)/k)

letting ordering cost(here missing) = 100

SO Quantity =88.31

b) cost expected = Q/2 *h + stockout cost = 44*1 + (88-58.87)/2 *2 =73.12

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