Resource and Revenue Management in Nonprofit Operations

TLDR: In this article, the authors model the problem as a multi-period stochastic dynamic program, where the goal is to decide how much of the current assets should be invested in revenue-customer service capacity, and at what price the service should be sold.

Abstract: Nonprofit firms sometimes engage in for-profit activities for the purpose of generating revenue to subsidize their mission activities. The organization is then confronted with a consumption versus investment trade-off, where investment corresponds to providing capacity for revenue customers, and consumption corresponds to serving mission customers. Exemplary of this approach are the Aravind Eye Hospitals in India, where profitable paying hospitals are used to subsidize care at free hospitals. We model this problem as a multiperiod stochastic dynamic program. In each period, the organization must decide how much of the current assets should be invested in revenue-customer service capacity, and at what price the service should be sold. We provide sufficient conditions under which the optimal capacity and pricing decisions are of threshold type. Similar results are derived when the selling price is fixed, but the banking of assets from one period to the next is allowed. We compare the performance of the optimal threshold policy with heuristics that may be more appealing to managers of nonprofit organizations, and we assess the value of banking and of dynamic pricing through numerical experiments.

Figures

Figure 4: Maximum percentage expected gain from banking over all possible initial asset levels. This maximum ratio of the two value functions is plotted over a range of prices (and same demand distributions).

Figure 3: Optimal policy with banking.

Figure 5: Ratio of the value functions with dynamic price and with fixed price.

Figure 1: Capacity provided for each class of customers. Value functions for fixed-proportion policy with different ratios, and maximum over all ratios.

Figure 6: Example of non-monotonic price: value function and optimal price.

Figure 2: Capacity provided for each class of customers. Max. of value functions for fixedproportion policies, and value function for optimal policy.

Full text

de Véricourt, Francis; Lobo, Miguel Sousa
Working Paper
Resource and Revenue Management in Nonprofit
Operations
ESMT Working Paper, No. 08-006
Provided in Cooperation with:
ESMT European School of Management and Technology, Berlin
Suggested Citation: de Véricourt, Francis; Lobo, Miguel Sousa (2008) : Resource and Revenue
Management in Nonprofit Operations, ESMT Working Paper, No. 08-006, European School of
Management and Technology (ESMT), Berlin,
https://nbn-resolving.de/urn:nbn:de:101:1-201106143506
This Version is available at:
http://hdl.handle.net/10419/96558
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ES
M
T
WORKING PAPER
July 3, 2008
ESMT No. 08-006
Resource and Revenue
Management
in Nonprofit Operations
Francis de Véricourt, ESMT
Miguel Sousa Lobo, Duke University
ISSN 1866-3494

1
This work was supported in part by Fuqua’s Center for the Advancement of Social
Entrepreneurship. Gregory Dees very generously provided much help in defining and framing the
problem, and in revising the paper. Bill Meehan of McKinsey, greatly helped improve a previous
version of the paper with many suggestions and insightful comments. The authors are grateful to
Dinah Vernik for her work on the numerical examples. We also thank for useful comments Beth
Anderson, Paul Zipkin, James Smith, Gregory DeCroix, and the participants at the Operations
Management Seminars at Fuqua, UCLA, INSEAD, LBS, University of Washington BS, University of
Chicago
GSB, Yale School of Management, and Tepper School of Business at Carnegie Mellon
University.
Contact: Francis de Véricourt; ESMT, Schlossplatz 1, 10178 Berlin, Germany; Tel: +49 (0)30 212 31-
1291, Email: devericourt@esmt.org
.
Abstract
Resource and Revenue Management in Nonprofit Operations
1
Author(s): Francis de Véricourt, ESMT
Miguel Sousa Lobo, Duke University
Nonprofit firms sometimes engage in for-profit activities for the purpose of
generating revenue to subsidize their mission activities. The organization is then
confronted with a consumption vs. investment tradeoff, where investment
corresponds to providing capacity for revenue customers, and consumption
corresponds to serving mission customers. Exemplary of this approach are the
Aravind Eye Hospitals in India, where profitable paying hospitals are used to
subsidize care at free hospitals. We model this problem as a multi-period
stochastic dynamic program. In each period, the organization must decide how
much of the current assets should be invested in revenue-customer service
capacity, and at what price the service should be sold. We provide sufficient
conditions under which the optimal capacity and pricing decisions are of
threshold type. Similar results are derived when the selling price is fixed but the
banking of assets from one period to the next is allowed. We compare the
performance of the optimal threshold policy with heuristics that may be more
appealing to managers of nonprofit organizations, and assess the value of banking
and of dynamic pricing through numerical experiments.
Keywords: capacity allocation, revenue management, dynamic pricing,
nonprofit

