Economic Models - Convex Optimization

Health Service Management 161
function is formulated.
min z = (10P 1 d − 1 + 9P 1d − 2 + 8P 1d − 3 + 7P 1d − 4 + 6P 1d − 5 + 5P 1d − 6
+ 4P 1 d − 7 + 3P 1d − 8 + 2P 1d − 9 + P 1d − 10 ) + (P 2d − 37 + P 2d − 38
+ P 2 d − 39 + 3P 2d − 42 + P 2d − 43 ) + P 3
31∑
i=22
di − ∑36
+ P 4
i=32
+ (P 5 d − 40 + P 5d − 41 ) + (P 6d − 21 + 2P 6d − 11 + 2P 6d − 12 + 3P 6d − 13
+ 4P 6 d − 14 + 5P 6d − 15 + 6P 6d − 16 + 7P 6d − 17 + 8P 6d − 18
+ 9P 6 d19 − + 10P 6d20 − ). (13)
d − i
4. Initial Results
With this specification of the goal programming model, I obtain the results
as given on the left side of Table 5 (solution I). It is easily verified that all
goals are achieved. Hence, this pattern dictated by the optimal solution is
readily applicable. It should be pointed out that according to this solution,
an average rate of total salary increase of about 4.9% is realized, whereas
the mean salary per worker increases from 15,232.1 to 19,372.1. In fact, this
average rate r (i.e., 4.9) has been computed from Eq. (1) in the following
way, using natural logs.
ln(x)
5
= ln(1 + r), where x = 1,026,720
807,300
and r = (y − 1) × 100, where y = e Z and Z = ln(x)
5
However, the charge per patient (∼740 ) is considered being higher,
when compared to the average of the local market, affecting thus the
competition level of the clinic.
5. Imposition of a New Constraint
Given the social character of health service, which has to be combined with
the fact that the unit under consideration must be competitive, it is necessary
to impose the following constraint.
X 43 + d44 − − d+ 44
= 700. (14)