Enabling Healthcare Delivery Through Vehicle Maintenance Li Chen Samuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, [email protected]Sang-Hyun Kim Yale School of Management, Yale University, New Haven, CT 06520, [email protected]Hau L. Lee Graduate School of Business, Stanford University, Stanford, CA 94305, [email protected]Difficulties in healthcare delivery in developing economies arise from poor road infrastructure of rural com- munities, where the bulk of the population reside. Although motorcycles are an effective means for delivering healthcare products, governments in developing economies lack expertise in providing proper maintenance and support services, resulting in frequent vehicle breakdowns. Riders for Health, a nonprofit social enter- prise, has developed specialized capabilities that enable significant enhancements in vehicle maintenance. The organization has engaged with the governments and provided its services using different contract schemes, with different performance outcomes in vehicle availability and costs. In this paper we develop an analytical model based on reliability theory to compare the outcomes of these contracts, and relate the findings to data collected from a 2.5-year implementation by Riders for Health in Zambia. We also study how different ele- ments of operational enhancements impact vehicle availability, and identify the conditions under which their interactions give rise to compromised performance. Interestingly, we find that prevention of minor failures, i.e., failures that can be addressed through vehicle repairs, always increases vehicle availability unlike other enhancements. This unambiguous benefit suggests that such basic tasks as following proper maintenance protocols and stocking the right amount of the right service parts are of utmost importance. Key words : Public Healthcare, Developing Economies, Social Responsibility, Reliability Theory History : August 30, 2016 1. Introduction Populations in developing economies face big challenges in their living standards. Besides poor economic conditions, healthcare provisions are often grossly inefficient or simply lacking, leading to low life expectancy. Such is the case of Sub-Saharan Africa, where the average life expectancy for men and women was reported to be about 53 years, compared to 78 years in the United States (World Health Organization 2013). The fraction of the population infected by diseases such as HIV/AIDS, malaria, measles, pneumonia, tuberculosis, and dehydrating diarrhea were much higher than that of the rest of the world (Lee et al. 2013). Maternal mortality rate exceeded 500 per 100,000 live births (Hogan et al. 2010). Despite the enormous needs, health provisions have been dismal, contributed by the fact that the majority of the population reside in rural areas where logistics infrastructures are inadequate or nonexistent. 1
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Enabling Healthcare Delivery Through Vehicle Maintenance
Li ChenSamuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, [email protected]
Sang-Hyun KimYale School of Management, Yale University, New Haven, CT 06520, [email protected]
Hau L. LeeGraduate School of Business, Stanford University, Stanford, CA 94305, [email protected]
Difficulties in healthcare delivery in developing economies arise from poor road infrastructure of rural com-
munities, where the bulk of the population reside. Although motorcycles are an effective means for delivering
healthcare products, governments in developing economies lack expertise in providing proper maintenance
and support services, resulting in frequent vehicle breakdowns. Riders for Health, a nonprofit social enter-
prise, has developed specialized capabilities that enable significant enhancements in vehicle maintenance. The
organization has engaged with the governments and provided its services using different contract schemes,
with different performance outcomes in vehicle availability and costs. In this paper we develop an analytical
model based on reliability theory to compare the outcomes of these contracts, and relate the findings to data
collected from a 2.5-year implementation by Riders for Health in Zambia. We also study how different ele-
ments of operational enhancements impact vehicle availability, and identify the conditions under which their
interactions give rise to compromised performance. Interestingly, we find that prevention of minor failures,
i.e., failures that can be addressed through vehicle repairs, always increases vehicle availability unlike other
enhancements. This unambiguous benefit suggests that such basic tasks as following proper maintenance
protocols and stocking the right amount of the right service parts are of utmost importance.
Key words : Public Healthcare, Developing Economies, Social Responsibility, Reliability Theory
History : August 30, 2016
1. Introduction
Populations in developing economies face big challenges in their living standards. Besides poor
economic conditions, healthcare provisions are often grossly inefficient or simply lacking, leading
to low life expectancy. Such is the case of Sub-Saharan Africa, where the average life expectancy
for men and women was reported to be about 53 years, compared to 78 years in the United States
(World Health Organization 2013). The fraction of the population infected by diseases such as
HIV/AIDS, malaria, measles, pneumonia, tuberculosis, and dehydrating diarrhea were much higher
than that of the rest of the world (Lee et al. 2013). Maternal mortality rate exceeded 500 per
100,000 live births (Hogan et al. 2010). Despite the enormous needs, health provisions have been
dismal, contributed by the fact that the majority of the population reside in rural areas where
logistics infrastructures are inadequate or nonexistent.
1
2
The United Nations (2014) reports that 60 percent of Africans lived in rural communities, defined
to be the ones without adequate infrastructure (e.g., paved roads, electricity, piped water or sew-
ers), education, or health services. Yet, 53 percent of the roads in Africa were unpaved (African
Development Bank 2014). As a result, many communities are accessible only by single-lane sand
or dirt paths. People requiring medical care are often forced to walk or be carried in a wheelbarrow
pushed by a relative in order to get to the nearest clinic, as doctors and nurses are unable to visit
such communities on a regular basis.
