A 3-R principle for characterizing failure in relief supply chains’ response to natural disasters Open Access

The proper evaluation of failure in relief supply chains, especially as it pertains to the different types and characteristics of disasters, is becoming increasingly important not only for observing the occurrence of natural disasters but also for monitoring the performance of logistics and relief supply chain activity in disaster relief operations. Generically, the focus of relief and humanitarian logistics literature has been concerned with how to reach affected areas and individuals with food, water, medicine, shelter and other relevant supplies as fast as possible (Kovacs and Spens, 2007; Falasca and Zobel, 2011; Buddas, 2014). Recently, however, accountability is increasingly being required from the different types of organizations that carry out such services, i.e. the UN agencies, e.g. World Food Program, the international agencies, e.g. Red Cross, and the NGOs, e.g. CARE. While the need for accountability, which underscores competition between the organizations, is increasingly being felt, the task of providing these services has become more complicated than ever before. Given the complexity involved in providing aid to disaster casualties today, humanitarian supply chains in relief functions can be stretched to points where they fail. In lay terms, supply chains in disaster relief can fail when they are unable to achieve their intended functions of delivering aid, equipment, manpower and needed supplies to save lives, property and also to alleviate living conditions to disaster casualties in need. Nevertheless, failure of supply chains in disaster relief operations is complex and could result from a variety of sources including climate, and the surrounding environmental conditions in general.

Natural disasters cause deaths and destroy infrastructure with increasing intensity and an unyielding regularity. Knowledge of the increasing number of natural and man-made disasters around the world is no longer new (e.g. Aylwin et al., 2006). Annually, about 500 disasters kill tens of thousands of people, and affect millions more in one way or another (Van Wassenhove, 2006). The irregularity of most natural disasters and their impact on lives and property create difficulties for planning authorities, search and rescue personnel as well as relief and aid workers. According to the EM-DAT disaster database, natural disasters have been responsible for the deaths of over 30 million people since the beginning of the last century. Over the 14-year period since 2000, an average of about 416 natural disasters occurs on a yearly basis around the world. The data also tell of the increasing number of people that are affected by these natural events. However, there has been a dramatic reduction in the actual number of people killed as a result of these disasters since 1990, due to increased planning and forecasting as a result of economic development and improved technology. Yet, pressure on humanitarian and relief supply chains has also been elevated by the escalating magnitude and frequency of the disasters in different places around the world, e.g. Haiti earthquake (2010), Japan tsunami (2011), USA tornadoes and floods (2011), to mention but a few. With rising frequency of disasters, and the corresponding increase in the number of affected people, providing aid to disaster casualties is becoming more complex. This has meant that humanitarian supply chains are becoming longer, moving faster, and going farther into previously unaffected areas. Thus, to succeed, humanitarian and relief supply chains that bring needed supplies into disaster areas need to be dynamic with regards to the environment in which they operate, the type and scale of their operations, and the type of aid they seek to offer. As such, the purpose of this paper is to develop a model for evaluating the probability of failure of relief supply chains in specific circumstances based on historical data (previous operations) while taking into account each supply chain’s characteristics.

Byman et al. (2000) describe NGOs as voluntary organizations that are independent of government control and which seek to provide humanitarian assistance to affected populations according to need. Given the supply chain objectives and activities of large and influential NGOs’ like the Red Cross, Red Crescent, Oxfam, CARE, etc., this paper also tries to investigate how the environment (i.e. external factors that cannot be controlled by the supply chain) affect the efficiency of the humanitarian supply chains that they operate.

While disruption to and performance of humanitarian networks have been discussed within humanitarian relief and aid literature (e.g. Kovacs and Tatham, 2009; Van der Laan et al., 2009; Beamon and Balcik, 2008), not much attention has been paid to what failure entails within relief and humanitarian supply chains, as well as how such failure may be evaluated and dealt with within this literature stream. Studying failure of humanitarian and relief supply chains is important for a number of reasons. For one, since the demand for accountability has been well established and increasingly being discussed within the humanitarian circles (e.g. Reynard, 2000; Wenar, 2006; Kreidler, 2011; Maxwell et al., 2012), data on failure of humanitarian and relief supply chains allow donors (governments, organizations and individuals) to decide when and where to donate so as to be sure that the cause they donate to will be assisted. Second, failure data provide a useful benchmark as well as a database of relief supply chain operations within humanitarian response.

