Fleet Management Coordination in Decentralized Humanitarian Operations Alfonso J. Pedraza-Martinez Kelley School of Business, Indiana University {[email protected]}

Sameer Hasija INSEAD, 1 Ayer Rajah Avenue, Singapore, 138676 {[email protected]}

Luk N. Van Wassenhove INSEAD, 77305 Fontainebleau Cedex, France {[email protected]}

We study incentive alignment for the coordination of operations in humanitarian settings. Our research focuses on transportation, the second-largest overhead cost (after personnel) for humanitarian organizations. Motivated by field research, we study the fleet size problem from a managerial perspective. In terms of transportation, our setup features a service-level-focused humanitarian program implemented by an international humanitarian organization with private information that affects the balance between service level and efficiency intended by the organization’s headquarter. The incentive alignment issue is complex because traditional instruments based on financial rewards and penalties are not considered to be viable options. This problem is further complicated by information asymmetry in the system due to the dispersed geographical locations of the parties. We design a novel mechanism based on an operational lever to coordinate incentives in this setting. Our study contributes to two streams of literature, humanitarian logistics, and incentives in operations management. Key words : Humanitarian Operations, Incentives, Logistics and Fleet Management

1.

Introduction

The need for humanitarian action has increased dramatically in the last few decades and is expected to rise significantly in the years to come (Thomas and Kopczak 2005). International organizations carrying out humanitarian action face serious challenges delivering the right goods and services to the right people at the right time and at the right cost (Van Wassenhove 2006). Relief and development programs—which include agriculture and nutrition assistance as well as basic health care provision—are the primary channels of humanitarian aid delivery carried out by international humanitarian organizations (IHOs). Every year IHOs spend more than $1.5 billion running an international fleet of nearly 80,000 four-wheel-drive (4WD) vehicles to support the delivery of humanitarian programs. Motivated by extensive field research, we study coordination issues in a two-party decentralized 4WD fleet management system supporting IHO’s programs. 1

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Our research builds on a larger field project to understand field vehicle fleet management in IHOs. The project includes three large IHOs using global procurement managed at the headquarter level: the International Committee of the Red Cross (ICRC), the International Federation of Red Cross and Red Crescent Societies (IFRC), and the World Food Programme (WFP). Staff interviews with various IHOs were conducted at their headquarters in Europe and the Middle East as well as at national and field program levels in the Middle East and Africa (see Pedraza-Martinez et al 2011 for more details on the extensive field work). In the rest of this section we briefly describe the research problem and use our findings from the field research to motivate the theoretical model studied in this paper. The fleet management system has two decision-making parties: the Program and the Headquarter. A Program is a set of related activities and resources with an aim defined by the IHO. Typically Program objectives include to service a determined population in a geographic region within a given timeframe that is determined by the funding received from donors, hence Programs strive to balance responsiveness and cost. Often located in remote areas of developing countries (the field), Programs provide assistance and help alleviate the suffering of people in the aftermath of disasters (relief). In addition, Programs implement activities to improve the quality of life of poor communities (development). Program objectives often results in transportation requirements to visit its beneficiaries. Notice that Program demand results in transportation needs instead of a given vehicle fleet defining the scope of Programs. Transportation requirements for relief and development are different. Relief Programs assign vehicles according to emergency priorities for disaster assessment or to coordinate the operations of search, rescue, and emergency aid distribution. In contrast, development Programs use vehicles for regular visits to villages or refugee camps for health care or to coordinate aid distribution. There is less urgency in development than in relief Programs and vehicles in the former are typically assigned to visits in order of requisition. We focus on fleet management in development Programs that have fleets of at least 20 vehicles in the same geographic location. Development Programs are henceforth referred to simply as Programs. As mentioned earlier, some examples of Programs include nutrition assistance and basic health care. In terms of transportation, a Program aims to have a vehicle available when needed by its staff to visit beneficiaries. Although speed in demand fulfillment is not necessarily critical, Programs must meet demand within a reasonable time frame. Given the long-term nature of Programs, visits that cannot be performed on time are accumulated. The Program incurs two main costs, the cost of delay and the cost of managing

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their fleets in the field. Delay refers to the dispatching queuing deferment of a visit. The cost of delay is a disutility associated with the lateness of program delivery. Program managers are usually more sensitive to delay costs. The larger the fleet, the lower the cost of delay. During the planning stage, the Program informs the Headquarter about its transportation needs. One of the functions of the Headquarter is to procure the fleet requested by the Program. The Headquarter, which is typically located in the United States or Europe, must balance the fleet’s cost of delay with its operating costs (the fleet management cost plus the running cost). During the planning stage, the Headquarter determines the optimal fleet size that will minimize the system’s cost. The fleet size includes a fleet “buffer” to guarantee that a reasonable proportion of visits will not suffer any delay. This buffer determines the average proportion of visits performed on time, i.e. the service level of the fleet: the larger the fleet buffer, the lower the cost of delay but the higher the operating cost. Similar to for-profit supply chains, IHOs also face agency issues that may lead to inefficiency due to their decentralized organization. In the following we briefly describe our observations from the field that highlight the agency issues that IHOs face in managing their fleet for development programs. O1: Transportation needs of the Program are stochastic and private information. Observation O1 creates asymmetric information between the Headquarter and the Program. The Headquarter may have some prior information about the Program’s transportation needs. However, due to the geographically dispersed nature of field operations and the stochasticity in the system the Headquarter cannot accurately infer the true transportation requirements of the Program without incurring significant monitoring costs. O2: The Program is provided with a dedicated fleet to run its operations and its objective is to minimize its disutility from delay in the system and the cost of managing the fleet in the field. O3: The objective of the Headquarter is to minimize the overall cost of the system, which includes the disutility of the delay in the system and the total operating cost (management and running costs) of the fleet. Observations O2 and O3 imply that the objectives of the Program and the Headquarter are only partially aligned as the Program is not concerned with the running cost of the fleet (more details on what the fleet management and running costs comprise of are provided in Section 3). Together observations O1, O2, and O3 create the agency issue of adverse selection, whereby the Program may have incentives to distort its

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stated transportation needs. In particular, because operating costs increase with the fleet size, the optimal fleet size for the Headquarter is smaller than the optimal size from the Program’s perspective. Therefore, the Program may have incentives to misreport its true needs in order to acquire a larger fleet. While such a behavior may be beneficial for the Program it distorts the service level-efficiency balance of the overall system. The agency issue in decentralized humanitarian organizations discussed above is illustrated by quotes from our interviews. For example one of the Headquarter staff remarked that I feel some of our programs have more vehicles than required. In fact, one of the senior fleet managers we interviewed in Geneva estimates that their programs have between 10% and 15% more vehicles than required. In contrast, when we asked about the fulfillment of his transportation needs, a development program manager in the Zambezia province of northern Mozambique said: Often we have to wait too long to have a vehicle available to go to the field. These comments refer to the system’s steady-state behavior, not to the occasional (and expected) mismatches between stochastic demand and stochastic supply. In fact, the fleet management system responds to stochastic demand by using the fleet buffer that should also balance the service level and the operating cost of the fleet. A simple way to fix such a distortion would be to transfer the accountability of the full operating cost of the fleet to the Program, however owing to the particular characteristic of humanitarian operations that stems from earmarked funding, it is not possible to do so. Moreover, standard mechanisms based on financial incentives are not considered viable in the humanitarian setting. This is primarily due to the organizational culture of IHOs, whose employees are driven by their motivation to serve and not by objectives as profit maximization (Lindenberg 2001, Mannell 2010). For instance, it is almost inconceivable that an IHO would incentivize volunteer medical doctors working in the field by using financial penalties and rewards. It is important at this point to note that most research in humanitarian operations assumes centralized decision making and no earmarking of funds. Our work is anchored in field research and we describe the actual constraints under which IHO have to operate. To sum: asymmetric information and misaligned incentives may lead to distortion of stated transportation needs by the Program. The inability of the Headquarter to (i) infer the true needs of the Program (due to stochasticity in the system and high monitoring costs), (ii) transfer the accountability of the full operating cost of the fleet to the Program (due to earmarking constraints), and (iii) use conventional financial mechanisms to align incentives poses a serious challenge to IHOs to overcome such a potential distortion.

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In this paper we develop a novel model that combines heavy traffic queuing theory and mechanism design to provide guidelines for IHOs on how to align incentives of the Program with the overall objective of the organization. In absence of the above mentioned mechanisms, this paper shows how the Headquarter can offer a fleet buffer “menu” contingent on the stated transportation needs to induce truthful revelation by the Program. In some instances our model is able to reduce the fleet excess by more than 10%, matching the intuition of senior fleet managers. We provide insights on the potential use of the mechanism in real humanitarian operations depending on type of activities conducted by Programs and the operating conditions of the fleet. The numerical study reveals a surprising result regarding the value of private information in a decentralized humanitarian system; the information rent is not monotonically increasing in the the ratio of transportation needs of different Programs. In fact, if the ratio is above certain threshold, the information rent extracted by all the Programs goes to zero. We believe that the unique characteristics of IHOs make the incentive misalignment issue an extremely interesting research topic, one that extends beyond a simple application of the principal–agent framework from the economics literature. Our work should appeal to the operations management community because it showcases the strategic importance of operational design for achieving tactical efficiency in a sector—namely, humanitarian operations—not generally viewed as pursuing such objective. The model proposed here can be used to advance the academic understanding of decentralized decision making in humanitarian operations. To the best of our knowledge, this is one of the first analytical studies of decentralized humanitarian operations that is completely informed by field research.