Well-maintained vehicles and motorcycles have therefore become a crucial missing link in the
healthcare delivery supply chain. In fact, given the poor road infrastructure, motorcycles are often
the most effective means of transport that allow health workers to visit sick patients and deliver
healthcare products such as medicines, test samples and results, education kits, condoms, and
malaria nets. Running a cost-effective operation of a vehicle fleet consisting of well-maintained and
reliable motorcycles requires specialized expertise and management control. Unfortunately, health
ministries of developing economies do not always possess these skills. This is why a social enterprise
(SE) with such capabilities can make a difference, as it supplements the health ministries’ efforts
in this endeavor and offers improvements. However, because the goals of an SE and a government
agency are not exactly aligned, the effectiveness of such a joint effort depends on the structure of
the contract established between the two parties. This is the subject of our study.
Our work is motivated by an SE named Riders for Health (Riders), a nonprofit organization set
up to provide African health ministries with cost-effective operations of consistently reliable vehicle
fleets used for healthcare deliveries. Before Riders’ involvement, the vehicles were managed by
local governments. Vehicles suffered from high operating costs and low availability due to a variety
of inefficiencies, such as lack of training and expertise, inconsistent maintenance procedures, and
shortages of service parts. With poor maintenance, vehicles needed repairs often, or they simply
stopped working. With poor repair skills and shortages of service parts, it took excessive amount
of time to repair or replace vehicles, leading to low vehicle availability.
Riders addressed these issues in multiple ways. The backgrounds of Riders’ cofounders were
instrumental, as they were a group of professional motorcycle racers with deep knowledge of the
operating characteristics of motorcycles. They were able to transform such knowledge into mainte-
nance and repair procedures, which were then passed onto technicians. They trained health workers
to perform simple self-maintenance procedures. They also set up an elaborate hub-and-spoke ser-
vice parts management system to ensure that service parts are supplied and replenished quickly
when needed. Armed with these innovations, the organization worked with health ministries of the
Zimbabwean, Gambian, and Zambian governments and produced very positive results: increased
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vehicle availability, extended vehicle life, improved health access and interventions, and enhanced
cost effectiveness (Tayan 2007, Mehta et al. 2016).
Despite the success, Riders faced important decisions in its work that raised interesting research
questions. When Riders engaged with local governments, it employed two different contracting
approaches. An approach called Transport Resource Management, which we refer to as Repair
Only Contract (ROC) in this paper, was the basis of standard outsourcing arrangements used in
most of earlier implementations in Zimbabwe and Gambia. Under ROC, Riders is responsible for
maintenance and repair of vehicles (and other maintenance-related tasks such as worker train-
ing), while the government controls vehicle replacements and purchases. A newer approach called
Transport Asset Management, which we refer to as Repair and Replacement Contract (RRC) in
this paper, was more prominently used in a later implementation in Gambia and Zambia, and
it became Riders’ preferred choice. Under RRC, in addition to the same maintenance and repair
tasks as under ROC, Riders is also responsible for vehicle replacements and purchases. The running
costs of this added responsibility can be spread over time and be reimbursed by health ministries
in multiple payment installments. The main benefit of RRC for Riders is that vehicles can be
replaced at time intervals deemed optimal by Riders. Another benefit is that RRC allows Riders
to standardize vehicle models, enabling streamlined fleet management and reduction of complexity
in the overall supply chain. Both ROC and RRC are performance-based contracts, as Riders are
compensated based on the actual mileage used; no payment is made for the duration of vehicle
downtime. Hence, successful implementations of the two contracting approaches depend on the
level of vehicle availability that Riders can provide through its share of fleet operation.
Why does Riders prefer RRC, which actually involves added work and challenges? It is not
easy to secure necessary funding for purchasing a fleet and pay for the setup, and doing so often
requires a long-term contractual commitment from the governments, who might be reluctant to
agree to such an arrangement. For example, financing for the RRC fleet in Gambia involved a
pioneering arrangement among Riders, Africa-based GT Bank, US-based Skoll Foundation, and
the Gambian Ministry of Health. (This is in contrast to ROC, under which the government is
free to switch on and off the services provided by Riders.) This question has a general implication
to a key decision in service outsourcing, namely whether to outsource a service process with or
without control of assets. A parallel can be made to the case of Crocs, a footwear company; Crocs’
outsourced production normally relied on the assets owned by contract manufacturers, but in one
case, it elected to retain control of production assets and lease them to a contract manufacturer
(Hoyt and Silverman 2007). Although differences exist between outsourcing of manufacturing and
outsourcing of services, the issue of controlling and replacing key assets arises in both.
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In addition to contract choices, the impacts of various operational enhancements offered by Riders
warrant an in-depth examination because they are the key determinants of vehicle availability.
These enhancements include preventive measures aimed at reducing the rate of minor repairs as
well as the rate of fatal vehicle failures, and remedial measures aimed at reducing downtimes
such as: training of technicians and provision of service parts to enable quick repair turnaround;
institutional support and process improvements to shorten the lead time to acquire new vehicles.
In this paper, we explore the research questions that arose from Riders’ experience. How do the
two contracting approaches compare in improving vehicle availability and cost effectiveness? What
causes the differences in the two approaches? How does each element of operational enhancements
offered by Riders impact vehicle availability and costs? Are all these elements equally important,
or does improvement of one lessens the need for another?