Failure, as a concept, connotes different ideas within different subject disciplines. For example, within production literature, failure and reliability analysis and mitigation perpetuation seek to prevent catastrophic failures of critical systems; and avoid deviation from acceptable performance standards (Mobley, 1999). Reliability analysis, on the other hand, seeks to prevent failure in systems by taking a prospective analysis approach, which offers practical lessons for identifying the sources of failure thus helping to improve their future operations. Conversely, studying failure in humanitarian and relief supply chains usually entails a rather retrospective analysis of the relief supply chain system, where there is usually no possibility of re-enacting a large-scale disaster in order to identify sources of potential failure within the system. Thus, the ability to estimate the probability of failure of relief supply chains in the aftermath of a disaster is crucial not only to customers of the relief chain (which has received much attention lately), but also to the operators as well as the stakeholders of the relief supply chain’s activities. With the customerization of the relief chain, brought about by increased need for accountability within such chains, there is a need to re-assess how relief and humanitarian supply chains should be evaluated, having customers in mind.

Logistics accounts for about 80 percent of the relief operations after a disaster (Trunick, 2005), and remains the backbone and origin of supply chain thinking (Waters, 2003; Kamauff, 2009). Thus, a failure of the humanitarian and relief supply chain can result in catastrophic consequences for the affected populations. Failure analysis therefore is critical in ensuring that relief operations become better over time, while achieving desired objectives more efficiently. Since the terms “humanitarian supply chain” and “relief supply chain” are used interchangeably within humanitarian literature, “humanitarian supply chain” will be used to denote both activities. That is, emergency disaster relief as a result of a present disaster event and emergency response to humanitarian conditions as a result of a disaster from which full recovery is yet to be achieved. Because supply chains, especially relief supply chains, are affected by the environment within which they operate, the characteristics of different natural disasters can exert different effects on the ability of humanitarian supply chains to perform its supposed function.

Section 2 presents a short discussion on natural hazards and the environment, recapping the basic terminology commonly utilized in the discussion of risk within the context of natural disasters. Here, natural disasters are characterized based on a number of criteria depicting a profile that suggests how humanitarian supply chains may be affected by the natural disasters they are responding to. In Section 3, the paper undertakes a conceptualization of failure within humanitarian relief supply chain activity, albeit from a marketing perspective. Section 4 outlines the model specification and data structure, while the simulation process is described in Section 5. Finally, in Section 6 the paper concludes with a discussion of the implication of the results and how its use may be dependent on several factors that are also important to the relief chain.

In 2011, the total number of casualties of major natural disasters (i.e. geological, flood related, drought related, and windstorms) was estimated at over 29,782 from 302 events affecting 206 million people (Guha-Sapir et al., 2013). While the number of people affected by natural disasters run into millions every year, the actual numbers of people killed as a direct result of natural disasters are far less. It is logical to assume that as more natural disasters occur in far removed locations around the world, there will be increasing proportions of casualties. Hence, it is important to appreciate the vulnerability of humanitarian supply chains bringing aid, equipment, manpower and supplies to disaster struck areas. In environmental terms, vulnerability is the degree of loss or damage resulting from a potentially damaging phenomenon. It covers losses of all types and may usually be calculated from experience (i.e. from existing records) and from a risk analysis, e.g. the probability of a flood hitting an area. However, the Center for Logistics and Supply Chain Management, at the Cranfield University (Cranfield School of Management, 2002) suggests that supply chain vulnerability could be seen as an exposure to disturbances emanating from risks within the supply chain as well as risks external to the chain. In this sense, the location where a disaster occurs poses a threat to the humanitarian supply chains.