2.

Literature Review

This paper contributes to the humanitarian logistics literature and to the incentives literature in operations management. There is increasing interest in the study of humanitarian operations (Altay and Green 2006). Extant literature on humanitarian logistics follows a classical optimization approach. Much of the research examines stochastic relief systems for either disaster preparedness or disaster response. For the most part, this literature applies operations research techniques to relief settings while assuming central planner coordination, and the objective can be oriented toward either service level or cost efficiency. Service-level-based objective functions have been studied in terms of time of response and demand fulfillment. Research on minimizing the time of response can be found in Chiu and Zheng (2007) and Campbell et al. (2008). Research exploring demand coverage includes the work of Batta and Mannur (1990), Ozdamar

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et al. (2004), De Angelis et al. (2007), Jia et al (2007), Yi and Ozdamar (2007), Saadatseresht et al. (2009), and Salmeron and Apte (2010). Cost-based objective functions are often represented in terms of monetary cost or travel distance. Cost minimization can be found in the work of Barbarosoglu et al. (2002), Barbarosoglu and Arda (2004), Beamon and Kotleba (2006), and Sheu (2007); minimizing the distance traveled has been explored by Cova and Johnson (2003), Chang et al. (2007), and Stepanov and Smith (2009). In their work, Stepanov and Smith also examine an service-level-based function of response time. Regnier (2008) models the trade-off between cost and service level in hurricane evacuation operations from the perspective of a central planner. In contrast to almost all the literature in humanitarian logistics, we analyze incentives in a decentralized system. Our model combines elements of heavy-traffic queueing and mechanism design. The use of queuing models for vehicle fleet management is well established in the literature; they have been used for analyzing police patrol systems (Green 1984, Green and Kolesar 1984a, 1984b, 1989, 2004), land vehicle fire fleets (Kolesar and Blum 1973, Ignall et al 1982), helicopter fire fleets (Bookbinder and Martell 1979), and ambulance fleets (Singer and Donoso 2008). These papers model transportation needs in centrally planed systems based on stochastic inter-arrival times. Our analysis adds decentralized decision making. In the incentives literature under asymmetric information each agent knows its own type, but the principal does not know any agent’s type (Green and Laffont 1977, Dasgupta et al 1979, Myerson, 1979, Harris and Townsend 1981, Maskin and Riley 1984). However, when offered an incentive-compatible menu of contracts, the agents reveal their types in accordance with the revelation principle. Adverse selection occurs when an agent’s trading decision is based on private information that adversely affects other trading agents (MasColell et al 1995). The incentives literature under adverse selection in operations management often models supply chain settings. Corbett (2001) studies supplier-buyer interaction using an order quantity/reorder point model. He finds that when the supplier has private information about set-up cost consignment stock reduces the impact of information asymmetry. When the buyer has private information on backorder cost the supplier overcompensates the buyer for the stockout cost. Iyer et al (2005) analyze a setting where both supplier’s capacity and resource allocation are private information to the supplier. The proposed mechanism includes a transfer price offered by the buyer. Netessine and Taylor (2007) use a two-type consumer model to study the impact of production schedule on product line design. They use a classic EOQ formulation with

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asymmetric information on the preferences of customers. The firm offers a differentiated menu of product quality and price to high and low valuation consumers. Lutze and Ozer (2008) model a system where a supplier and a buyer (retailer) share the consequences of demand uncertainty but the retailer’s unit penalty cost is private information. They characterize the optimal lead times and payments that the supplier should offer to the buyer. The supplier’s objective is to minimize its expected inventory cost. Hasija et al (2008) explore pay-per-call and pay-per-time contracts in call-centers when there is information asymmetry about worker productivity. In this service setting as in the previous manufacturing ones coordination is achieved via financial transfer payments. Departing from financial mechanisms, Su and Zenios (2006) explore the efficiency–equity trade-off in kidney transplantation. Financial transfers are not possible in this setting, so the authors propose a kidney’s allocation rule that reflects the greater willingness of lower-risk patients to wait for an organ of higher quality. Following Su and Zenios (2006) we propose a non-financial mechanism for system coordination but instead of an allocation rule we use a capacity rule (fleet size) for fleet coordination.

3.

The Fleet Management System

In this section we provide assumptions that we use to develop a non-trivial yet tractable mathematical model that captures the essential field-based observations of decentralized humanitarian organizations discussed in Section 1. The system consists of two parties: the Headquarter and the Program. Based on system cost considerations, the Headquarter decides a service level for the fleet (fleet buffer) and then procures the vehicles from a global source. The Headquarter is responsible for the total cost of the system, which includes the running cost of the fleet, the fleet management cost in the field, and the cost of delay. The running cost of the fleet, r, is the average running cost per vehicle per unit of time; it includes maintenance, repairs, and fuel costs (Pedraza-Martinez and Van Wassenhove 2012). The running cost is an overhead cost to the IHO. The fleet management cost, c, is the average management cost per vehicle per unit of time. Pedraza-Martinez et al (2011) find that the Program is responsible for c. During our field visits, we observed that senior humanitarian staff in the field often dedicate a portion of their time to fleet scheduling and routing. The fleet management cost also includes the cost of vehicle drivers, whose importance to Program delivery is due to their knowledge of local language and geography. Finally, the fleet management cost includes the cost of information systems and spreadsheets to track fleet scheduling and routing in the field. The field management cost in the field is a direct cost for the Program. We refer to c + r as the operating cost of the fleet.

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The cost of delay, w, is measured per field visit per unit of time. The Program incurs this cost and it is accountable for it. Although the cost of delay is not a cash cost to the Program, it results in a disutility associated with the delay in carrying out Program delivery. To simplify our analysis and capture both the disutility of delay and the tensions of this decentralized system, we assume a constant marginal cost. The Program reports its transportation needs to the Headquarter and uses the fleet to coordinate and execute the “last mile” distribution to beneficiaries. The Program heavily relies on the fleet for transportation of staff to visit beneficiaries, as well as for the transport of materials, and of items for distribution to beneficiaries (Pedraza-Martinez et al 2011). Although demand is more stable over time in development than in relief settings, humanitarian development work does exhibit some stochasticity—in both arrivals and service times—owing the mobility of beneficiaries and the unpredictability of operating conditions in terms of weather, road conditions, and security. Demand rarely disappears entirely, and in fact it tends to accumulate when vehicles are not available to carry out visits to beneficiaries. We use a queuing model to capture the system’s stochasticity and the nature of work accumulation when the Program faces a fleet shortage and denote the Program’s transportation needs by lambda (λ). The transportation needs are measured as the rate of visits per unit of time. Service times denoted by mu (µ) are also stochastic. For simplicity we assume that the service rate µ = 1, which corresponds to adopting the scale of mean service times (Whitt 1992). To balance the system costs —the operating cost and the cost of delay— the Headquarter decides on the fleet size. In a deterministic setting the minimum fleet size for the system would be equal to the offered load, λ/µ. However, a fleet buffer is required to maintain system stability given the inherent variability of interarrival and service times. In other words, the fleet buffer is the extra number of vehicles needed to protect the system from stochasticity and thereby achieve a predetermined service level. To analytically capture the central trade-off, service level and efficiency, we use an Erlang-C queueing model that very nicely captures the trade-off and yet yields itself to analytical tractability. Considering that within the Program all visits have the same priority, we follow a first-come, first-served queuing discipline. We use heavy traffic approximations under the so-called rationalized regime to represent average delay in the system. The Halfin–Whitt (1981) delay function, π(y), is an asymptotically exact approximation to the probability of delay, Pr{wait> 0}. The value of π(y) may be written as:  −1 yΦ(y) π(y) = 1 + , φ(y)

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where Φ(y) and φ(y) are the unit normal cdf and pdf, respectively. The service level of the fleet is the average proportion of visits that are made without delay. The Program in our model neither engages in emergency response activities nor in highly scheduled regular work; rather, it carries out delay-sensitive and stochastically arriving developmental activities. Therefore we believe that the rationalized regime is appropriate for this setting. Borst et al (2004) show that a square-root staffing rule is asymptotically optimal for a system operating in the rationalized regime. Following Halfin and Whitt (1981), Grassmann (1988), Whitt (1992), Borst et al (2004), and Hasija et al (2005), we use the square-root staffing rule √ F (γ) = λ + γ(c, r, w) λ

(1)

to calculate fleet size. Denoted by γ, the buffer factor is the key decision variable in establishing the fleet buffer. The optimal buffer factor can be obtained via optimization methods by balancing the importance of delays in visits with fleet operating costs. The effectiveness of the square-root rule is increasing in fleet size, and has been shown to be a robust approximation of the optimal system size of fleets of 20 or more vehicles. Borst et al (2004) and Hasija et al (2005) report that, for a given buffer factor γ, the average number of visits in the queue is Q(γ) = Using µ = 1 and replacing F by its definition in (1), we obtain √ π(γ) λ Q(γ) = . γ

3.1.

π (γ )λ F µ−λ

.