To answer these questions, we formulate a model of vehicle maintenance with two decision mak-
ers: an SE and a government. It is the SE who possess the capabilities for operational enhancements
and proposes a contract to the government. The two parties have different objective functions, and
they agree to divide responsibilities for managing a fleet of vehicles used for a healthcare delivery
program. Analyzing this model, we demonstrate how ROC and RRC give rise to different perfor-
mance outcomes, and explain why an SE would prefer pushing for a RRC-like contract. We use a
2.5-year dataset from an empirical study in Zambia sponsored by the Gates Foundation (Mehta et
al. 2015 and 2016) to see if our model predictions are corroborated by the data.
Our analysis also reveals that, in general, an operational enhancement in a single dimension
does not necessarily increase vehicle availability. For example, there are conditions under which
prevention of major failures or reduction of repair lead time lowers availability. This happens
because one element of operational enhancements may interact nontrivially with another element,
sometimes compromising the effectiveness of the latter. Interestingly, prevention of minor failures
always leads to higher availability. This observation indicates that priority should be given to
preventing minor failures, involving such tasks as following proper maintenance protocols, checking
tire pressure and inspecting vehicle conditions on a regular basis, changing oil filters periodically
and using correct motor oils, and employing sound inventory control of oil filters and lug nuts. It
is these simple, mundane tasks that bring unambiguous benefits to vehicle availability.
2. Related Literature
The logistics systems of healthcare delivery in developing economies, the focus of our paper, have
been a topic of recent research from the perspectives of organizational structure, skills, capacity,
inventory, and fleet management. Bossert et al. (2007) examine the organizational structure of the
logistics system, and evaluate the effectiveness of decentralized systems in Ghana and Guatemala.
5
Matome et al. (2008) also find evidence in East Africa that having the right skill sets of the
operations management staffs can make a big difference. Deo et al. (2015) study capacity allocation
problem for infant HIV diagnosis networks in sub-Saharan Africa, the same geographical region as
considered in our paper. Inventory control to ensure availability of medicine in Zambia is the focus
of the study by Leung et al. (2016). Building on a number of cases and projects, Pedraza-Martinez
and Wassenhove (2012) identify challenges in health care delivery arising from fleet management:
aging fleets, excessive fleet sizes, low fleet standardization, and service delays.
There are several references that are more germane to our paper. Pedraza-Martinez and Wassen-
hove (2013) examine empirical field data of vehicle replacement for the International Committee
of Red Cross, and find that, due to incentive issues, the practice was quite different from the
replacement guideline of the International Committee of Red Cross. The case of Riders for Health,
which motivates our research, has been studied from different angles. These include McCoy and
Lee (2014) who focus on the equity issue of allocating vehicles to different villages, and Mehta et
al. (2016) who empirically evaluate Riders’ contribution to health worker productivity.
Our work is distinct from these papers not only in the modeling approach but also in our focus
on operational decisions that determine vehicle availability, the key enabler of Riders’ success.
The modeling approach we adopt this paper is based on the framework developed in the theory
of reliability and machine maintenance (e.g., Barlow and Proschan 1996, Nakagawa 2005). The
decisions faced by Riders are naturally captured by the standard modeling approaches found in
this literature, as vehicle repairs and replacements play central roles in Riders’ operations. Among
the numerous articles published in this area of research (see Wang 2002 for a survey), the model
developed by Beichelt (1976, 2006) is particularly relevant to our work because it generalizes
the model of Barlow and Hunter (1960) and others by including both major and minor types of
machine failures that trigger replacements and repairs, a key challenge faced by Riders. We adopt
the model of Beichelt (1976, 2006) and customize it to fit our problem setting, using it as a basis
for characterizing equilibrium of a contracting problem and performing comparative statics.
Contracting has been one of the main areas of research in operations management. Our paper
extends this tradition, but in a non-standard setting where incentives for social responsibility bring
new dynamics. The contracts we study in this paper are performance-based, i.e., payments for
outsourced services are based on realized service outcomes. Kim et al. (2007, 2010, 2016) and
Guajardo et al. (2012) investigate merits and risks of implementing such contracts, and they
discuss the “servicization” business model in which a service provider assumes asset ownership
and transforms itself as a total solution provider. This concept is similar to the RRC approach
that Riders has actively pursued in recent years. Our paper also contributes to the emerging area
of sustainability and social responsibility in supply chain management, where research has gone
6
beyond the usual cost and profit measures to include environmental and welfare impacts, thus
demonstrating that the actions and incentives of supply chain firms have far-reaching consequences.
Recent examples of this stream of research include Chen et al. (2013), Kim (2015), Chen and Lee
(2016), Cho et al. (2016), and Chen et al. (2016).
3. Model
We consider a contractual relationship between two risk-neutral entities: a nonprofit social enter-
prise (“SE,” such as Riders) and a government agency in charge of its country’s public healthcare
policies (“government,” such as the Ministry of Health in Zambia). The government funds and
operates a healthcare delivery program (“program”) aimed at distributing healthcare products and
services to the population in remote regions. The government, who used to run the program on its
own, considers running the program in collaboration with SE, who brings an expertise in vehicle
maintenance and management. A contract that defines the program’s division of responsibilities
and payment terms is set up between the two parties. For expositional convenience, we use the
pronoun “she” to refer to SE and “he” to refer to the government.
Under the program, health workers are deployed to remote regions by means of light transporta-
tion vehicles such as motorcycles (“vehicles”). A key driver of the program’s success is vehicle
uptime, as health workers cannot be deployed if vehicles are inoperative. This is especially impor-
tant because vehicles are subject to frequent breakdowns due to harsh road conditions in remote
regions. Vehicle uptime can be managed through careful maintenance planning, which SE has an
expertise on. A fleet of vehicles is owned and maintained by either the government or SE, depending
on a contractual arrangement.
