2. Project part
Test case
‘Biogen’ LLC is a producer of medicines and biomedical products in the region. It is known that the peak demand for some drugs accounted for the summer period (cardiovascular drugs and analgesics) – 20 tenge; the second group (anti-infective, inflammatory drugs) – 15 tenge. According to the observations of the last few years, service marketing firm found that it can be implemented within two months considered in warm weather 3050 conv. u products of the first group 1100 conv. u production of the second group, in cold weather – 1525 conv. u products of the first group and 3690 conv. u the second group.
Due to possible changes in weather the task – to determine the firm’s strategy in output, ensuring maximum revenue from the sale of the sale price at 40 tenge per 1 conv. u products of the first group and 30 tenge. – The second group.
Solution. The firm has two strategies:
A1- this year will be the warm weather
A2-the weather is cold
If the firm decides strategy A1 and will actually warm weather (nature strategy B1), then released products (3050 conv. Units. Preparations of the first group and the second group in 1100 conv) is fully implemented and revenue is
3050(40-20 + 1100*(30-15)=77500 tenge
In cool weather conditions (nature of strategy B2) preparations of the second group will be sold completely, and only the first group in the amount of 1525 conv. u and part of the preparations will remain unrealized. Revenue is
1525*(40-20) + 1100*(30-15)-20*(3050-1525)=16500 tenge
Similarly, if the firm decides A2 strategy, and in fact will be the cold weather, the income will be
1525*(40-20) + 3690*(30-15)=85850 tenge
With warm weather revenue is
1525*(40-20)*1100(30-15)-(3690-1100)*15=8150 tenge
Considering the company and weather as two players get payoff matrix
B1 B2
The price of the game lies in the range
Of the payoff matrix shows that under all conditions the firm’s revenue is not less than 16 500 tenge, but if the weather conditions coincide with the chosen strategy, the firm’s revenue could reach 77 500 tenge.
Find a solution to the game.
Denote the likelihood of firm strategy A1 through x1, A2-through strategy x2, and x1=1-x2 deciding game graphic method, we obtain at
The
price game 
=46986
tenge
Optimal production plan of drugs will be
0.56*(3050;1100)+0.44*(1525;3690)=(2379;2239.6)
Thus, the company is advantageously carried out during September and October 2379 conv. u preparations of the first group and 2239.6 cond. u preparations of the second group, then in any weather it will receive income of at least 46 986 tenge. In the face of uncertainty, if the company is not possible to use a mixed strategy (contracts with other organizations), to determine the optimal strategy of the firm use criteria nature.
Wald's maximin model:
tenge,
Company strategy is advisable to use A1
Criterion of maximum:
tenge
It is advisable to use the strategy A2
Hurwitz criterion: for definiteness
then apply for the firm’s strategy A1
tenge
Strategy for A2
tenge
max(53100,54770)=54770 tenge
appropriate to use the company strategy A2.
Savage criterion. The maximum element in the first column – 77500, the second column – 85850.
Elements of matrix are the risks of expression
Now
we have 
Risk matrix has the form
min{max(max
)}=min(69350,69350)=69350
tenge
it is advisable to use the strategy A1 or A2
Therefore, it is advisable to adopt a strategy of the company A1 or A2. Note that each of the criteria considered cannot be considered quite satisfactore for the final selection decisions, but their joint analysis allows more to visualize the implications of those or other management decisions.
With a known probability distribution of different states of nature decision criterion is the maximum expected payoff.
Let it be known for the problem, that the probabilities of warm and cold weather are equal and 0.5, then the optimal strategy of the firm is defined as follows.
max{(0.5*77500+0.5*16500);(0.5*8150+0.5*85850)}=(47000;47000)=47000 tenge
Company strategy is advisable to use the A1 or A2