(2)

Centralized Benchmark

The planner in a centralized system aims to minimize the total system cost, which is given by the average cost of delay wQ(γ) plus the average operating cost of the fleet (c + r)F (γ). The central planner’s problem is thus min Ccen (γ) = wQ(γ) + (c + r)F (γ). 0<γ

After substituting (1) and (2) in (3), we can rewrite the central planner’s problem as √ √ π(γ) λ min Ccen (γ) = w + (c + r)(λ + γ λ). 0<γ γ

(3)

(4)

The cost function (4) is unimodal (Borst et al 2004). It has a finite and positive minimum value, γ ∗ (c, r, w), that is independent of λ and depends only on the cost parameters of the system (Hasija et al 2005); γ ∗ (c, r, w) = arg min Ccen (γ)

(5)

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is the optimal buffer factor for the centralized benchmark. The key assumption here is that the central planner knows the Program’s transportation needs. As we show next, however, decentralized decision-making and private information render the centralized benchmark impossible to implement in the current system.

3.2.

Current Decentralized System

Program managers are evaluated based on the achievement of Program objectives in terms of demand fulfillment as well as operational costs. Concerning fleets, planning for more vehicles would result in a higher rate of demand fulfillment and higher service level. However, it would also result in greater funding requirements that would increase the programs fleet management cost. For these reasons, program managers have incentives to balance both their cost of delay and the fleet management cost. Therefore, the objectives of the managers are perfectly aligned with that of the program, however, as we show, such objectives may be misaligned with the overall goal of the organization due to the localized view of programs and their managers. If the Program reported its true needs then the average system cost would be as in equation (3). Yet because the Program is not accountable for the running cost of the fleet, the weight that the Program gives to delay exceeds the weight given by the Headquarter. To find its optimal buffer factor, the Program solves: min Cpro (γ) = wQ(γ) + cF (γ); 0<γ

(6)

the optimal buffer factor for the Program is then γ¯ (c, w) = arg min Cpro (γ).

(7)

As in equation (5), the Program’s optimal buffer factor depends only on w and its cost parameter c. This allows us to state a lemma that captures the misalignment of incentives between the Headquarter and the Program (All proofs are given in Appendix 1). Lemma 1. γ ∗ (c, r, w) < γ¯ (c, w). When combined with equation (1), Lemma 1 implies that the optimal fleet size for the Headquarter is smaller than the optimal fleet size for the Program. In other words, both the Headquarter and the Program consider the full cost of delay, but the Program considers only a portion of the operating cost whereas the Headquarter fully internalizes that cost. Since the operating cost increases with the fleet size, it follows that

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the Headquarter’s optimal fleet size is smaller than the optimum calculated by the Program. This result is consistent with our field observations, in particular with the concerns of the Headquarter about oversized fleets. The result is also consistent with the Program’s concerns about not having enough vehicles to optimize their service. The true transportation needs are known only by the Program. The misaligned incentives and private information create adverse selection whereby the Program may misreport its actual transportation needs. We abstract the Program as being one of two types: a program with low transportation needs, L, or a program with high transportation needs, H. Therefore, λL < λH . This standard assumption helps us to capture the main trade-offs of service level and efficiency while keeping the model analytically tractable. Assuming more than two types would significantly complicate the analysis without yielding commensurate insights. In reality, we observed that λH is easy to estimate because the maximum number of vehicles is determined by the total number of humanitarian staff in the Program. So for a health care Program , the IHO would procure no more vehicles than available medical staff. Nevertheless, improved coordination in fleet scheduling could result in ˆ i , the Program of a decrease in transportation needs, leading to λL . By stating its transportation needs, λ ˆ i ) such that type i ∈ {L, H} would target an intended buffer factor δ(λ p ˆi + γ λ ˆ − λi λ ˆi) = √ i δ(λ . λi

(8)

ˆ i ) |ˆ From (8) it follows that δ(λ λi =λi = γ. Let

ˆ L ) |ˆ ˆ δL = δ(λ ˆ H =λL . λL =λH , and δH = δ(λH ) |λ

(9)

Note that δL > γ and δH < γ both follow from λL < λH . For a Program of type i, the current system’s cost would be: ˆ i )) = wQi (δ(λ ˆ i )) + (c + r)Fi (δ(λ ˆ i )). Cpro (δ(λ

(10)

Also note that for γ = γ ∗ in (8) we have Ccen (γ ∗ ) < Cpro (δi ). Observe first of all that, in the current system, the high-type Program always reveals its true transportation needs. This finding is formalized in the following proposition. Proposition 1. In the current system, Cpro (γ ∗ ) < Cpro (δH ).

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The intuition behind Proposition 1 is that, for the high-type Program, the intended buffer factor from distorting transportation needs is actually lower than the buffer factor estimated by the Headquarter. Additionally, the buffer factor offered by the Headquarter is lower than the optimal buffer factor for the Program (Lemma 1). Because the cost function for the Program is unimodal with a minimum in γ¯ (see equation (7)), it is always cheaper for the high-type Program to reveal the truth. Otherwise, the extra cost of delay would cancel out the savings on fleet management. We are left with the low-type Program, which states its true transportation needs as long as Cpro (γ ∗ ) < Cpro (δL ). This suggests the existence of a threshold for truth telling, as formalized in our next proposition. Proposition 2. For any given values of λL and λH , there exists a truth-telling threshold γˆL such that γˆL 6= γ ∗ and: i) if γ < γˆ , then Cpro (γ) > Cpro (δL ); ii) if γ > γˆ , then Cpro (γ) < Cpro (δL ). The threshold value satisfies Cpro (δL ) = Cpro (γ ∗ ). Since δL depends not only on γ ∗ but also on λL and λH , it follows that—for a fixed value of γ ∗ —the truth-telling threshold depends on the ratio of λH to λL . The threshold indicates that if the ratio λH /λL is sufficiently high then the low-type Program’s savings in cost of delay are canceled out by the extra cost of fleet management. In short: the Headquarter knows that high-type Programs will not distort their needs and that low-type Programs will distort their needs only for values of γ < γˆL . A straightforward way to coordinate the system would be to make the Program, not the Headquarter, accountable for the fleet’s running costs. The running costs are an overhead and the Headquarter, which is considered a support function, is accountable for these costs. But in the humanitarian sector, the internal transfer of such overhead is not possible due to earmarking constraints imposed by donors. The Headquarter is aware that the Program’s stated transportation needs may be inflated and it may respond to the possibility of such distortion by monitoring the Program’s reported needs. During our field visits, we observed that Programs often have detailed data on fleet use and transportation needs in the field. Typically the data is in printed form and ready for auditing purposes, but it is not stored in a way that can be easily accessed by the Headquarter. Because there are not trustworthy information systems on transportation needs at the national level, the Headquarter may send staff to the field to monitor the Program’s estimated workload in situ. Due to the geographical dispersion of field operations in large and difficult to access remote

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regions, the lack of information systems and the inherent stochasticity in the system, it is not possible for the Headquarter to accurately infer the true transportation needs of the Program without incurring substantial monitoring costs. Additionally, given the humanitarian nature of Program delivery, it is not feasible for the Headquarter to impose a penalty on the Program (see appendix 2). Hence, the expensive monitoring effort is ineffective to deter transportation needs distortion because Programs that misreport are not penalized when caught. Recall that the Headquarter in our case is merely a central fleet management support group. Programs, supported by donors earmarking their donations for specific purposes and beneficiaries, are highly independent. Therefore, the Headquarter faces the challenge of designing a mechanism that induces truthful revelation by the Program. Such mechanism design problems under adverse selection scenarios have been extensively studied in the Economics literature. However, unlike the typical for-profit setting studied in that literature, in our setting financial rewards and penalties are considered infeasible in the humanitarian world. This makes the mechanisms design problem faced by the Headquarter challenging. Next, we will explore a different, capacity-based mechanism to induce truth revelation from the Program.

4.

Operational Mechanism

In this section we propose a novel mechanism design for truth revelation that is based on a particular operational lever: the buffer factor proposed by the Headquarter. The Headquarter cannot know the Program’s true transportation needs, but it does have some idea —just not a very accurate one. We therefore assume that the prior beliefs of the Headquarter can be summarized as follows: ( λL with probability q λi = λH with probability 1 − q We use the principal–agent framework where the Headquarter (the principal) allocates to a Program of type i (the agent) an outcome F (i.e., a fleet size) as a function of the Program’s self-reported type. This dynamics is operationalized by the Headquarter committing to an offered buffer factor γi in response to the ˆ i . The Program reports a type profile λ ˆ i , after which the mechanism Program’s stated transportation need λ is executed. The objective of the Headquarter is to minimize the system cost for a given distribution of Program types. The incentive compatibility (IC) constraints consist of offering each Program type i = {L, H} a buffer factor γi that ensures Cpro (γi ) ≤ Cpro (δi ). During our field visits, we observed that Programs do not have an outside option because the Headquarter procures the fleet. Hence the individual rationality (IR) constraints are defined by the requirement that the

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Headquarter offers each Program type a buffer factor large enough to protect the system from stochasticity, (i.e., γi > 0). The mechanism is formulated as min

0<γL ,0<γH

E[Cmec (γL , γH )] = q [wQ(γL ) + (c + r)F (γL )] + (1 − q) [wQ(γH ) + (c + r)F (γH )] s.t.

(11)

(ICL ) :

wQ(γL ) + cF (γL ) ≤ wQ(δL ) + cF (δL ),

(ICH ) :

wQ(γH ) + cF (γH ) ≤ wQ(δH ) + cF (δH ).

