Question

A manufacturer of toys is interested to know whether he should launch a deluxe model or a popular model of a toy. if the deluxe model is launched the probabilities that the mkt will be good,fair or poor are given by 0.4,0.3 and 0.3 respectively with payoffs of shs 180,000,shs 100,000 and shs -20,000 respectively.if the popular model is introduced the corresponding probabilities are given by 0.3, 0.4, and 0.3 with respective payoffs of shs 200,000,shs 150,000 and -20,000.advice on which model to be launched.

Answer 1

The decision tree for the given is drawn below:

ROLL-BACK TECHNIQUE

A decision tree is analysed using the roll-back technique. This technique proceeds from the last decision in the sequence and works back to the first for each of the possible decisions. There are two rules concerning roll-back technique in the decision tree analysis:

(i) If branches emanate from a circle, the total expected payoff may be calculated by summing the expected value of all the branches.

(ii) If branches emanate from a square, we calculate the total expected benefit for each branch emanating from the square and let the total expected payoff be equal to the value of the branch with the highest expected benefit.

Let us analyse the tree given above by the roll back technique. Here point '1' is the decision point and C & D are the chance nodes.

$$EMV (at C) = .4 \times Rs.1,80,000 + .3 \times Rs.1,00,000 + .3 \times (Rs. -20,000)$$ $$= Rs.72,000 + Rs.30,000 - Rs.6,000 = Rs.96,000$$ $$EMV (at D) = .3 \times Rs.2,00,000 + .4 \times Rs.1,50,000 + .3 \times (Rs. -20,000)$$ $$= Rs.60,000 + Rs.60,000 - Rs.6,000 = Rs.1,14,000.$$

The decision point '1' is to introduce the popular model since it results in the highest EMV.