Although the government and SE share a common interest in running a successful healthcare
delivery program, they differ in several aspects. First, they possess different levels of knowledge
and capabilities for maintaining vehicles, such as an understanding of industry best-practices or
an exclusive access to a service parts distribution network. We assume that SE is endowed with
superior knowledge and techniques at the time of contracting. (We operationalize this idea in
§3.2 using model parameters.) Second, whereas the government can support the program through
its fiscal budget, SE relies on external financial sources to run its part of the program. In this
paper we assume that SE’s operating costs are covered entirely by the government through a
contractual agreement. Third, the goals of the two entities are not exactly aligned. Whereas the
government weighs benefits and costs of the program in relation to those of other concurrent
healthcare initiatives that compete for a finite pool of budget, SE—for whom collaborating with
the government in this program is the only way she can accomplish her mission of improving health
access for as many lives as possible—focuses on creating the maximum vehicle uptime as long as
her operating costs are covered.
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3.1 Vehicle Repairs and Replacements
In order to highlight the main tradeoff in vehicle maintenance decisions, we focus on a simplified
setting where the size of vehicle fleet is normalized to one, i.e., at any given point in time, the
fleet consists of a single vehicle. (Note that this normalization does not mean the same vehicle
remains in the fleet indefinitely, because an existing vehicle can be replaced by a new vehicle.)
This simplification allows us to clearly define performance measures that are amenable to a game-
theoretic analysis.
At a given point in time, a vehicle in the fleet is either available for service (“up”) or unavailable
after experiencing a random failure and being disabled (“down”). The vehicle can create value only
if it is available and utilized. Reliability of the vehicle degrades over time as it ages, becoming more
prone to random breakdowns (“failures”) as it gains mileage. It is important to distinguish vehicle
age from calendar time; since the vehicle ages only when it is used, aging is suspended while it is
down. Since failures occur only when the vehicle is used, the time unit on which the failure arrival
process is based is vehicle age, not calendar time. The same assumption is commonly found in the
reliability theory literature and others, including Pedraza-Martinez and Wassenhove (2013).
A vehicle experiences two types of failures: minor failure and major failure. A minor failure
disables the vehicle temporarily but is non-fatal, as the vehicle can be eventually fixed and restored
to service (e.g., a flat tire that can be replaced by a spare tire). On the other hand, a major failure
is fatal and it disables the vehicle permanently (e.g., failure of an engine that cannot be swapped).
We assume that the rates at which these two types of failures occur are independent and increase
with age. Specifically, we assume that the failure rates take the form of ph (t) for major failures
and qh (t) for minor failures. The common age-dependent function of the failure rates, h (t), is an
increasing function that starts from h(0) = 0 and diverges to h(∞) =∞. Let H (t) ≡∫ t0h (y)dy.
The parameters p≥ 0 and q≥ 0 are scaling factors for h (t) that determine the total rate of failures
as well as relative prevalence of the two failure types.
Once a failure occurs, it is addressed by either a repair or a replacement. A repair is performed
on a vehicle disabled by a minor failure, and it restores the vehicle back to working condition. If,
on the other hand, a repair cannot be done because the vehicle suffers a major failure, the disabled
vehicle is scrapped and replaced by a new unit. To be precise, a vehicle replacement triggered by a
major failure (vehicle’s “premature death”) is categorized as an unscheduled replacement because
such a replacement cannot be planned in advance due to the random nature of failure events.
By contrast, a scheduled replacement refers to a planned replacement of a vehicle that reaches
its end-of-life (vehicle’s “retirement”). Whereas repairs and unscheduled replacements are reactive
responses triggered by unpredictable random events (minor failures and major failures), scheduled
replacements are preventive in nature.
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A repair and a replacement have different impacts on the age of a vehicle in the fleet. Whereas
completion of a replacement resets the age of a vehicle in the fleet to zero as a new vehicle is
brought in, completion of a repair does not change the age; the age at repair completion remains
the same as that at the repair start because the vehicle does not gain mileage during repairs. (In
the reliability theory literature such repairs are called minimal repairs; see Nakagawa 2005.) We
assume that a fixed cost k is incurred each time a repair is performed, while a fixed cost K is
incurred whenever a vehicle is replaced, regardless of whether it is unscheduled or scheduled. With
the latter assumption, we implicitly assume that the majority of what constitutes K is the cost of
acquiring a new vehicle, with other overhead costs ignored.
A scheduled replacement is done whenever the age of a vehicle currently in the fleet reaches τ
time units, provided that no major failure has occurred by then. We refer to τ as vehicle retirement
age. (Recall that the age τ does not include vehicle downtimes due to repairs.) If a major failure
occurs before τ is reached, then an unscheduled replacement is triggered and the vehicle age is
reset to zero. We assume that a scheduled replacement is completed instantaneously because τ
is known in advance and therefore a replacement vehicle can be procured early. By contrast, it
takes positive lead times to complete a repair and an unscheduled replacement because they are
prompted by unpredictable failures. A repair lead time depends on such factors as labor capacity
or service parts inventory. A replacement lead time depends on accessibility to a vehicle provider,
complexity of customs clearance process if the vehicle is to be imported, and vehicle registration
and documentation, etc. A vehicle is down during these lead times. We use the notations l and L
to denote expected lead times for a repair and for an unscheduled replacement, respectively.