The left-hand side of the IC constraints in (11) is the type-i Program’s cost with a fleet buffer γi ; the righthand side of the IC constraints in (11) is type-i Program’s cost when distorting its needs. The intended fleet buffer δi is defined by (9). We now show that there exist fleet buffers γL and γH such that both Program types have incentives to reveal their true transportation needs. We consider the cases of both IC constraints loose, one IC constraint tight, and both IC constraints tight. Let γ˜L = {γ 6= γL : Cpro (γ) = Cpro (γL )}.

(12)

Then there are two ways to make the low-type Program’s IC constraint tight. The first way is by forcing γL = δL , and the second way is to choose γH such that δL = γ˜L . Proposition 3. There exist two regions for induced truth revelation via the operational mechanism as follows. R1: Equal fleet size region, where γH < γ ∗ < γL such that F (γL ) = F (γH ). R2: Different fleet size region, where γ ∗ < γL , and γ ∗ < γH such that F (γL ) < (γH ) and the regions for induced truth telling are separated by the threshold T1 . When both constraints are loose, neither type of Program has the incentive to distort its transportation needs; in other words, there exists a natural truth-telling region. Natural truth revelation follows directly from Proposition 2. This result is formalized in the following corollary. Corollary 1. R3: A natural truth telling region for the operational mechanism is defined by γ ∗ = γL = γH such that FL < FH .

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

15

The three regions characterized by Proposition 3 and Corollary 1 can be depicted in the space defined by the transportation needs ratio and probability types; see figure 1. In R1 both IC constraints in mechanism (11) are binding. The Headquarter offers δH = γH < γ ∗ < γL = γL such that both Program types receive the same fleet size, F (γL ) = F (γH ). This region exists for values of λH /λL near unity and is bounded by T1 , a threshold defined implicitly by the cost parameters of the system, (c,r and w), the lambda ratio (λH /λL ) and the low-type probability (q). When parameters fall in R1, truth revelation is achieved by making the low-type Program indifferent between reporting its true needs and distorting those needs —that is by making the low type IC constraint tight via γL = δL . The extra cost of inducing truth revelation by low-type programs is mitigated by reducing δL via the decrease of γH such that γH = δH . Our numerical experiments show that cost mitigation is mediated by the probability q that a Program is a low-need type. Increasing q beyond the threshold T1 reduces the width of R1. Because γH = δH , in R1 the high-type Program is indifferent between

0
revealing its true transportation needs and misreporting those needs.

R1:

R2:

R3:

FL = FH

FL < FH

FL < FH

γH < γ*< γL

γ*< γL , γ*< γH

γ* = γL = γH Natural Truth Revelation

T1

T2

λH/λL Figure 1

Truth-telling regions in the space of transportation needs ratio by probability type, or (γH /γL , q)-space

In R2 of Proposition 3, only the IC constraint for the low-type Program in (11) is binding. Both γL and γH are greater than γ ∗ , which means that the Headquarter gives incentives to both Program types. For low values of q the Headquarter keeps γH closer to γ ∗ (by setting γ ∗ < γH < γL ), because Programs are more likely to be of high type. By splitting the buffer factor, the Headquarter avoids a big increase in the high-type Program cost while making the low-type Program’s IC constraint tight via δL = γ˜L . For large values of q, the increased likelihood that Programs are of low type switches the order of incentives to γ ∗ < γL < γH . The closer γL is to γ ∗ , the lower the cost for the system. As q increases, the region R2 becomes more favorable for

16

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

the system than the region R1. In R2 the high-type Program is better-off revealing its true transportation needs because the condition δH < γH < γ¯ implies that Cpro (γH ) < Cpro (δH ). Truth revelation in R3, as characterized by corollary 1, is achieved without incentives. With parameter values falling in this region, a low-type Program has no incentives to distort its transportation needs because doing so would guarantee that the cost of fleet management outweighs the savings achieved by reduced delays. On the other hand, a high-type Program will not distort its needs because it would then receive a fleet too small for its needs; in this case, the cost of delay would outweigh the savings in fleet management. It is interesting that T2 is independent of q. This threshold depends only on the cost parameters (c, r, w), and the λH /λL ratio. Thus, by choosing distinctive fleet buffers γL and γH (instead of a unique γ ∗ ), the Headquarter can create operational incentives for truth revelation. There are two ways of achieving truth revelation via the operational mechanism: induced and natural. For induced truth revelation we find that the IC constraint of the low-type Program will always be binding. Such incentives may be able to increase system efficiency without requiring that the reported needs of Programs be monitored. The λH /λL ratio (transportation needs ratio) depends on several factors. According to a senior IHO fleet manager, the types of activities carried out by the Program affect the ratio. For example, intensive vaccination programs following relief operations may need frequent trips to villages while water and sanitation programs may only need sporadic visits. The number of routes connecting villages also affects the λH /λL ratio. While rural villages are often connected with urban centers by only one or a small number of routes, more urbanized areas may be connected by a larger number of routes. The more available alternative routes between different villages, the easier the coordination of Program transportation needs, which reduces λL resulting in an increase of the λH /λL ratio. Due to their road infrastructure and low urbanization, field sites like Democratic Republic of Congo, Chad, Niger and South Sudan would fall in R1. Field sites with better road infrastructure or higher levels of urbanization like Zimbabwe, Colombia, and Pakistan would fall in region R2. Field sites in countries like Nicaragua and El Salvador in Central America as well as Georgia and Azerbaijan would fall in R3. Although its urbanization is much higher than the one of previous countries classified in R1, Haiti would also fall in that region mostly due to its heavy workload following the relief operation in the aftermath of the 2010 earthquake and its poor road infrastructure. In the next section we explore different models’ predictions regarding not only the (reduced) value of lowtype Programs’ information but also potential cost savings for the overall system. The operational mechanism

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

17

has the counterintuitive result that the greater the difference between types, the lower the value of private information for the low-type Program. This result is examined in detail in subsection 5.1.

5.

Numerical Study

This section presents a numerical study that complements the analytical insights presented in section 4. The base case uses weekly planning for a time horizon of 52 weeks. The running and management costs of the fleet are calculated following the research by Pedraza-Martinez and Van Wassenhove (2012) on vehicle replacement in a humanitarian setting. The running cost per vehicle is established at $17,000 per year, which is equivalent to $269.23 per week; this cost includes maintenance, repairs, and fuel. The fleet management cost is set to be 15% of the running cost; it includes staff time for coordinating fleet management as well as the salary of vehicle drivers, which depends on the Program (Pedraza-Martinez et al 2011). The normalized demand rate for the low-type Program is λL = 60 visits per week. This is equivalent to a fleet of 60 vehicles that are 100% utilized. We compare the cost of the centralized benchmark, the current decentralized system, and the operational mechanism (figure 2 ). 27,000 26,000

Cost ($)

25,000

c = r = w= q = λL=

40.38 269.23 400.00 0.5 60.00

Current decentralized system

24,000 Centralized benchmark

23,000 Operational mechanism

22,000

T2

T1

21,000 20,000 1.01

R1

R2

1.06

1.11

1.16

R3

1.21

1.26

1.31

λH/λL

Figure 2

System cost comparison

The cost of the current decentralized system suffers from a fleet excess caused by the inflation of transportation needs by the low-type Program. This inflation holds for parameter values below the threshold T2 for “natural truth revelation”. Note that in R1 the mechanism does not produce significant savings when compared with the current system. This is due to the joint effect of incentive conflicts and information asymmetries, which lead to inefficient system performance (Corbett 2001). In this region, the Headquarter

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

18

offers the same fleet size to both Programs. That strategy makes the low-type Program indifferent between revealing the truth and distorting its needs. In R2, the Headquarter makes the low-type Program indifferent between revealing its true needs and distorting them by offering γ ∗ < γL . The system cost in this region is controlled by choosing γL according to the proportion of low-type Programs: the higher this proportion, the closer is γL to γ ∗ . In R3 there is no need for incentives because truth revelation is achieved naturally. These results for R1 are quite intuitive. However it was surprising to us that, the larger the difference in types in R2, the lower the value of information for the low-type Program, which disappears in R3. We examine this result in more detail next.

5.1.