Thus, relief supply chains do not only have to contend with the disturbances that take place within the chain itself, which have been well documented within business supply chains (e.g. see Jüttner et al., 2003; Chopra and Sodhi, 2004; Giunipero and Eltantawy, 2004; Zsidisin et al., 2004; Zsidisin, 2003). Humanitarian supply chains also have to deal with disturbances from the environment within which they operate. These environmental risks external to the supply chain could be manifest in the form of hazards. A hazard is defined as the probability of change in the environment, of a given magnitude, within a specific time period and occurring in a particular area (Bennett and Doyle, 1997; Ortuño et al., 2013). This is quite different from what a disaster might connote in terms of analyzing the supply chain for risk sources.

Though no generally accepted definition for what a disaster entails has been agreed upon due to the disciplinary dependency of the term (Turner and Pidgeon, 1997), it has been extensively used to describe natural and man-made, sudden, severe and disruptive events, that goes beyond the local capacity of response (Ortuño et al., 2014). Thus, the relationship between a hazard and a disaster is the event itself; for example an earthquake that occurs in the ocean’s depths is a natural hazard occurrence, however, a Tsunami resulting from such an earthquake turns that hazard into a natural disaster where lives, property, livelihoods, etc., are lost. For humanitarian supply chain purposes, it is necessary to introduce these terms in a manner that lends usefulness to its application in the different phases of sudden and disruptive events.

Kovacs and Spens (2007) define the three stages of disaster relief operations (see also Lee and Zbinden, 2003) as the preparation, the immediate response and the reconstruction phases. While it is possible to have these three phases occur within a short period of time, it is also the case that the later phases can stretch for long periods spanning years and some times decades.

Moreover, as the transition from one phase to another is not usually well defined, the three phases could very well represent a general continuum, which for humanitarian supply chain purposes may be classified as hazard analysis, disaster management and humanitarian situation much in the same way as Kovacs and Spens (2007). In addition, a fourth stage called normalcy is introduced. This refers to a stage where the area struck by a hazard exhibits conditions similar to those that were prevalent before the occurrence of the disaster Figure 1.

From the period before the disaster strikes, hazard analysis depicts all efforts at anticipating certain given hazards including taking account of the characteristics of hazards in order to estimate the amount of risk that supply chains would face. Disaster management phase describes the risk for supply chains when the disaster has struck and humanitarian situations refers to areas that have suffered a prolonged effect of a natural hazard so much so that it is unable to attain previous status before the event. The relationship between disaster management and humanitarian situation indicates the possibility of humanitarian situations sometimes falling back into disaster management mode. Finally, normalcy is a return to the status quo before the event, or something close to it. In this vein, supply chain operations in hazard and disaster relief is seen as a cyclical procedure that emphasizes the hazard analysis aspect of a given event as the trigger for the cycle of events that take place once a natural hazard occurs. Since the environment determines how well the supply chain can operate in such situations, it is sensible to consider such cycles and thus risks to humanitarian supply chains in light of the different hazards, as different natural hazards will affect relief supply chain efforts in different ways.

Environmental studies have traditionally been approached from two different perspectives (Bryant, 2005). First, is the perspective that sees environmental studies as a study of the effects of humans on the environment and whether such effect can irreversibly change the environment. This perspective studies the effects of man on the climate and land use practices. The second perspective is one that views natural hazards and phenomena from a religious standpoint as “acts of God.” This view disregards the question of human impact on the environment and assumes such calamities as being beyond the control of man.

The distinction between these perspectives can have implications for the humanitarian supply chain. For example, O’Keefe et al. (1976), Hewitt (1983) and Wisner et al. (2004) suggest that the reaction of a population in the wake of a natural disaster is contextual and mostly more constrained by social, economic and political factors than by the perception of individual risk. Also, Merli (2010) argues that the interpretations of disasters are highly heterogeneous and can be contingent on local-socio historical and ethno-political contexts; of which religion and tradition form large parts of. Bankoff (2004), Schmuck (2000) and Gillard and Paton (1999) argue that religion may be used as a coping strategy in the face of recurring hazards and disasters among religious communities. Prayer is also said to have similar effect in disaster situations (Bankoff, 2004; Mitchell, 2003). And as such, religion cannot be detached from the larger picture of disasters and how affected individuals cope.