1 Introdu ction
There are today 20 million blind eyes in India and, as life spans increase and more people reach the
age for high incidence of cataracts, 2 million new blind eyes are ad ded each year. Currently, only
1 million eyes are being operated in India each year, resulting in much unmet demand. To add ress
an even more dire situation in 1976, Dr. G. Venkataswamy built a small paying hospital, mostly
with the small initial capital of his family.
1
The paying hospital was expanded through 1977, and
a first free hospital was built in 1978. In Dr. Venkataswamy’s words, “from the revenue generated
from operations [at the ground floor of the firs t paying hospital] we built the next floor, and so
on until we had a nice five-story facility. And then with the money generated there, we built the
Free Hospital” (Rangan 1994, page 7). After much growth over 30 years, the Aravind hospitals
throughout Tamil-Nadu now perform well over one hundred thousand operations each year (Shah
and Murty 2004).
While the Aravin d story has become noted as an especially successful case, this pattern is not
unique and is becoming more common. Nonprofit organizations often engage in a mix of activities,
some of which are designed primarily to generate excess revenue to subsidize other activities that
more directly serve the organization’s charitable mission. This h as led nonprofit researchers to
address the strategic question of how to construct an optimal portfolio of activities (Gruber and
Mohr 1982; O s ter 1995). However, few have paid attention to the pr actical decisions about resource
and capacity allocation that mu s t be mad e once a given portfolio of activities has been selected.
2
In this paper, we use a modeling approach to develop insights regarding the optimal allocation of
resources between revenue-generating and mission-serving activities over time in an organization
that seeks to maximize its mission impact.
In order to isolate the tradeoffs involved in balancing revenue-generating and mission-serving
activities across many time periods , we have constructed a simplified mod el of an organization with
just two activities and two corresponding customer groups. Adapting a convention introduced by
Weisbrod (1998), we refer to R-activities as those that generate more revenue than costs. They serve
R-customers, which at Aravind are the patients at the paying hospitals. R-activities also may, but
need not, generate mission impact. While the mission impact of operating on a paying customer at
Aravind is not zero, it is significantly smaller than for free customers given that alternative for-profit
hospitals are available to paying customers. We refer to M-activities as those that generate positive
1
“I mortgaged my house and raised enough money to start”, Dr. Venkataswamy, in Rangan (1994, page 7).
2
One exception is Young ( 2004). He addresses a broad range of resource-allocation issues, within and across
activities, using a marginal contribution framework. The main differences between his analysis and ours are 1) we
capture the tradeoff between spending on mission activities now versus in the future, 2) we allow for randomness is
demand for the revenue-producing activities, and 3) our model does not assume decreasing marginal social return.
2