Reduced Value of Private Information for the Low-Type Program

We begin by plotting the buffer factors in the (λH /λL , q, γ)-space. The horizontal axis represents the transportation needs ratio λH /λL ; the depth axis represents the low-type Program probability q; and the vertical axis represents the fleet buffer for the i type Program. Figure 3 is complemented by figure 4, which shows the projection of γL and γH in the (λH /λL , γ)-space, and by figure 5, which shows the projection of γL and γH in the (q, γ)-space. First, note that the Headquarter incentivizes the low-type Program in the induced truth-telling region R1 by choosing γ ∗ < γL (Figures 4a and 5a). To mitigate the extra cost of this strategy, the Headquarter simultaneously decreases the fleet buffer for the high-type Program by choosing γH < γ ∗ (Figure 4b and λH /λL = 1, 01 in figure 5b). Thus, the Headquarter forces the indifference conditions γH = δH < γ ∗ < γL = δL . For low values of q in R1 both γL and γH are close to γ ∗ . If q increases, the Headquarter offers a lower γH , which reduces δL . the Headquarter makes the low-type Program indifferent between revealing the truth and inflating its needs by offering γL = δL . The extra cost of delay for the high-type Program is offset by the reduction in operating cost of the low-type Program’s fleet. Second, Figure 4a shows that, in R2, the higher the ratio λH /λL of high-type to low-type needs, the lower the value of incentives given to the low-type Program. For low values of q, the Headquarter gives incentives to both Program types by choosing γ ∗ < γH < γL < γ¯ < δL = γ˜ . To keep the system cost balanced, the Headquarter offers the low-type Program a fleet buffer that is greater than γ ∗ but is decreasing in the proportion q of low-type Programs (Figure 5a). In fact, for large values of q it is more efficient for the Headquarter to offer γ ∗ < γL < γH < γ¯ < δL = γ˜ . Nevertheless, decreasing γL increases γ˜ and so, to achieve the indifference condition δL = γ˜ , the Headquarter must offer the high-type Program a bigger fleet buffer when

Fleet buffer γL

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

γL

γ*=0.925

A x i s   T i t γeHl  

γ*=0.925 R1

R1

R2

T1 1.01

1.04

1.07

R3

T2 1.1

1.13

1.16

1.19

λH/λL

1.22

1.25

(a) Low type Program Figure 3

R2

T1

0,825 0,625 q 0,425 0,225

1

7

13

T2 19

25

0,025

1.28

19

31

37

λH/λL

43

49

55

Series33 Series25 q Series17 Series9

R3

Series1

(b) High type Program Fleet buffers in the (λH /λL , q, γ) space

3

3

q = 0.975 q = 0.7

2.5

q = 0.975 q = 0.7

2.5

q = 0.5

q = 0.5

q = 0.3 2

q = 0.3 2

q = 0.025

1.5

q = 0.025

1.5

γL

γH 1

0.5 0 1.01 1.01

1

γ* R1

R2

T1

1.06

1.11

1.16 1.15

1.21

0.5

R3

T2

1.26 1.25

0 1.01 1.01

1.31

γ* R1

R2

T1

1.06

1.11

1.16 1.15

λH/λL

1.26 1.25

1.31

(b) High type Program Fleet buffers as function of λH /λL

λH/λL = 1.15

1.5

λH/λL = 1.15

λH/λL = 1.01

1

1

γL

γH λH/λL = 1.25

λH/λL = 1.25

λH/λL = 1.01

0.5

γ*

0 0.025 0.025

1.21

λH/λL

(a) Low type Program Figure 4

1.5

R3

T2

0.5

γ*

0 0.25

0.3

0.475

0.5 q

0.70.7

(a) Low Type Program Figure 5

0.925 0.975

0.025 0.025

0.25

0.3

0.475

0.5 q

0.70.7

0.925 0.975

(b) High Type Program Fleet buffers as a function of q

q = 0.975 (Figure 5b). This counterintuitive result follows because there is a partial alignment of incentives between the Headquarter and the Program, which have the same cost structure. Hence there is a region, R3,

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

20

in which the difference between types is so great that it becomes costly for the low-type Program to distort its type. That is, any such distortion would result in marginal fleet management costs increasing more than the decreasing marginal cost of delay implied by a larger fleet size. This loss of information rent for the low-type Program underscores the value of this mechanism for the Headquarter when difference between types is great.

5.2.

Sensitivity Analysis of the Cost of Delay

Next we perform a sensitivity analysis with respect to w. Note that the cost of delay depends on the nature of the development program (e.g. agriculture, shelter, sanitation, health). We study the sensitivity of the system to changes in this parameter by choosing w = {100, 200, 400, 600, 800}. We also use q = {0.025, 0.3, 0.5, 0.7, 0.975} and lambda ratios λH /λL = {1.01, 1.15, 1.25}. The sensitivity analysis summarizes changes in the Headquarter’s optimal fleet buffer γ ∗ and the Program’s optimal fleet buffer γ¯ ; see table 1. Note that a decrease in the cost of delay (w) causes a decrease in both the optimal fleet buffer for the Headquarter (γ ∗ ) and in the optimal fleet buffer for the Program (¯ γ ). The lower the cost of delay, the lower the relative weight of the service level component of the system’s objective function. Conversely, an increase in w increases both γ ∗ and γ¯ . Nevertheless, these changes in the optimal fleet buffer are not linear in w. In case λH /λL = 1.15, for instance, decreasing w by 50% decreases γ ∗ by 23.24% whereas increasing w by 50% increases γ ∗ by only 15.02%. Observe that decreasing w expands R3, the natural truth-telling region. Lower w implies that the fleet management cost for the Program is relatively higher, in which case the Program has less incentive to distort its transportation needs in order to secure a bigger fleet. On the other hand, increasing w slightly decreases R3. The sensitivity analysis takes as its base case the current decentralized system. The cost savings associated with the central planner and the operational mechanism are calculated in comparison to this base case. Note that the cost savings for the systems are increasing not only in q, the proportion of low-type Programs, but also in the ratio of high-type and low-type needs, λH /λL . Observe that the mechanism produces savings of about 10% when q = 0.7 and λH /λL = 1.25; these savings increase to more than 15% when q = 0.975 and λH /λL = 1.25. These savings match the intuition of the Headquarter staff quoted in the Introduction. This section has presented a cost comparison among the different regimes analyzed in the paper, and it has illustrated graphically the Headquarter’s strategy of achieving truth revelation via the operational mechanism. That strategy varies as a function of parameter values. Whereas in R1 the Headquarter offers

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

w=

100

λH /λL = 1.01 200 400 600

800

100

λH /λL = 1.15 200 400 600

800

100

21

λH /λL = 1.25 200 400 600

800

γ∗ γ ¯ T1‡ T2

0.529 1.246 1.055 1.220

0.710 1.468 1.065 1.250

0.925 1.701 1.070 1.265

1.064 1.840 1.070 1.265

1.166 1.939 1.070 1.270

Fleet Buffer Measures† 0.529 0.710 0.925 1.064 1.166 1.246 1.468 1.701 1.840 1.939 1.055 1.065 1.070 1.070 1.070 1.220 1.250 1.265 1.265 1.270

0.529 1.246 1.055 1.220

0.710 1.468 1.065 1.250

0.925 1.701 1.070 1.265

1.064 1.840 1.070 1.265

1.166 1.939 1.070 1.270

q 0.025 0.300 0.500 0.700 0.975

0.630 0.607 0.588 0.567 0.533

0.811 0.787 0.767 0.746 0.713

1.028 1.002 0.982 0.961 0.928

1.167 1.141 1.121 1.099 1.067

1.270 1.244 1.223 1.202 1.170

Low Type Program Fleet Buffer. γL 0.673 0.924 1.182 1.331 1.434 0.670 0.918 1.174 1.322 1.425 0.665 0.909 1.162 1.310 1.413 0.655 0.890 1.138 1.284 1.388 0.560 0.750 0.972 1.114 1.217

0.529 0.529 0.529 0.529 0.529

0.710 0.710 0.710 0.710 0.710

0.943 0.943 0.943 0.942 0.934

1.088 1.088 1.087 1.087 1.075

1.191 1.191 1.191 1.190 1.178

q 0.025 0.300 0.500 0.700 0.975

0.527 0.504 0.486 0.465 0.431

0.708 0.683 0.664 0.643 0.610

0.923 0.898 0.878 0.856 0.824

1.062 1.036 1.016 0.994 0.962

1.164 1.138 1.118 1.096 1.064

High Type Program Fleet Buffer. γH 0.530 0.711 0.927 1.066 1.168 0.541 0.729 0.950 1.091 1.193 0.557 0.755 0.983 1.125 1.228 0.594 0.815 1.057 1.201 1.304 1.018 1.404 1.736 1.901 2.006

0.529 0.529 0.529 0.529 0.529

0.710 0.710 0.710 0.710 0.710

0.925 0.926 0.928 0.931 0.980

1.064 1.066 1.068 1.072 1.138

1.167 1.168 1.170 1.175 1.243

25308 23967 22991 22016 20674

25890 24532 23544 22556 21198

26632 26370 26180 25990 25728

27023 26756 26561 26367 26100

27303 27035 26839 26644 26375

SYSTEM COSTS q 0.025 0.300 0.500 0.700 0.975

20745 20699 20666 20632 20586

21270 21222 21187 21152 21105

21846 21797 21761 21725 21676

22197 22147 22111 22075 22025

22450 22399 22363 22326 22276

Current Decentralized System ($) 23465 24022 24636 25010 25280 23263 23795 24391 24761 25028 23116 23629 24214 24579 24845 22969 23464 24036 24397 24662 22767 23236 23792 24147 24410

SYSTEM SAVINGS (%) VS. CURRENT DECENTRALIZED SYSTEM q 0.025 0.300 0.500 0.700 0.975

0.01 0.05 0.08 0.10 0.14

0.01 0.04 0.06 0.09 0.12

0.01 0.04 0.06 0.08 0.11

0.00 0.03 0.05 0.07 0.10

0.01 0.03 0.05 0.07 0.10

Centralized Benchmark 0.24 0.22 0.22 0.22 2.84 2.70 2.61 2.58 4.75 4.53 4.38 4.33 6.70 6.39 6.18 6.10 9.40 8.98 8.70 8.58

q Operational Mechanism 0.025 0.00 0.00 0.00 0.00 0.00 0.23 0.21 0.20 0.20 0.300 0.00 0.00 0.00 0.00 0.00 2.73 2.53 2.39 2.36 0.500 0.01 0.01 0.01 0.01 0.01 4.58 4.24 4.03 3.97 0.700 0.04 0.04 0.04 0.04 0.04 6.47 6.01 5.73 5.64 0.975 0.13 0.11 0.10 0.10 0.09 9.31 8.84 8.53 8.42 † The fleet buffer measures remain constant to changes in λH /λL ‡q = 0, 5

Table 1

0.22 2.57 4.31 6.07 8.54

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

0.38 4.62 7.75 10.93 15.37

0.38 4.57 7.68 10.83 15.23

0.38 4.56 7.64 10.78 15.16

0.20 2.35 3.96 5.62 8.37

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

0.38 4.62 7.75 10.92 15.37

0.38 4.57 7.67 10.82 15.23

0.38 4.55 7.64 10.77 15.16

Sensitivity of results to changes in w

the same fleet size to both Program types, in R2 its strategy consists of offering incentives to both Program types while keeping closer to γ ∗ the fleet buffer for whichever Program type is predominant. Finally, this section included a sensitivity analysis with respect to w. The effectiveness of the proposed mechanism as compared with the current decentralized system is increasing in w provided the parameters fall into the induced truth regions.

