Question

probabilities

Problem 2. (Inventory problem.) Suppose that the bicycle dis- tributor is offered very favourable terms on the purchase of the model under consideration, whose production is to be discounted. The unit cost of each bicycle is $20. Each bicycle can be sold, in the period 20-25 December, for $45, for a profit of $25. The problem is that the distributor does not know the exact demand. Suppose he lives in a small village and estimates the demand D to be 0, 1, or 2, equiprobably. Bicycles unsold in the mentioned period 20-25 December, will be sold later for a much cheaper price; besides they occupy some space in the storage, etc. Thus each of them gives income (not profit!) of only $7. Find the best number of bicycles, y*, to be bought by the dis- tributor (a) Use the expected value criterion. (b) Draw the decision tree and analyse it in the usual way.

Answer 1

							PROFIT for y=
							Y=0	Y=1	Y=2
		Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap
							$0	($13)	($26)	Loss per unit=20-7=13
				p=(1/3)
							$0	$25	$12	(25-13)
				p(1/3)
				p=(1/3)
							$0	$25	$50
	Expected Profit for y=0: (1/3)*0+(1/3)*0+(1/3)*0=	$0
	Expected Profit for y=1: (1/3)*-13+(1/3)*25+(1/3)*25=	$12.33
	Expected Profit for y=0: (1/3)*0+(1/3)*0+(1/3)*0=	$12
	Best Number of bicycles to be bought	1
		PROFIT for y= Y=1 Y=2 Demand=0 SO ($13) ($26) Loss per unit=20-7=13 p=(1/3) Demand=1 $0 $25 $12 (25-13) P(1/3) p=(1/3) Demand=2 $0 $25 $50