Thus, an affected region with the latter perspective would tend to focus on the helplessness of the situation and would be more welcoming to humanitarian supply chains that deliver aid and assistance after such events. On the other hand, a region that holds the former perspective belief about the environment might tend to be more hostile to humanitarian supply chains, even though they bring aid and assistance. They tend to blame stakeholders as being part of the cause of the problem and as such claim a right to aid and assistance.

However, a description of natural disasters can be used to differentiate its characteristics in order to systematically estimate the susceptibility of humanitarian supply chains. Because different disasters exhibit varying characteristics, the vulnerability of humanitarian supply chains may also vary from one natural disaster to another. Bennett and Doyle (1997) characterize natural disasters against seven fundamental criteria; however, six of them are relevant for failure in humanitarian supply chains and include magnitude, frequency, timing, duration, area, and speed.

Magnitude is one of the most popularly used methods of expressing the severity of a natural disaster occurrence and in profiling natural hazards. It is used as a measure of the size or intensity of a natural hazard. Natural hazards occur with varying magnitudes, and maintain a direct relationship to the number of people killed and sometimes to the total number of casualties of a particular natural disaster. Magnitude may be measured by the number of lives lost, as applied in the Bradford disaster scale (BDS) (Keller and Al-Madhari, 1996) which is based on the logarithm of the number of people killed by a certain natural disaster, and by the amount of reinsurable damage caused as proposed by Keller and Al-Madhari (1993). Technically, different scales for measuring the intensity of natural hazards exist and are used in different ways. For example, the Richter magnitude and Mercalli intensity (Modern Mercalli, MM or MMI) scales are seismic scales used to determine the intensity of earthquakes and its aftershocks. The Saffir-Simpson, Fujita and the volcanic explosivity index are used for measuring intensities of hurricanes, tornadoes and volcanic eruptions, respectively.

This is the number of times a particular natural hazard occurs at a certain location over a given period of time, usually 12 months. Frequency has a special emphasis on hazard analysis especially with respect to the area or region in that every occurrence of the event is different and manifested in different ways on the location.

If the frequency is such that events tightly follow each other, then supply chains responding to events within this location can be disrupted, delayed or even detached from other parts of the supply chain. For example, Table I classifies some major types of disasters with respect to frequency according to Alexander (1999).

The particular time of occurrence of certain hazards might follow some regularity so much that it becomes possible to draw temporary patterns of occurrence of a natural hazard. The occurrence of these hazards could also exhibit randomness. For example, hazards such as the hurricanes and tornadoes occurring in different parts of the USA and floods in Bangladesh are based on specific seasonal and climatic events.

This describes the total length of time over which a natural hazards persists, i.e. from when it starts to when it ends.

While natural hazard occurrence could last anywhere from a few seconds to several years (Table II), the number of fatalities from a natural hazard is usually said to be proportional to its duration. That is, the longer the duration of a natural hazard, the higher the likelihood that it will be more devastating, in general. However, for natural hazards with short duration and devastating effects like earthquakes, duration may be less of a factor in comparison to other natural hazards, e.g. volcanic eruptions, floods, etc.

This is the geographical extent or area affected by the occurrence of a natural hazard. The physical space affected by a hazard may vary depending on the magnitude and the duration of the natural hazard. Areal extent is important because it can also be directly related to the magnitude of the disaster. Effects of this profile on humanitarian supply chains will depend to a large extent on the type, magnitude and frequency of the disaster.

The total time taken from the first appearance of a natural hazard to the maximum intensity of the event is used to determine the speed of the natural hazard. Because natural hazards with high speed, e.g. tsunamis that emanate from earthquakes, tornadoes, etc are more likely to result in greater disasters in a short period of time, humanitarian supply chains may not be affected by this characteristic profile of natural disasters, given the absence of other criteria.