mission impact, but require a financial subsidy.
3
They serve M-customers, which at Aravind are the
patients at the free hospitals, who come from India’s poorest economic classes. The organization
begins with an endowment of resources and is attempting to be self-sufficient, with its R-activities
funding its M-activities (we do, however, also consider the case where the organization may receive
grants over time).
With increased competition for philanthropic and government fu nding over the past two decades,
nonprofits are under increased pressure to generate more revenue from their own R-activities, even
if they are r elatively low on mission contribution, to allow for cross subsidy within the nonprofit.
As a result of this pressure, the creation of revenue-generating ventures has become a major topic
of discussion in the nonprofit field over the past two decades. See, for instance, Skloot (1983),
Skloot (1987), Skloot (1988), Dees (1998), Young (2002), Oster, Massarsky, and Beinhacker (1995),
Foster and Bradach (2005), Weisbrod (2005). Numerous ‘how to’ guides have been produced to
help nonprofits develop profit-making ventures. See, for instance, Steckel, Simons, and Lengsfelder
(1989), Alter (2000), Boschee (2001), Anderson, Dees, and Emerson (2002), Larson and Forth
(2002), Robinson (2002), Dees (2004).
This kind of nonprofit cross-subsidy can take different forms and other examples can be cited
in addition to Aravind. The Boston Symphony Orchestra runs its ‘Boston Pops’ series using some
of the same musicians and f acilities as the regular orchestra, and relies on the revenues to subsidize
other orchestra activities that are artistically important but less lucrative (Oster 1995). This
pattern is common among performing arts organizations that schedule more popular performances
to subsidize more artistically important, but less popular ones. Consider the reliance of ballet
companies on seasonal performances of ‘T he Nutcracker’ or theatre companies that rely on popular
mus icals or plays. Sometimes social service agencies will use key resources, such as their staff,
facilities, or equipment, to deliver marketable products that subsidize more charitable operations.
For instance, CIPO Productions, a Brazilian organization, provides impoverished young people with
training in photography, video production, and Web design, and helps subsidize these activities
with revenue from selling the use of its production and computer equipment to customers who
can pay (Elstrodt, Schindler, and Waslander 2004). Brinckerhoff (2000, p. 16) describes an Illinois
school for behaviorally-challenged adolescents that has created a bus iness using its staff expertise
to deliver workshops on ‘Dealing with Difficult Teenagers’, for which it charges admission. The net
3
We are only concerned with net financial contribution. An M-activity may generate some revenue that covers
part of its operational costs. As long as t he net financial contribution of producing a unit of this go od or service
is negative, we can model it as a pure mission good with costs equal to the net negative financial contribution.
Similarly, an R-activity must produce a net positive financial contribution that can be used in future periods to
subsidize M-activities.
3

Frequently asked questions

Q1. What have the authors contributed in "Resource and revenue management in nonprofit operations" ?

In this paper, the authors focus on the tradeoff between revenue-generating and mission-serving activities in an organization that seeks to maximize its mission impact. 

Q2. What kind of organization provides impoverished young people with training in photography, video production, and?

For instance, CIPO Productions, a Brazilian organization, provides impoverished young people with training in photography, video production, and Web design, and helps subsidize these activities with revenue from selling the use of its production and computer equipment to customers who can pay (Elstrodt, Schindler, and Waslander 2004). 

Q3. What is the way to show that the optimal policy is of a threshold type?

For any continuous increasing function v(·) such that v(0) = 0, H̃v(·) is well defined and p̃(y), the maximizer of Hv(·, y), is interior (p̃(y) ∈]0, p[) since Hv(0, y) = Hv(p, y) = 0 for any y ∈ R+. Concavity of H̃vt+1(·) guaranties in turn that the social-impact-to-go function vt(·) is increasing and concave and that the optimal policy is of threshold type. 

Q4. What is the social impact of serving one R-customer?

When revenue-generating activities are also related to the mission of the organization, the authors denote by τ the social impact of serving one R-customer. 

Q5. What is the closely related to their model?

The control of dividends problem studied by Li, Shubik, and Sobel (2003), which includes inventory-replenishment decisions, seems to be the most closely related to their model. 

Q6. What is the optimal price for pt(y)?

since r(·) is non-monotone strictly concave, r(·) and hence Hvt(·, y) are increasing in p for p < p and the optimal price p̃t(y) is bounded from below by p (the maximizer of r(·)). 

Q7. What is the way to show that a distribution with an increasing failure rate is conca?

More generally, for any distribution defined over [0,+∞[ with an increasing generalized failure rate, g(θ) > 1 holds if the distribution is truncated at θ such that g(θ) > 1, and scaled accordingly. 

Q8. What would be the way to indicate a net financial yield?

Fundraising costs could be deducted from donations to indicate a net financial yield, which presumably would be positive, but with low or zero direct mission impact. 

Q9. What is the way to show that if condition (10) holds, then Hvt?

The authors will show that if condition (10) holds, then Hvt(p, y) is concave along the optimal price, which implies thatH̃vt(y) = max 0≤p≤p Hvt(p, y) (11)is concave in y. 

Q10. What are the main differences between Young's analysis and ours?

The main differences between his analysis and ours are 1) the authors capture the tradeoff between spending on mission activities now versus in the future, 2) the authors allow for randomness is demand for the revenue-producing activities, and 3) their model does not assume decreasing marginal social return. 

Q11. What is the way to determine the optimal price for a nonprofit?

Since nonprofits may be able to set their prices strategically, the authors also analyze a version of the model that allows for dynamic pricing decisions.