Problem Data Effect of Buffer Capacity on Daily Profit

Contribution Margin $($$ per day$)$ $$3,333$ $ per patient Number of PACU Beds $($K$)$

Cost of PACU Bed $($$$250)$ per bed per day $012345$ Units

Number of Rehab Beds $($c$)25$ Arrivals Average Rate Joining System $($R$)7\mathrm{.}01377\mathrm{.}27\mathrm{.}37\mathrm{.}37\mathrm{.}47\mathrm{.}5$ patients per day

Arrival Rate $($Ri$)8$ patients per day Average Rate Leaving wihout Service $1\mathrm{.}00\mathrm{.}80\mathrm{.}70\mathrm{.}70\mathrm{.}60\mathrm{.}5$ patients per day

Capacity of Each Server $($Rp$)0\mathrm{.}3333$ patients per day Probability System is Full $12\mathrm{.}3\%10\mathrm{.}6\%9\mathrm{.}2\%8\mathrm{.}1\%7\mathrm{.}2\%6\mathrm{.}5\%$

Waiting Line Avg. Number Waiting in Queue $($Ii$)-0\mathrm{.}10\mathrm{.}30\mathrm{.}50\mathrm{.}81\mathrm{.}0$ patients

Avg. Waiting Time $($Ti$)-0\mathrm{.}010\mathrm{.}040\mathrm{.}070\mathrm{.}100\mathrm{.}14$ days

Service Avg. Utilization of the Servers $($u$)84\mathrm{.}2\%85\mathrm{.}8\%87\mathrm{.}1\%88\mathrm{.}2\%89\mathrm{.}0\%89\mathrm{.}8\%$

Avg. No$.$ Customers Being Served $21\mathrm{.}021\mathrm{.}521\mathrm{.}822\mathrm{.}022\mathrm{.}322\mathrm{.}4$ patients

Total System Avg. No$.$ in System $($I$)21\mathrm{.}021\mathrm{.}622\mathrm{.}122\mathrm{.}523\mathrm{.}023\mathrm{.}5$ patients

Avg. Time in System $($T$)3\mathrm{.}003\mathrm{.}013\mathrm{.}043\mathrm{.}073\mathrm{.}103\mathrm{.}14$ days

Financials Daily Contribution Margin $$23,379$ $$23,845$ $$24,207$ $$24,498$ $$24,735$ $$24,933$

Daily Cost of PACU Beds $$0($$$250)($$$500)($$$750)($$$1,000)($$$1,250)$

Total Profit $$23,379$ $$23,595$ $$23,707$ $$23,748$ $$23,735$ $$23,683$