While research carried out in this manuscript does not allow for such conclusions relating to the relationships between profiles and the consequent nature of disasters, it is evident that over time, the number of fatal victims of natural disasters has decreased somewhat steadily, albeit at a small rate. At the same time, the magnitude of many natural disaster types has increased over the same period. Coping mechanisms such as education, planning, technological sophistication, increased cooperation in monitoring hazards, etc. are some of the measures that have helped in this regard. What the profiles presented here, however, does is to simply show that the phenomenon we know as natural disasters is highly complex and multi-dimensional; and that we still lack the necessary research base to comprehend a phenomenon of this magnitude and importance.

Failure of humanitarian supply chain can occur in all stages of a relief operation. It can take different forms ranging from poor accountability to management lapses to strategic supply chain disruption. The severity of failure depends on the characteristics of the specific category of disaster event. Several challenges are manifest in trying to define failure in humanitarian/relief supply chains. Affected populations that depend on humanitarian aid and support for basic necessities after a disaster are unlikely to report failure of the humanitarian supply chain operators. As a result of that, humanitarian supply chain operators may be oblivious to the fact that the supply chain has been deficient in some way, and continue working in the same way. Also, lessons of single failure cases may not easily be generalized due to unique characteristics of some cases.

In the hazard analysis stage of preparing for an event, there is usually an inbuilt capacity of the sum total of supply chains anticipated to deliver aid to the area. On the other hand, there is also an anticipated need of assessing the supplies to be required after the occurrence of the event, given as a function of time.

Failure of the relief supply chain can be defined as its inability to deliver all needed supplies, information, and aid to a current disaster location. Similarly, the capacity of the relief chain is the volume of material, information or aid it is able to deliver to the release point per unit of time.

Theoretically, an attempt to estimate relief supply chain failure should incorporate risks manifesting from the stages of the relief cycle mentioned earlier, i.e. hazard analysis, disaster management and humanitarian situations. In the first stage, failure of the humanitarian supply chain can come about as a lack of planning for and anticipation of events which include considering the different characteristics of the most likely hazards and how its impact would affect lives and property. Using recurrence interval probabilities is a popular method of obtaining the most likely hazards. In this stage, the Equation (1) may be used in a modeling capacity to replicate the degree of failure of a relief supply chain.

In the second stage, failure might be encountered in the process of responding to a disaster event. Problems of accessibility (natural or man-made), funding, multiplicity of roles, politics within and between NGOs and governments, profile of the given natural disaster, etc., make up all but one small part of humanitarian supply chain complexity. Because natural disasters can occur in a political space, its anticipation, mitigation and response can very well be political. Political incentives can affect how successful prevention, mitigation and damage from natural disasters are dealt with in a particular location (Cohen and Werker, 2008).

The other part of humanitarian supply chain complexity reflect the characteristic problems of regular business supply chains such as competing goals and objectives, need for cost reduction, complex operating environments, etc. Together, they make humanitarian supply chain operations a very complex undertaking.

The process of determining the humanitarian supply chain failure may be carried out as a continuous process throughout the relief period.

In the final stage, the humanitarian situation stage, probability of failure to the supply chain is somewhat reduced and attention on the event is greatly diminished, and as such the pressure on these humanitarian supply chains are not as intense as those of relief chains. The difference between relief chains and humanitarian chains is essentially the urgency of the relief operation and the attention accorded these two types of situations. Humanitarian situations mostly occur as an antecedent of the inability of a hazard struck area to return to pre-disaster economic and social conditions. In the following section, in trying to operationalize failure in humanitarian supply chains, a new complex variable, the customer, is introduced.