The retirement age τ is the decision variable that we focus on in this paper (the same focus is
commonly found in the reliability theory literature). It is the most impactful managerial decision
in practice, and its choice reflects the tradeoffs among key performance outcomes including vehicle
availability, repair cost, and replacement cost. All other variables are assumed to be exogenously
given. Among them, the variables that directly impact vehicle availability—l, L, q, and p—play
important roles in our analysis, as we discuss next.
3.2 Operational Enhancements
SE contributes to the program by bringing an expertise in fleet operations, which we call operational
enhancements. We consider four ways in which an enhancement can be made, divided into two
groups: (a) prevention and remediation of minor failures, and (b) prevention and remediation of
major failures. With the first group of enhancements, SE brings parameter values l and q—repair
lead time and the rate of minor failures—that are smaller than what the government is endowed
with, denoted by l0 and q0. In other words, SE’s involvement in the program will mitigate the impact
9
of minor failures by shortening the time it takes to restore a vehicle (remediation) and reducing the
frequency of minor failures (prevention). Similarly, for the second group of enhancements SE brings
parameter values L and p—unscheduled replacement lead time and the rate of major failures—that
are smaller than the government’s endowments L0 and p0, mitigating the impact of major failures.
SE will bring a combination of these enhancements when she participates in the program. As such,
it is of managerial interest to find out which combination works better than others.
3.3 Performance Measures
All performance measures are defined in long-run time averages, evaluated by applying the renewal-
reward theorem. Recall that the age of a vehicle in the fleet is reset to zero whenever a replacement
is complete; this event marks the start of a renewal cycle. Because a replacement is done on
either a scheduled or an unscheduled basis, the length of a renewal cycle depends on both the
vehicle retirement age τ and the probability that a major failure occurs before τ . The expected
cycle length consists of three components: 1) expected vehicle age at the time of replacement; 2)
expected cumulative repair downtimes until replacement; 3) expected downtime after an unsched-
uled replacement. To evaluate these components, let Y be the random variable of vehicle age at
the time of first major failure conditional on no vehicle retirement (τ =∞). Let F (t)≡Pr(Y < t)
and define F (t) ≡ 1− F (t) and M (τ) ≡∫ τ0F (t)dt. Because major failures occur at rate ph (t)
(see §3.1), the following relationships hold: F′(t)/F (t) =−ph (t) and F (t) = exp(−pH (t)) where
H (t) =∫ t0h (y)dy. The mean of Y is denoted by µ≡E [Y ] =M (∞). In addition, define
S (t)≡ h (t)M (t)− (1/p)F (t) , (1)
which appears frequently in our analysis (its properties are presented in Lemma A1 found in the
Online Appendix). Note that F (t), M (t), and S (t) all depend on the failure rate scaling factor p,
unlike h (t) and H (t).
With finite retirement age τ <∞, a vehicle is replaced at age min{Y, τ}. Hence, the expected
replacement age is equal to E [min{Y, τ}] = M (τ), which also represents the expected vehicle
uptime in a single cycle. This is the first component of the expected cycle length. The second
component, expected cumulative repair downtimes until replacement, is equal to l×N (τ) where l is
the expected repair lead time and N (τ) is the expected number of minor failures until replacement
at vehicle age min{Y, τ}. The latter is evaluated as N (τ) =∫ τ0qh (t)Pr (Y > t)dt= (q/p)F (τ) (see
Beichelt 2006, pp. 138-140). Finally the last component, expected downtime after an unscheduled
replacement, is equal to L×Pr(Y < τ) = LF (τ) where L is the expected replacement lead time.
Adding up the three components yields the expected cycle length
T (τ)≡M (τ) + (L+ lq/p)F (τ) . (2)
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Three performance measures are used in our analysis: 1) long-run average vehicle availability,
denoted by A (τ); 2) long-run average vehicle repair cost, denoted by C (τ); 3) long-run average
vehicle replacement cost due to both scheduled and unscheduled replacements, denoted by R(τ).
Vehicle availability A (τ) measures the fraction of time that the fleet has an operating vehicle, and
as such, it is proportional to M (τ), the expected vehicle uptime in a cycle. Repair cost C (τ) is
equal to fixed cost k times the expected number of repairs in a cycle, N (τ). Replacement cost R (τ)
is equal to fixed cost K times the number of replacements in a cycle, which is exactly one because
each renewal cycle ends with a replacement. Using the expression of N (τ) evaluated above, we
apply the renewal-reward theorem to obtain
A (τ) =M (τ)/T (τ) , C (τ) = (kq/p)F (τ)/T (τ) , R (τ) =K/T (τ) . (3)
The government and SE make decisions based on the performance measures in (3). As we noted
above, the goals of the government and SE are not exactly aligned. Whereas the government
makes a decision to balance the benefits and costs of the program, SE tries to maximize vehicle
availability to the fullest extent. We capture this difference by assuming that the two parties have
heterogeneous valuations for vehicle availability; the government assigns a finite valuation v <∞
to each unit of vehicle uptime, whereas SE effectively assigns an infinite valuation to uptime. The
government’s valuation v reflects the opportunity cost of fund spent on ensuring vehicle availability
(e.g., the same fund could be used to support other competing social welfare programs). We assume
throughout the paper that v is common knowledge.