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

22

6.

Conclusions and Further Research

This paper, which is completely informed by field research, studies a decentralized two-party fleet management system in a humanitarian setting. Located in the field, Programs are service oriented and have private information on their transportation needs, which are fulfilled using vehicle fleets. Often located in the United States or Europe, the Headquarter ’s main objective is to balance the service level and operating cost of the fleet. Differences in objectives, distant geographic locations, and the private information of Programs about their true transportation needs combine to create an adverse selection problem. The Headquarter is concerned about excess fleet sizes; Programs are concerned about not having enough vehicles for their transportation needs. We develop a mathematically tractable model to analyze this problem while respecting exogenous constraints on internal budget allocation that are characteristic of the humanitarian context. We find that the concerns of the system’s two parties are rational from each party’s perspective. This is because the optimal buffer factor offered by the Headquarter is lower than the optimal buffer factor intended by the Program. Hence the low-type Program’s incentive to inflate its reported needs results in a fleet excess that justifies concerns of the Headquarter, and the buffer factor offered by the Headquarter justify the concerns regarding the lack of vehicles from the high-type Program. Nevertheless, we find that—for appropriate parameter combinations—the current system has a “natural” truth-telling threshold that enables the centralized benchmark solution to be achieved. In the current fleet management system, the high-type Program always reveals its true transportation needs. Otherwise, that Program would receive a lower buffer factor than the one calculated by the Headquarter, increasing even more the Program’s delay costs. The threshold for natural truth telling arises when the extra fleet management cost resulting from the fleet excess requested by the low-type Program dominates the savings resulting from a reduction in the cost of delay. Coordinating incentives is especially challenging in our humanitarian context because financial transfer payments are not a viable way to induce truth revelation by the Programs. We propose a novel mechanism, based on operational capacity, for coordinating incentives in this system. The mechanism consists of the Headquarter offering different fleet buffer factors to the different Program types. We demonstrate the existence of three mutually exclusive and jointly exhaustive regions for truth revelation under the proposed mechanism: the equal fleet size region R1; the different fleet size region R2; and the natural truth revelation region R3. In R1 the Headquarter achieves truth revelation by offering both Program types the same fleet size; this strategy renders the low-type Program indifferent between inflating its transportation needs and revealing

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

23

the truth. Due to the difficulties to coordinate Program transportation needs, Programs in field sites with low urbanization and poor road infrastructure would fall in R1. Some country examples are Democratic Republic of Congo, Chad, Niger and South Sudan. In R2 both Program types are offered fleet buffers that exceed the current system’s optimum. When the probability of a Program being of low-type is small, a low-type Program is offered a buffer factor such that the Program’s cost when inflating its needs is exactly equal to the cost of revealing its true needs. When the low-type probability reaches a certain threshold, it is cheaper for the Headquarter to incentivize the high-type Program. By offering the high type a larger fleet buffer, the Headquarter increases the low-type Program’s intended fleet buffer enough to make the latter indifferent between revealing its needs and inflating them. Programs in field sites with higher urbanization and better road infrastructure would fall in R2. Some country examples are Zimbabwe, Colombia and Pakistan. Finally, under some combinations of parameters that are independent of the low-type probability, the system reaches a natural truth-telling region. In R3, as in the current decentralized system, the extra cost of fleet management deters the low-type Program from inflating its transportation needs. Programs in field sites with medium to high urbanization and relatively good infrastructure would fall in R3. Some country examples are El Salvador and Georgia. Of course, the workload is an important consideration that depends on the type of activity the Program carries out. For instance, Haiti is a country of small size, and highly urbanized but Program workload tends to be heavy, pushing Haiti to R1. Our numerical section complements the foregoing analysis. First, it allows us to explain the counterintuitive loss of value of private information for the low-type Program as a function of its increasing difference from the high-type Program. Second, our numerical experiments show how system behavior responds to changes in the cost of delay. As expected, a decrease in that cost reduces the optimal fleet buffers for the system, and an increase in the cost of delay increases the system’s fleet buffers. However, the change in the optimal fleet buffers is not linear to changes in the cost of delay a response; likewise, the thresholds that define the regions for truth telling are much more sensitive to decreases than to increases in the cost of delay. The reason is that a decrease in the cost of delay rapidly flattens the Program’s cost function, which in turn increases the size of the natural truth revelation region. This paper introduces a tractable mathematical model for analyzing incentive alignment in decentralized humanitarian settings. Some interesting extensions of this work include fleet pooling and the joint analysis of relief and development transportation needs, which are issues faced by humanitarian fleet managers in practice.

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

24

Appendix. 1. Proofs Proof of Lemma 1:

Note that:   0 √ ∂Ccen (γ, ) wπ (γ) wπ(γ) +c+r = − λ ∂γ γ γ2

(13)

  0 √ ∂Cpro (γ) wπ (γ) wπ(γ) + c λ. = − 2 ∂γ γ γ

(14)

and

Hence √ ∂Cpro (γ) ∂Ccen (γ, λ) = − r λ, ∂γ ∂γ √ ∂Ccen (γ, λ) ∂Cpro (γ) = − r λ, ∂γ ∂γ ∗ γ =γ ∗ (c,r,w) γ =γ (c,r,w) √ ∂Cpro (γ) = 0 − r λ < 0. ∗ ∂γ γ =γ (c,r,w)

Because Cpro (γ) is unimodal with a finite minimum, Cpro (c, w) decreases for values of γ such that γ ∗ (c, r, w) < γ and reaches its minimum at γ = γ¯ (c, w). This implies that γ ∗ (c, r, w) < γ¯ (c, w). 

√ λ +γ ∗ λ −λ Given the central benchmark solution γ ∗ , we have δH = L √ L H ; δH < λH ∂Cpro (γ ) ∗ γ follows from λL < λH . Since ∂γ ∗ < 0 (from lemma 1), and due to the fact that the cost function Proof of Proposition 1:

γ =γ

Cpro (γ) is unimodal with minimum at γ¯ , and given that from lemma 1 we know that γ ∗ < γ¯ , it follows that Cpro (γ ∗ ) < Cpro (δH ).

 Note that γ¯ < γˆL . If δL < γˆL , then Cpro (δL ) < Cpro (γ ∗ ). If δL = γˆL , then

Proof of Proposition 2:

Cpro (δL ) = Cpro (γ ∗ ). Finally, if γˆL < δL , then Cpro (γ ∗ ) < Cpro (δL ). Hence, γˆL defines the truth-telling region for the low-type Program. Proof of Proposition 3:

 First, we rewrite the mechanism in extended form as √  p wπ(γL ) λL + (c + r)(λL + γL λL ) γL √   p wπ(γH ) λH + (1 − q) + (c + r)(λH + γH λH ) γH 

min

0<γL ,0<γH

E[Cmec ] =q

s.t. (ICL ) (ICH )

√ √ p p wπ(γL ) λL wπ(δL ) λL + c(λL + γL λL ) ≤ + c(λL + δL λL ), γL δL √ √ p p wπ(γH ) λH wπ(δH ) λH + c(λH + γH λH ) ≤ + c(λH + δH λH ). γH δH

(15)

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

25

Second, we build the mechanism’s Lagrangian function L as follows: √ √     p p wπ(γL ) λL wπ(γH ) λH L(γL , γH , α1 , α2 ) =q + (c + r)(λL + γL λL ) + (1 − q) + (c + r)(λH + γH λH ) γL γH (16) √ √    p p wπ(γL ) λL wπ(δL ) λL + α1 + c(λL + γL λL ) − + c(λL + δL λL ) γL δL √ √    p p wπ(δH ) λH wπ(γH ) λH + α2 + c(λH + γH λH ) − + c(λH + δH λH ) , γH δH

where α1 and α2 are the Lagrange multipliers for ICL and ICH , respectively. Third, we derive the first-order conditions (FOCs) of (16):  0 p  0 p p ∂L wπ (γL ) wπ(γL ) wπ (δH ) wπ(δH ) = (q + α1 ) − + c λ + qr λ − α − + c λL = 0; L L 2 2 ∂γL γ γL2 δH δH p p L 0  p ∂L wπ (γH ) wπ(γH ) wπ 0 (δL ) wπ(δL ) +c λH + (1 − q)r λH − α1 +c λH = 0. = (1 − q + α2 ) − − 2 ∂γH γH γH δL δL2 √ √ 0 Letting f (γ) = wπγ(γ ) − wπγ(2γ ) + c and then dividing by λL (resp., by λH ) in the first (resp., second) equation above we can rewrite the FOCs as ∂L = (q + α1 )f (γL ) − α2 f (δH ) + qr = 0, ∂γL ∂L = (1 − q + α2 )f (γH ) − α1 f (δL ) + (1 − q)r = 0. ∂γH

(17) (18)

Observe that p ∂Cpro (γ) = f (γ ) λL , L ∂γ γ =γL p ∂Ccen (γ) = (f (γL ) + r) λL . ∂γ γ =γL Substituting (19) and (20) in (17) and (18) allows us to rewrite the FOCs as ∂Ccen (γ) ∂Cpro (γ) ∂Cpro (γ) + α1 − α2 =0 q ∂γ ∂γ ∂γ γ =γL γ =γL γ =δH ∂Ccen (γ) ∂Cpro (γ) ∂Cpro (γ) (1 − q) + α − α =0 2 1 ∂γ ∂γ ∂γ γ =γH γ =γH γ =δL

(19) (20)

(21) (22)

Equations (9) together with λL < λH imply that γH < δ L ,

(23)

δH < γ L .

