LAPLACE APPROACH

This equation is used to solve a  two (3) state of nature LAPLACE APPROACH which simply looks for the average of the total number of states of nature. eg S1, S2 means there are two possible states hence the average is 1/2=0.5; if S1, S2 , S3 average = 1/3 but this particular equation is for three states only. After that is done sum up each row then select the maximum 

EXAMPLE

Given the Following

STEP 1:     S1       S2       S2                                  STEP 2:         S1             S2           S2                MAX

Action                                                                     Action                                                                

D1              15         9           21                                D1              (15 x1/3) + (9 x1/3) + ( 21 x1/3)  =   15

D2              30         15         12                                D2             (30 x1/3) + (15 x1/3) + ( 12 x1/3) =   19    ← best decision                                     

D3              3          45           18                               D3             (3 x1/3)  + (9 x1/3) + ( 21 x1/3)    =   11                            

D2 is the best option when using LAPLACE approach

REFERENCES

Gichuhi, K J & Ndung'u, N D (2013) Quantitative Methods for Business Management : Decision Analysis and Trees. Nairobi : Finesse.