Economic Models - Convex Optimization

162 Anna-Maria Mouza
Thus, the total number of constrains has become 44. It should be noted
that minimizing d
44 + in the objective function, an upper limit of 700 is
set to the average charge per patient. Hence, I added in the objective as in
Eq. (13) the following term
2P 2 d
44
+
which implies that the restriction regarding the maximum average charge
per patient has been considered as a second priority goal, properly weighed.
5.1. Second-Run Results
With the new constraint, the solution obtained is presented on the right
side of Table 5 (solution II). I observe that constraint Eq. (14) is binding,
and in order to achieve the level of gross profit set by the decision
maker, the solution dictates that the total salary expenses must be reduced
by 118,180.125, which is the value of the deviational variable d21 − , shown
in Eq. (7). Evaluating the results of the second run, one may argue as to
Table 5.
Solution I (left) and solution II (right).
No. Variable name Value No. Variable name Value
The simplex solution (Number of patients = 3625)
87 ×1 10.000 89 ×1 10.000
88 ×2 1.000 90 ×2 1.000
89 ×3 3.000 91 ×3 3.000
90 ×4 14.000 92 ×4 14.000
91 ×5 3.000 93 ×5 3.000
92 ×6 1.000 94 ×6 1.000
93 ×7 3.000 95 ×7 3.000
94 ×8 4.000 96 ×8 4.000
95 ×9 4.000 97 ×9 4.000
96 ×10 10.000 98 ×10 10.000
97 ×11 356,222.000 99 ×11 356,222.000
98 ×12 33,054.000 100 ×12 33,054.000
99 ×13 68,040.000 101 ×13 68,040.000
100 ×14 199,290.000 102 ×14 199,290.000
101 ×15 74,307.000 103 ×15 74,307.000
102 ×16 36,190.000 104 ×16 36,190.000
(Continued )