Kunfu Company is planning to build a new manufacturing and distribution facility in TT, KK, SS, CC or AA. The company has estimated the facility cost in each country will vary depending on the economic conditions prevailing. The table below provides the cost under three different economic conditions.
Region Economic Climate
Improved Same Worsen
TT 2170 1910 1520
KK 1900 1850 1760
SS 1920 1710 1490
CC 2250 1680 1380
AA 2500 2120 1250
Determine the best decision, using the following decision criteria:
i) Minimin
ii) Minimax
iii) Hurwicz (á = 0.7)
iv) Equal likelihood
To determine the best decision using the given decision criteria, we need to analyze the costs under different economic conditions for each region.
i) Minimin: In this criterion, we select the region with the minimum cost under the worst economic condition.
- For TT: Minimum cost = 1520
- For KK: Minimum cost = 1760
- For SS: Minimum cost = 1490
- For CC: Minimum cost = 1380
- For AA: Minimum cost = 1250
Based on the minimin criterion, we select region AA with a minimum cost of 1250 under the worst economic condition.
ii) Minimax: Here, we select the region that gives the maximum cost under the best economic condition.
- For TT: Maximum cost = 2170
- For KK: Maximum cost = 1900
- For SS: Maximum cost = 1920
- For CC: Maximum cost = 2250
- For AA: Maximum cost = 2500
According to the minimax criterion, we select region AA with a maximum cost of 2500 under the best economic condition.
iii) Hurwicz (α = 0.7): The Hurwicz criterion takes into account both the best and worst case scenarios, using a weightage factor (α) to balance between optimism and pessimism.
To determine the decision for each region, we use the formula:
Decision = α * Maximum Cost + (1 - α) * Minimum Cost
- For TT: Decision = 0.7 * 2170 + 0.3 * 1520 = 1953
- For KK: Decision = 0.7 * 1900 + 0.3 * 1760 = 1850
- For SS: Decision = 0.7 * 1920 + 0.3 * 1490 = 1766
- For CC: Decision = 0.7 * 2250 + 0.3 * 1380 = 1911
- For AA: Decision = 0.7 * 2500 + 0.3 * 1250 = 2050
According to the Hurwicz criterion, we select region AA with a decision value of 2050.
iv) Equal likelihood: In this criterion, we calculate the average cost under all economic conditions for each region and select the region with the lowest average cost.
- For TT: Average cost = (2170 + 1910 + 1520) / 3 = 1866.67
- For KK: Average cost = (1900 + 1850 + 1760) / 3 = 1836.67
- For SS: Average cost = (1920 + 1710 + 1490) / 3 = 1706.67
- For CC: Average cost = (2250 + 1680 + 1380) / 3 = 1770
- For AA: Average cost = (2500 + 2120 + 1250) / 3 = 1956.67
Based on the equal likelihood criterion, we select region SS with the lowest average cost of 1706.67.
In conclusion:
i) Minimin criterion: TT (1520)
ii) Minimax criterion: AA (2500)
iii) Hurwicz (α = 0.7) criterion: AA (2050)
iv) Equal likelihood criterion: SS (1706.67)
These are the best decisions based on the given decision criteria.