3.4 Contracting
For expositional convenience, we assume that the government already has the program running,
performing all fleet management tasks by himself including vehicle repairs and replacements. We
refer to this “do-it-alone” approach by the government as his default option. In general, the gov-
ernment will be better off by switching from the default option to using the service offered by SE,
because SE’s involvement brings efficiency gain that can be shared through operational enhance-
ments. At time zero, SE proposes a take-it-or-leave-it contract to the government. The contract
specifies the division of tasks and payment terms, and the government accepts the contract if it
is preferable to maintaining the default option. We assume that the government is the only entity
capable of financing the program, and therefore payments are transferred from the government to
SE. Although the government has a financial advantage, it is SE who can provide solutions that
improve the program. Hence, we assume that a contract proposal is made by SE who offers the
terms that the government finds acceptable.
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We consider two contracting scenarios that differ by contracting parties’ responsibilities. They
are summarized as follows, with the default option added to the list in order to highlight the
differences.
0. Default Option: The government owns the fleet and replaces vehicles by determining τ . The
government also performs vehicle repairs.
1. Repair Only Contract (ROC): The government owns the fleet and replaces vehicles by
determining τ . Vehicle repairs are outsourced to SE. The government compensates SE based on
realized vehicle uptime.
2. Repair and Replacement Contract (RRC): Fleet ownership is transferred to SE. SE
replaces vehicles by determining τ and performs vehicle repairs. The government compensates SE
based on realized vehicle uptime.
As we noted in §1, ROC and RRC capture the essence of Transport Resource Management
and Transport Asset Management contracts employed by Riders. Under ROC, SE is responsible
for vehicle maintenance including repairs, but not vehicle replacements. Under RRC, by contrast,
SE is responsible for entire fleet operations including vehicle repairs and replacements. The lat-
ter arrangement requires a transfer of fleet ownership, because only the rightful owner of assets
can make decisions on replacing them periodically and incur associated costs; decisions on asset
acquisitions cannot be outsourced without ceding control of them. Comparing the two contractual
arrangements through the lens of contract theory, we expect RRC to create higher efficiency than
ROC does because SE becomes the residual claimant under RRC; by internalizing both repair
costs and replacement costs, SE will make decisions that bring a net efficiency improvement to
the overall system. Despite the expected advantage of RRC, ROC has been more widely used by
Riders, especially in the earlier implementations in Zimbabwe and Gambia (Tayan 2007).
Under both ROC and RRC, SE is compensated based on realized vehicle uptime. (In practice, the
compensation can also be based on actual usage of the vehicle. Because usage and uptime are often
directly correlated, for simplicity, we assume that the compensation is based on uptime.) Therefore,
all contracts are performance-based: SE’s compensation depends on realized performance outcome
rather than the amount of resources consumed. Such performance-based contracts are gaining
popularity in a number of industries for managing outsourced maintenance operations (Kim et al.
2007, 2010, 2016, Guajardo et al. 2012, Jain et al. 2013), and Riders has adopted the same practice.
To be consistent with observed contracts, we only consider a linear contract that stipulates the
government to transfer a constant dollar amount r for each unit of realized vehicle uptime.
SE’s goal is maximizing vehicle availability. She sets the terms of ROC and RRC such that
they achieve this goal while satisfying a few conditions that ensure a successful implementation
of the contract. The conditions are the following. First, SE receives sufficient funding from the
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government to cover the cost of running her share of fleet operations, be it repairs only (under
ROC) or repairs and replacements together (under RRC). We call this SE’s surplus constraint.
Second, the government will not incur costs beyond what he is already spending under the default
option. This is called the government’s budget constraint. Third, the level of vehicle availability
attained under the contract exceeds the level that can be achieved by the government employing
the default option. This is called availability constraint. SE designs a contract that meets all of these
criteria by adjusting her offer of compensation rate r, augmenting it with her optimal choice of
vehicle retirement age τ under RRC. In summary, SE solves the following constrained optimization
problem under both ROC and RRC:
max A s.t. Π≥ψ and B ≤ b0 and A≥ a0. (4)
The three constraints in (4) are SE’s surplus constraint, government’s budget constraint, and
availability constraint, in the stated order. Here, Π denotes SE’s expected surplus and B denotes
the government’s expected total costs incurred under the proposed contract. The exact forms of
Π and B depend on whether ROC or RRC is employed, and we specify them later when the
contracts are analyzed. The constant ψ appearing in SE’s surplus constraint Π≥ψ represents the
cost of maintaining her levels of operational enhancements. We assume that ψ is sufficiently small
such that it does not exceed b0, the government’s total cost in the default option. Because social
enterprises such as Riders operate on a nonprofit basis, in reality this constraint should be binding:
Π = ψ. We assume inequality Π ≥ ψ instead, and examine later if the binding constraint—SE’s
break-even condition—emerges as an equilibrium outcome.
The right hand-side of the government’s budget constraint, b0, which we call baseline budget, rep-
resents the total cost that the government incurs if he employs the default option. By imposing the
budget constraint, we assume that the government is unwilling to increase spending beyond what
he already incurs under the default option, a common constraint faced by government agencies.
