Sodaco is considering producing a new product: Chocovan soda. Sodaco estimates t

Question

Sodaco is considering producing a new product: Chocovan soda. Sodaco estimates that the annual demand for Chocovan, D(in thousands of cases), has the following mass function: P(D 30) .30, P(D 50) .40, P(D 80) .30. Each case of Chocovan sells for $5 and incurs a variable cost of $3. It costs $800,0 to build a plant to produce Chocovan. Assume that if $1 is received every year (forever), this is equivalent to receiving $10 at the present time. Considering the reward for each action and state of the world to be in terms of net present value, use each decision criterion of this section to determine whether Sodaco should build the plant. Minimax, maximin, maximax

Explanation / Answer

The reward matrix (in hundreds of thousands of dollars) is as follows:

                         Annual Demand

               30,000          50,000       80,000

Build          68 = 2       108 = 2      168 = 8

Not Build             0              0             0

To find the Maximin decision look at

               Minimum Reward

Build                2

Don't Build           0*

Thus Maximin decision is Don't Build.

To find the Maximax decision look at

                    Maximum Reward

Build               8*

Don't Build         0

Thus Maximax decision is to Build.

The regret matrix is as follows

                    Demand                  

               30,000    50,000     80,000 Maximum Regret

Build          2         0          0        2*   

Don't Build    0         2          8        8

Thus Minimax Regret decision is to Build.

Expected Reward from Build = .30(2) + .4(2) + .3(8) = $260,000

Expected Reward from Don't Build = $0

Thus expected reward is maximized by Build decision.

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