(24)

p p (δL − γL ) λL = (γH − δH ) λH .

(25)

Combining the definitions of δL and δH yields

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

26

Equation (25) implies the following set of conditions: γL = δL iff γH = δH ;

γL < δL iff δH < γH ; δL < γL iff γH < δH .

(26)

Finally, we characterize the induced truth telling-region stated in the proposition. Characterization of R1: Suppose 0 < α1 and 0 < α2 . Note that 0 < α1 implies Cpro (γL ) = Cpro (δL ) and that 0 < α2 implies Cpro (γH ) = Cpro (δH ). There are three mutually exclusive and jointly exhaustive possibilities: either (1) δL < γ¯ , or (2) δL = γ¯ , or (3) γ¯ < δL . Case 1 : δL < γ¯ . Note that δL < γ¯ implies that either δL < γ¯ < γL or δL = γL . First, suppose that δL < γ¯ < γL . Then, γH < δH (by 26) and γH < δL < γ¯ ; hence Cpro (δL ) < Cpro (γH ) follows because the Program’s cost function is well-behaved. For Cpro (γH ) = Cpro (λH ) to be true it must be that γ¯ < δH . Also, δH < γL (by (23)), which implies that Cpro (δH ) < Cpro (γL ). But Cpro (γL ) = Cpro (δL ) (because we supposed 0 < α1 ). It follows that Cpro (δH ) < Cpro (γL ) = Cpro (δL ) < Cpro (γH ), which is a contradiction because α2 > 0 implies Cpro (δH ) = Cpro (γH ). Second, suppose that δL = γL . This implies γH = δH (by (26)) and γH < γL follows (by (24)) and the fact that δL = γL ). This also implies δL = γL < γ¯ (by 0 < α1 ). Using these facts in the FOCs (21) and (22) and then adding them we obtain ∂Ccen (γ) q ∂γ

γ =γL

∂Ccen (γ) + (1 − q) ∂γ

= 0.

(27)

γ =γH

Equation (27) holds in only three possible cases: (i) when γL = γH = γ ∗ , which would contradict γH < γL ; (ii) when γL < γ ∗ < γH , which would contradict γH < γL , and (iii) when γH < γ ∗ < γL . This third possibility is feasible and leads to the condition δH = γH < γ ∗ < γL = δL < γ¯ .

(28)

Case 2 : δL = γ¯ . This implies γL = δL = γ¯ (since the Program cost function is unimodal) and also implies that γH = δH < γ¯ . Using these facts in the FOCs (21) and (22) and then adding them, we again get equation (27). As in Case 1, this equation holds in only three possible cases: (i) when γL = γH = γ ∗ , which would contradict γH < γL ; (ii) when γL < γ ∗ < γH , which would contradict γH < γL ; and (iii) when γH < γ ∗ < γL . The third possibility leads to the condition δH = γH < γ ∗ < γL = δL = γ¯ .

(29)

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

27

Case 3 : γ¯ < δL . The proof for this case follows the same logic that the one for Case 1. Note that γ¯ < δL implies either γL < γ¯ < δL or γ¯ < δL = γL . First, suppose that γL < γ¯ < δL . This implies δH < γH (by 26) and δH < γL < γ¯ . It follows that Cpro (γL ) < Cpro (δH ) (given that the Program cost function is well-behaved ). Because the cost function of the program is unimodal, for Cpro (δH ) = Cpro (γH ) to hold, we must have γ¯ < γH < δL , which implies Cpro (γH ) < Cpro (δL ). Hence we have Cpro (γH ) < Cpro (δL ) = Cpro (γL ) < Cpro (δH ), which contradicts the condition Cpro (γH ) = Cpro (δH ) (because we assumed 0 < α2 ). Second, suppose that γ¯ < δL = γL ; this implies δH = γH . By using these relations in FOCs (21) and (22) and then adding them, we get equation (27). Following the same reasoning as used in Cases 1 and 2, we derive the following condition: δH = γH < γ ∗ < γ¯ < γL = δL

(30)

We can combine conditions (28)–(30) in the following condition, which characterizes R1 in Proposition 3: δH = γH < γ ∗ < γL = δL .

(31)

Note that (31) implies FL = FH in R1. Depending on parameter values, the Headquarter must increase costs for the high-type Program in order to make the low-type Program indifferent between misreporting and truth revelation. Characterization of R2 Suppose that 0 < α1 and α2 = 0. Then the FOCs (21) and (22) become ∂Cpro (γ) ∂Ccen (γ) + α = 0, 1 ∂γ ∂γ γ =γL γ =γL ∂Ccen (γ) ∂Cpro (γ) (1 − q) − α1 = 0. ∂γ ∂γ q

γ =γH

Condition (32) holds when

∂Ccen (γ ) ∂γ



and



have opposite signs, which occurs only when γ =γL

γ ∗ < γL < γ¯ Condition (33) holds when both

∂Ccen (γ ) ∂γ γ =γH



and

(33)

γ =δL

∂Cpro (γ ) ∂γ

γ =γL

(32)

(34)

∂Cpro (γ ) ∂γ γ =δL



have the same sign. This happens in two

mutually exclusive cases: (i) γH < γ ∗ and δL < γ¯ ; or (ii) γ ∗ < γH and γ¯ < δL . (i) Combining condition (34) with γH < γ ∗ and δL < γ¯ yields γ ∗ < γL < γ¯ , γH < γ ∗ , and δL < γ¯ . We assumed that 0 < α1 , so this implies that Cpro (γL ) = Cpro (δL ); we also assumed that α2 = 0, which implies Cpro (γH ) < Cpro (δH ). Since γL < γ¯ and δL < γ¯ , follows that γL = δL . This implies γH = δH (from one of the conditions 26) and so Cpro (γH ) = Cpro (δH ), contradicting Cpro (γH ) < Cpro (δH ).

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

28

(ii) Combining (34) with γ ∗ < γH and γ¯ < δL yields γ ∗ < γL < γ¯ , γ ∗ < γH , and γ¯ < δL . Recall the definition of γ˜L presented in (12). We must have γ¯ < γ˜L = δL , for otherwise the low-type Program would claim high transportation needs and thus violate the revelation principle. Therefore, γ ∗ < γL < γ¯ < γ˜L = δL ,

γ ∗ < γH , and δH < γH .

These conditions can be divided into three subcases as follows: (a) γ ∗ < γH < γL < γ¯ < γ˜L = δL and δH < γH ; (b) γ ∗ < γL < γH < γ¯ < γ˜L = δL and δH < γL ; (c) γ ∗ < γL < γ¯ < γH < γ˜L = δL and δH < γL . The region R2 is characterized by (a) for low values of q and by (b) and (c) for high values of q. wπ 0 (γ ) γ

Next, we demonstrate the existence of the threshold T1 in Proposition 3. Let g(γ) =

− wπγ(2γ ) + (c + r),

and note that p p  ∂γH  qg(γL ) λL + (1 − q)g(γH ) λH =0 ∂γL

(35)

is a required condition for the FOC of the mechanism. The justification is as follows. First, for R1 we know that γL = δL and γH = δH . Replacing these values in the FOCs (17) and (18) yields (q + α1 )f (γL ) − α2 f (γH ) + qr = 0, (1 − q + α2 )f (γH ) − α1 f (γL ) + (1 − q)r = 0. Solving the system for α1 and α2 , we get q(f (γL ) + r) + (1 − q)(f (γH ) + r) = 0. The equivalence between (35) and (36) follows because

∂γH ∂γL

√ λ = √ L in (36). λH

Second, for R2 we know that α2 = 0. Hence the FOCs (17) and (18) become and

∂L ∂γH

(36)

∂L ∂γL

= (q + α1 )f (γL ) + qr = 0,

r) = (1 − q)f (γH ) − α1 f (δL ) + (1 − q)r = 0. Then we have α1 = − q(ff((γγLL)+ such that )

q(f (γL ) + r) f (δL ) + (1 − q)r = 0, f (γL ) f (γL ) q(f (γL ) + r) + (1 − q)(f (γH ) + r) = 0. f (δL ) √ λL +˜ γL λL −λH H H √ Recall the relation δL = γ˜L in R2, so γH = . We can write ∂γ = ∂γ ∂γL ∂γ ˜L (1 − q)f (γH ) +