While the budget constraint is demanded by the government, the availability constraint A≥ a0 is
required by SE. Because SE hopes to improve vehicle availability by running the program jointly
with the government, a contract should not be offered if it does not raise vehicle availability above
baseline availability a0, the level already achieved by the government under the default option. Note
that the availability constraint together with the budget constraint ensure that the government is
better off contracting with SE; the government finds that his spending will not increase (B ≤ b0)
and availability will go up (A≥ a0), leading him accept the offer and earn higher expected utility
than under the default option (vA−B ≥ va0− b0).
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4. Equilibrium Analysis
In this section we characterize the equilibria under ROC and RRC and discuss their properties. We
first study the government’s optimal decision in the default option, which establishes the baseline
budget b0 and the baseline availability a0 that SE takes into account when she designs a contract.
This is followed by specification of equilibria under ROC and RRC. Comparison of the equilibria
is presented at the end of the section.
4.1 Default Option: Repairs and Replacements by Government
We first consider the government’s default option. The government is endowed with failure rates
q0h (t) and p0h (t) for minor and major failures, and it is expected that each repair will take l0 time
units and each unscheduled replacement will take L0 time units. For clarity, we use the subscript
“0” to denote the functions defined in §3 that are evaluated at these parameter values. For example,
S0 (t) denotes the function S (t) defined in (1) evaluated at p= p0, and similarly we write A0 (τ),
C0 (τ), and R0 (τ) for the performance measures in (3) with l= l0, L=L0, q= q0, and p= p0.
Recall that the government assigns the value v to each unit of vehicle uptime. Hence, his long-run
average value of social benefits is equal to vA0 (τ). In addition, the government incurs the repair
cost C0 (τ) and replacement cost R0 (τ) because he performs both repairs and replacements under
the default option. As a result, the government’s expected utility is
U0 (τ)≡ vA0 (τ)−C0 (τ)−R0 (τ) . (5)
The government optimally chooses the vehicle retirement age τ to maximize this function, which
we denote as τ ∗0 .
To see how the optimal decision is made, it is instructive to examine the tradeoff contained in
the utility function U0 (τ). The following intuitive results can be shown: A′0 (τ)< 0, C ′0 (τ)> 0, and
R′0 (τ)< 0 (see Lemma A2 found in the Online Appendix). That is, delaying vehicle retirements
(larger τ) results in lower availability, higher repair cost, and lower replacement cost; availability
goes down and repair cost goes up because a vehicle experiences more failures as it waits longer
before being retired, and replacement cost goes down as replacements are scheduled less frequently.
Thus, a government that considers delaying vehicle replacements trades off lower value of social
benefits and higher repair cost against the savings in replacement cost. These opposing forces are
balanced at the optimal value τ = τ ∗0 , which is specified as follows.
Proposition 1 (Optimum under default option) The government’s expected utility U0 (τ) in
(5) has a unique positive maximum at τ = τ ∗0 > 0 if
Proposition 4 reveals how SE takes advantage of her ability to eliminate agency cost under RRC:
she invests it in vehicle replacements, shortening vehicle retirement age (τ † ≥ τ ‡) and bringing new
vehicles to the fleet more often than what the government might have done under ROC. As a result,
replacement cost is higher under RRC (R(τ †) ≤ R(τ ‡)) but vehicle breakdowns occur less often
than under ROC, lowering repair cost (C(τ †)≥C(τ ‡)) and increasing availability (A(τ †)≤A(τ ‡)).
A caveat is that total cost of the entire system—sum of repair cost and replacement cost—is higher
under RRC: C(τ †) +R(τ †)≤C(τ ‡) +R(τ ‡).
We now relate these results to empirical observations made by Mehta et al. (2015), who report
findings from their 2.5-year field study of Riders’ operations in Zambia. They collected data on
fleet operations under the government default, ROC, and RRC. The study was based on a ran-
domized field experiment in which test regions had vehicles managed by Riders as well as some
by the government, and control regions with vehicles managed by the government. There were 70
motorcycles tracked under RRC, and 3 under ROC. Table 1 summarizes the key observations. Note
that the unit of measure reported in Table 1—commonly used by governments—is CPK (Cost Per
Kilometer). This measure directly captures cost efficiency, but it captures vehicle availability as
well. The linkage is that, all else being equal, a shortened distance travelled by a vehicle due to
low availability increases CPK.
From Table 1, we see that total CPK for maintenance/repair, insurance, and depreciation under
ROC was $0.107, whereas the corresponding CPK under RRC was $0.145. Moreover, the depreci-
ation part under ROC was $0.015 whereas that under RRC was $0.055. We do not have detailed
data on the availability levels of ROC versus RRC, but assuming that they do not differ signifi-
cantly, a higher CPK would imply a higher average cost under the cost measure used in our model.
Hence, higher total CPK and higher depreciation CPK under RRC over ROC noted above indi-
cate C(τ †) +R(τ †)≤ C(τ ‡) +R(τ ‡) and R(τ †)≤R(τ ‡), respectively, as predicted by Proposition
4. Given the small sample size of the vehicles under ROC, we cannot attach concrete statistical
significance to these results. But directionally, they corroborate our analytical findings.
In addition to the comparison between ROC and RRC, we also see from Table 1 that total
CPK was higher under the government default than under ROC and RRC ($0.451 vs. $0.201 and
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$0.295). What contributes to this difference is that the level of vehicle availability was much lower
under the government default (as we shall see later from the numbers reported in Table 2 for RRC),
which shortened the distance travelled by vehicles.
