Imagine you are the VP of Human Resources for a large health system. One of your
ID: 2415087 • Letter: I
Question
Imagine you are the VP of Human Resources for a large health system. One of your biggest responsibilities is to oversee the provision of health care benefits for the system’s employees and their families. In fact, behind employee salaries, ‘health benefits’ is the biggest line item in the system’s budget. Your CFO is worried about next year’s budget and has approached you with a need to reduce spending on health benefits – or at least cut down on the increase in spending as much as possible.
Your group is self-insured and currently uses your local BC/BS provider as a third party administrator (TPA). Your group of 10,000 employees has 20,000 covered lives (or members) and currently uses only the BC/BS PPO plan. Your current utilization profile looks like this:
Cost Cat.
Measure
units/ year
$/svc
Inpatient
Adm/1000/yr
80
$ 15,000
Outpatient
Svcs/1000/yr
4,000
$ 300
Professional
Vis/1000/yr
5,000
$ 288
Ancillary
svcs /1000/yr
500
$ 480
Pharmacy
Script/member
15
$ 48
BC/BS has given you guidance about next year’s likely trends. They expect both unit prices ($/svc) and utilization (units per year) to increase by 5% per year. They have suggested two alternate delivery models for your employees that could save you money:
Narrow-network HMO – Using your own system as the basis for a narrower network option, you could continue to offer essentially the same benefit structure as you currently do. The limited choice of providers would deliver your benefits with no rise in utilization (you would still incur the 5% rise in unit price)
High Deductible Health Plan (HDHP) – In this choice, you would continue to use the BC/BS large network, but your employees would be given a $5,000 deductible. The size of the deductible means that your employees would decrease their utilization of services by 5%.
Neither alternative is especially attractive to your employees. Therefore, you’ll need to plan to put incentives in place in the form of greater premium contribution and/or HSA funding. Unfortunately, it’s not as simple as a single dollar amount per employee. For the HMO, it will cost $30 per year to convince the first 500 employees to switch, $60 for the next 500, etc. For the HDHP, you’ll need to do better (people really don’t like high-deductible plans). For this plan, it will cost $60 for the first 500 employees to switch, $120 for the second 500, etc.
Your job – from the available facts, calculate the current year’s spending by category and in total. Then, calculate the expected spending next year assuming no changes are made to the plan. Finally, show the optimal mix of PPO, HMO and HDHP members in order to minimize total expense to the health system. Keep in mind, the incentives given to employees to choose a lower cost option should be considered a cost.
Cost Cat.
Measure
units/ year
$/svc
Inpatient
Adm/1000/yr
80
$ 15,000
Outpatient
Svcs/1000/yr
4,000
$ 300
Professional
Vis/1000/yr
5,000
$ 288
Ancillary
svcs /1000/yr
500
$ 480
Pharmacy
Script/member
15
$ 48
Explanation / Answer
a)Current year's spending:
b) next year's spending: increasing uti;lization per unit and unit price by 5%,
c) decision variables: let a,b,c be the number of employees under PPO, HMO and HDHP respectively.
constraints: a+b+c=10000
a,b,c>=0
Objective function:
Expense of PPO in next year = E1 = [(2a/1000)*(84*15750+4200*315+5250*302+525*504)]+[a*16*50]
for HMO:
Expense of HMO = H
say b/500=x,
hence cost of convincing employees to shift to HMO = x*(30+30*2+30*3+....+30*x) = x*30*(1+2+3+....+x) = 30*x*{x*(x+1)/2} = 30 * (x^2) (x+1) /2
Hence, E2= [30 * (x^2) (x+1) /2] + [(2*b/1000)*(84*15750+4000*315+5000*302+500*504)+(b*15*50)]
Expense of HDHP = E3
in HDHP utilzation decreases by 5% and unit price increases by 5% because we would continue to use the BC/BS large network.
say c/500=y
hence cost of convincing employees to shift to HDHP = 60 * (y^2) (y+1) /2 (solved like in HMO)
hence,E3= [60 * (y^2)(y+1) /2] + [(2*c/1000)*(76*15750+3800*315+4750*302+475*504)+(c*14*50)]
Objective Function is to Minimize E1+E2+E3
Cost Cat. Measure utilization unit price total utilization total price units/ year $/svc Inpatient Adm/1000/yr 80 15,000 1,600 240,00,000 Outpatient Svcs/1000/yr 4,000 300 80,000 240,00,000 Professional Vis/1000/yr 5,000 288 1,00,000 288,00,000 Ancillary svcs /1000/yr 500 480 10,000 48,00,000 Pharmacy Script/member 15 48 3,00,000 144,00,000 TOTAL 4,91,600 960,00,000 total utilization (=units/year*20,000 members/1000) for all categories except Pharmacy. total utilization for pharmacy (=units/year*20,000 members) total price (=total utilization*unit price)Related Questions
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