Question

Assuming that p=2, v=1.25, g=0.50, B=0.50 If demand is characterized by the empirical probability distribution given below, what is the optimal profit? D f(D) 12 0.1 13 0.4 14 0.2 15 0.2 16 0.1

Answer 1

Cu = 2 - 1.25 = 0.75

Co = 1.25 - 0.5 = 0.75

Critical fractile = Cu/(Cu+Co) = 0.75/(0.75+0.75) = 0.5

Refer cumulative probability distribution table to lookup for f(D) greater than 0.5

D	f(D)	∑f(D)
12	0.10	0.10
13	0.40	0.50
14	0.20	0.70
15	0.20	0.90
16	0.10	1.00

Correspodning value of f(D) = 0.7 which is greater than 0.5

Therefore,for optimal order quantity, Q = 14

Expected shortage, L = (15-14)*.2+(16-14)*.1 = 0.4

Average demand, D' = 12*.1+13*.4+14*.2+15*.2+16*.1 = 13.8

Average sales, S = D' - L = 13.8-0.4 = 13.4

Expected leftover, V = Q - S = 14 - 13.4 = 0.6

Expected profit = S*Cu - V*Co = 13.4*0.75 - 0.6*0.75 = 9.6