The findings in Proposition 4 indicate that RRC equips SE with better ability to further her
goal of maximizing vehicle availability, by allowing SE to serve as a “total solution provider” who
manages entire aspects of fleet operations. This explains why RRC has become Riders’ preferred
choice. Despite the advantage, practical hurdles make it difficult to implement RRC because it
requires a significant upfront capital investment to allow SE’s vehicle ownership and purchases. For
example, Riders’ RRC implementation in Gambia was made possible by loan guarantees from the
Africa-based GT Bank and the US-based Skoll Foundation (Lee et al. 2013). Similar arrangements
were required in other countries, such as financial support from the Gates Foundation for RRC
implementation in Zambia (Mehta et al. 2015).
5. Impact of Operational Enhancements
Thus far we have focused on the properties of equilibria, with fixed levels of SE’s operational
enhancements. These enhancements are captured by model parameters l, L, q, and p; these rep-
resent enhancements because their values are smaller than l0, L0, q0, and p0 that the government
possesses under the default option. In this section, we investigate how these enhancements impact
the optimal choice of vehicle retirement age τ and vehicle availability.
Table 2 summarizes performance outcomes of Riders’ operations in Zambia reported by Mehta
et al. (2016). As the table shows, 19% of the motorcycles managed by the government died over the
study period. By contrast, motorcycles managed by Riders under RRC had 0% major failures over
the same period. This corresponds to p < p0. Riders also invested in training healthcare workers
to self-check the vehicles and follow standard protocols, such as ensuring that the filters are clean
and tires have adequate pressure. These efforts correspond to q < q0. In addition, Riders built a
hub-and-spoke system for service parts inventory management to improve responsiveness to repair
requests. This corresponds to l < l0. Finally, Riders standardized vehicle models in the fleet, pre-
arranged vehicle purchases with financial institutions, and streamlined the documentation and
vehicle preparation processes, so that vehicle replacements can be done quickly when a need arises.
This corresponds to L<L0.
As expected from these enhancements, Table 2 shows that vehicle availability increased under
Riders’ management, going up from 1.3 days per week under the government’s management to 5.5
days per week. We can also see from the table that the benefits of increased vehicle availability
resulted in higher productivity of health workers, measured in terms of number of outreach trips,
patient visits, immunizations, child growth monitoring, and health education sessions. (Note that
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Table 2 Performance Comparisons (Source: Mehta et al. 2016)
Riders RRC, Government Default,Test Regions Control Regions
Number of motorcycles 70 47Uptime days per week 5.5 1.3% of Vehicles died at end of study period 0% 19%No. of outreach trips per week 1.0 0.1No. of patient visits per week 34.3 8.6No. of immunizations per week 10.3 0.08No. of child growth monitoring per week 13.7 10.3No. of health education sessions per week 23.0 2.4
the importance attached to the numbers on these healthcare interventions can be viewed as a
reflection of v, the value placed by the government on vehicle availability.)
Building on the equilibrium analysis of the last section, we now study how these enhancements
influence the optimal choice of τ which in turn determine availability and costs. In particular, we
perform comparative statics and study the isolated impact of varying each of the four parameters.
This analysis allows us to answer questions such as: How does reducing repair lead time l change
vehicle availability? Does eliminating major failures (reduce p to zero) lead to higher availability?
Is there a particular combination of enhancements that is preferred to others?
We define “enhancement variables” that represent the magnitudes of enhancements as el ≡ l0− l,
eL ≡L0−L, eq ≡ q0−q, and ep ≡ p0−p and use them as a basis of our discussions. For example, ep =
0 means no enhancement is made in reducing major failures, while ep = p0 means that maximum
enhancement is made, since major failures are eliminated at that value (p= 0). To improve clarity,
we group these four variables in two categories and investigate each category separately. The
variables el and eq are grouped together as enhancements in prevention and remediation of minor
failures (discussed in §5.1); greater eq prevents occurrences of minor failures, and larger el remedies
the aftereffect of a minor failure, i.e., larger el shortens downtime while a vehicle is undergoing a
repair. Similarly, eL and ep are grouped together as enhancements in prevention and remediation
of major failures (discussed in §5.2).
As we observed in the last section, RRC represents an improvement over ROC because of the
former’s ability to eliminate efficiency loss. In fact, it can be shown using the results of Propositions
2 and 3 that a feasible ROC does not exist in a wider range of parameter combinations compared
to RRC. Reflecting this advantage of RRC and a trend towards more RRC adoption in practice
(e.g., Riders’ case), in the remainder of this section we focus exclusively on RRC. Additionally, for
expositional ease, henceforth we normalize the parameter ψ to zero.
5.1 Prevention and Remediation of Minor Failures
We first study the impact of prevention and remediation of minor failures, captured by the vari-
ables eq and el. Increasing these variables have both direct and indirect impacts on performance
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outcomes. Direct impact refers to exogenous effects on performance measures A (τ), C (τ), and
R (τ) when τ is fixed; for example, all else being equal, we expect that availability will increase
as failures occur less often (larger eq) or repairs are completed more quickly (larger el). On the
other hand, indirect impact refers to the endogenous effects on performance measures due to an
adjustment in the optimal choice of τ . It is the net of these two impacts that determines the system
behavior. We examine the direct impact first.
Lemma 2 For given τ , the performance measures defined in (3) change in el and eq as follows.