λH

and

∂γ ˜L ∂γL

=

f (γL ) f (˜ γL )

(37) ∂γ ˜L ∂γL

. Note that

. The equivalence between (35) and (37) follows.

dC Keeping λL fixed, the next step is to obtain dλ : H " #   p  ∂γH  dC wπ(γH ) γH =(1 − q) + (c + r) 1 + √ + g(γH ) λH √ dλH 2γH λH 2 γH ∂λH

∂γH ∂γ ˜L

√ λL √ =

λH

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

29

 p p  ∂γH  ∂γL + qg(γL ) λL + (1 − q)g(γH ) λH ∂λH ∂γL By (35) the second line of this expression is equal to zero. As a result,    p  ∂γH  dC wπ(γH ) γH √ = (1 − q) + (c + r) 1 + √ + g(γH ) λH . dλH ∂λH 2γH λH 2 λH √ λ +γ 1 λ −λ 1 In R1 let γH = L L√ L H . Then

(38)

λH

√ 1 1 λL + γL λL ∂γH − √ =− ∂λH 2(λH )3/2 2 λH √ λL + γL1 λL + λH √ =− 2λH λH such that √  p   p  ∂γH   wπ 0 (γH ) wπ(γH ) λL γL1 λL + λH √ g(γH ) λH + c + r (− λ ) = − H 2 ∂λH γH γH 2λH λH √   1 λL + γL λL + λH wπ(γH ) wπ 0 (γH ) − = − (c + r) . 2 2λH γH γH Replacing for

dC dλH

and simplifying yields

 0 1     1 1 1 ) ) wπ 0 (γH dC π (γH ) π 0 (γH wπ(γH w − − + (39) = (1 − q) √ 1 1 2 1 ) dλH γH 2 (γH γH λH √ 2 λL λL +˜ γL ∂γ 2 − √1 . Following the same reasoning we used for = − On the other hand, for R2 we have ∂λH 2(λ )3/2 H H

2

λH

2 1 , for R2 we have with γH R1 and replacing γH

 0 2     2 2 2 dC ) π (γH ) π 0 (γH ) wπ 0 (γH w wπ(γH − − . = (1 − q) √ + 2 2 2 2 ) dλH γH 2 (γH γH λH 2 1 . If we show that < γ ∗ < γH Note that γH d dλH

(C1 − C2 ) ≥ 0. The second part of

function. Next we show that Replacing, we obtain

π (γ ) γ



π (γ ) γ

π 0 (γ )

2

dC dλH

dC dλH

(40)

1 , then this is equivalent to showing that is decreasing in γH

1 in (39) is decreasing in γH because it is the slope of a convex

π 0 (γ )

2

is decreasing in γ. Observe that π 0 (γ) = π(γγ ) − γπ(γ) − π(γγ ) . h i 2 = 12 3πγ(γ ) + γπ(γ) − π(γγ ) . Taking the derivative with respect to γ and −

2

simplifying now yields     6 6 2 2 − γ + 2 + 3 π(γ) + + 3 [π(γ)]2 − 2 [π(γ)]3 ≤ 0. 2 γ γ γ Therefore,

d dλH

√ (C1 − C2 ) ≥ 0 is monotonic. For λH = λL we know that C1 < C2 , but for λH = λL + γ¯ λL we

have C1 > C2 . This implies the existence of a threshold T1 such that C1 < C2 for λH < T1 , C1 ≥ C2 for λH ≥ T1 . 

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

30

(γ ) Suppose α1 = 0 and α2 = 0. From (21) we get: q ∂Ccen = 0. Because ∂γ γ =γL (γ ) Ccen (γ) is unimodal, we conclude that ∂Ccen = 0 holds only for γL = γ ∗ , the centralized solution ∂γ γ =γL (γ ) found in equation (5). A similar argument for condition (22) leads to (1 − q) ∂Ccen = 0, which holds ∂γ γ =γ Proof of Corollary 1:

H





only for γH = γ . Then the solution is γL = γH = γ . the Headquarter proposes γL = γH = γ ∗ when γ˜L < δL . The explanation is as follows. Since Cpro (γ) is unimodal with minimum in γ¯ and since γ ∗ < γ¯ it follows ∂C (γ ) that γ¯ < γ˜L . Hence 0 < pro . Therefore, γ˜ < δL implies that Cpro (γ ∗ ) = Cpro (˜ γ ) < Cpro (δL ). On the ∂γ γ =˜ γ ∂C (γ ) other hand, the high-type Program would report its true needs because δH < γL = γ ∗ and pro < 0, ∂γ γ =γ ∗ implying that Cpro (γ ∗ ) < Cpro (δH ).



Appendix. 2. Decentralized System with Monitoring As shown here, monitoring the Program does not resolve the effect of distortion due to asymmetric inforˆ i by mation and misaligned incentives. Before procuring the fleet, the Headquarter may randomly monitor λ carefully checking the Program’s data records. We mathematically capture the Headquarter’s decision to randomly monitor the Program using the decision variable p that represents the probability with which the Headquarter will monitor the Program. If the Headquarter is dealing with multiple Programs (each with a dedicated fleet and individual transportation needs), then the p should be interpreted as the expected proportion of Programs that will be monitored. The monitoring cost is m(p). We assume that by sending staff to the field, the Headquarter can accurately estimate of the Program’s transportation needs. Hence the Program’s problem becomes   ˆ i ))] = p (wQi (γ) + cFi (γ)) + (1 − p) wQi (δ(λ ˆ i )) + cFi (δ(λ ˆ i )) . min Ep [Cpro (δ(λ

ˆ i∈{L,H} λ

(41)

This means that the Headquarter’s monitoring effort should focus on Programs reporting high levels of transportation needs. The Headquarter chooses to monitor by solving ˆ i )) = p[q(wQL (γ) + (c + r)FL (γ)) + (1 − q)(wQH (γ) + (c + r)FH (γ))] minCmon (γ, δi (λ p

(42)

ˆ L )) + (c + r)FL (δ(λ ˆ L )) + (1 − q)(wQH (δ(λ ˆ H )) + (c + r)FH (δ(λ ˆ H ))] + m(p). + (1 − p)[q(wQL (δ(λ The results of Propositions 1 and 2 allow us to solve the monitoring problem via backward induction: ( ˆ L = λH , min{m0−1 (q[(c + r)[FL (δL ) − FL (γ)] − w[QL (γ) − QL (δL )]]), 1} if λ P= (43) 0 otherwise. Note, however, that there is no penalty for distortion; in other words, the Program’s stated transportation needs are independent of the monitoring effort by the Headquarter. In consequence, the Headquarter’s

Pedraza-Martinez, Hasija, and Van Wassenhove: Fleet Coordination in Decentralized Humanitarian Operations

31

monitoring effort has no effect on whether the Program reveals its true type. The proof of this statement is as follows. A Program of type i would report its true transportation needs if wQ(γ) + cF (γ) ≤ p(wQ(γ) + cF (γ)) + (1 − p)(wQ(δi ) + cF (δi )) because wQ(γ) + cF (γ) = p (wQ(γ) + cF (γ)) + (1 − p) (wQ(γ) + cF (γ)). This statement yields the truth-telling condition wQ(γ) + cF (γ) ≤ wQ(δi ) + cF (δi ). The proof now follows because the condition for truth telling does not depend on p, the Headquarter’s monitoring effort. The lack of penalties for distortion characteristic of this humanitarian system makes monitoring an ineffective tool to deter Program’s need distortion. In other words, monitoring does not have an influence on whether the programs truly reveal their types.

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Google Maps helps drive success of fleet-management app - Services
Google and the Google logo are trademarks of Google Inc. All other company and product names may be trademarks of the respective companies with which they are associated. About. • ISSCO is part of the ISS Group and delivers innovative technologies

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Mar 31, 2007 - low, it is Common Knowledge that a general switch to S2 would be profitable to everyone: if not, a lack of coordination would once again be at stake; as we consider reasonable conventions, we will assume next that some users have no in

ASPIRATION LEARNING IN COORDINATION GAMES 1 ... - CiteSeerX
‡Department of Electrical and Computer Engineering, The University of Texas .... class of games that is a generalized version of so-called coordination games.

Reversibility in Dynamic Coordination Problems
May 11, 2012 - late but also on the early investment level. Payoffs exhibit backward ... strategic as the agents are uncertain about others' actions. Our paper belongs to a booming literature on dynamic global games. One strand of ... second strand s

Coordination in a Social Network
both reduced by a good design;. • a utility a for ... and many poorly designed services have no chances; ... phone, fax, e-mail, conferencing tools, instant messag-.

ASPIRATION LEARNING IN COORDINATION GAMES 1 ... - CiteSeerX
This work was supported by ONR project N00014- ... ‡Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, ...... 365–375. [16] R. Komali, A. B. MacKenzie, and R. P. Gilles, Effect of selfish node ...

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Online PDF Fleet Telematics: Real-time management and planning of commercial vehicle operations (Operations Research/Computer Science Interfaces ...

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Dynamic Inefficiency in Decentralized Capital Markets - André Kurmann
Oct 19, 2017 - Πjm(vm(kP j) − vm((1 − δ)s+1. kP i)) − (kP j − (1 − δ)s+1. kP i. ) ] (38) where v (k) for any k is given by (34) evaluated at. ˆ λ = λ(θD)(1 − φ). Similar to Proposition 5, comparison of (22)-(23) with (30)-(31) mak