The optimal solution was provided by the GSPP model using CPLEX 11 .
In Table 3, column one represents the name of the instance, while columns two and three are the optimal solutions and the computational time required by the GSPP, respectively.
Columns three and four show the optimal solutions and the computational time using the GSPP. Furthermore, columns five to seven display the best solutions obtained by [T.sup.2][S.sup.*] in 30 trials, the required time, and the gaps relative to the optimal solutions for [T.sup.2][S.sup.*], respectively.
Tables 3-6 show the time required for GSPP, PTA/LP, CS, [T.sup.2][S.sup.*], [T.sup.2][S.sup.*] + PR, [SA.sub.RS], and IG.
is located in the Rittenhouse Square area of downtown Philadelphia..
provides specialized inpatient long-term acute care, and medical and physical rehabilitation for patients transferred from medical, surgical, and intensive care at the University of Penn Health System's three hospitals.
So, [[delta].sub.1] is a RGSPP while [[delta].sub.2] is a LGSPP and [[delta].sub.3] is a GSPP. Geometrically, [[delta].sub.1] is a rotation through an angle of [pi] while [[delta].sub.2] and [[delta].sub.3] are reflections in the axes of symmetry parallel to the sides.
So, I and [delta] are both RGSPPs and LGSPPs which implies I and [delta] are GSPPs i.e I, [delta] [member of] GSP[P.sub.[rho]]([S.sub.2]) and I, [delta] [member of] GSP[P.sub.[rho]]([S.sub.2]) [??] I, [delta] [member of] GSPP([S.sub.2]).
Following Example 3.1, there are 2 RGSPPs, 2 LGSPPs and 2 GSPPs in [S.sub.2] while from Lemma 3.1, there are 4 RGSPPs, 4 LGSPPs and 2 GSPPs in [S.sub.3].
The historically strong operating profitability reflects effective expense management practices and the benefits derived from the GSPP partnership.
Management anticipated that profitability would be challenged by increased competition from Lehigh Valley Health Network, which opened a 34-bed inpatient rehabilitation unit in July 2015 and by decreased rates resulting from the renegotiation of a significant GSPP commercial payor contract.