In marketing science, a customer is anyone whose needs are met by a supplier, vendor or seller in exchange for a monetary or other valuable compensation (Kotler and Keller, 2012; Kendall, 2007). Also, anyone who receives products, i.e. goods, ideas or services from a supplier, vendor or seller in exchange for a monetary or other valuable compensation. Customers are external to an organizational unit, and reaching them constitutes the foundation of any business activity. According to marketing’s core philosophy (the marketing concept), the success of every business is founded on clarifying and satisfying the needs and wants of its customers better than other businesses (Kotler and Keller, 2012). Marketing scientists stress that the customer-focus is applicable to both for-profit and not-for-profit organizations, i.e. any organization that has to meet needs and wants of an external group or individuals and that has to compete for resources, customers and account for its success (Kotler and Keller, 2012). Customer-focus has been expanded to include stakeholders, defined as any group or individuals who have an interest in or concern for the success or failure of the organization. Customer satisfaction, service quality and relationship management are among measures of success in dealing with the customer point of view (Grönroos, 2004). To achieve these, organizations must engage in practices that deliver superior value and service to their customers than what other competing organizations or channels can provide, thus enhancing the level of customer satisfaction (Mallik, 2010; Grönroos, 2006; Vargo and Lusch, 2008; Mentzer, 2004; Heskett, 1994).

The increasing proliferation of accountability within humanitarian and relief aid has brought customer issues, such as performance, capability, feedback, etc., to the fore. As a result of this, the operators of humanitarian and relief supply chains are faced with issues that continuously seek to identify and communicate solutions and performance to those customers they are accountable to. As such, customers in such complex set ups like the humanitarian aid and relief chain may be divided into two, where on the one hand customers (upstream) make the orders and provide funding, and on the other hand consumers (downstream) receive and benefit from the orders. Diverse views regarding who customers of a relief supply chain should be pervade recent humanitarian logistics literature. While, for example, Beamon and Balcik (2008) view beneficiaries as customers for purposes of operationally analyzing the logistics function of the aid mission, Oloruntoba and Gray (2006) insist that the effective customer of the relief supply chain remains the donor, mostly because of the erratic nature surrounding funding for relief (Bennett and Kottasz, 2000). Considering the different arguments for and against, there is no right or wrong position to this issue, as focus on what is perceived to be the more important aspect of the relief chain at that point in time should remain paramount. However, failure encompasses the whole relief chain and requires all perspectives to estimate failure in relief supply chains. As such, customers within humanitarian supply chains refer to upstream customers (donors) and downstream customers (beneficiaries). The reason for this is that implementing a successful relief mission requires input from both customers located at opposite ends of the relief chain. Thus, a relief mission, initiated and partly funded by the customer upstream is only accomplished by delivering the necessary items, to the customer downstream. In other words, both customers need to be satisfied, in one way or the other.

Functionally achieving this entails marketing, logistics as well as supply chain management approaches used to integrate suppliers, manufacturers, logistics centers, wholesalers and retailers to create value at the right time, to the right location and in the right quantity, in an efficient manner (Simchi-Levi et al., 2003). The logistics management principle of the 7Rs (the right product, in the right quantity, in the right condition, at the right place, at the right time, for the right customer, at the right cost; Chartered Institute of Logistics & Transport) is strongly related to customer service and the quality of such service. And as such, customer service from a logistics point of view is grounded on the accomplishment of these 7Rs (Mallik, 2010). Therefore focus on customer service within humanitarian supply and relief chains should bear similar importance to any other supply chain within business logistics. However, due to the crisis nature of natural disasters in general, and to some extent humanitarian relief operations, establishing and defining failure in humanitarian supply chains require a streamlining of the 7Rs into three critically important and robust criteria upon which sufficient customer service within humanitarian supply chains may be based, and these include delivering the right product, to the right place, at the right time, henceforth 3Rs. These 3Rs summarize the modern logistics management and marketing approaches to customerization and competitive success. They present a simplified but robust approach to meeting the needs of casualties of natural disasters as fast as possible. In this paper, the 3Rs principle is used as the basis upon which failure in humanitarian supply chains may be determined. This principle in relation to failure in humanitarian supply chains is further developed in the following section.

In order to operationalize and evaluate failure in humanitarian supply chains with regard to the 3R principle, we assume that the success of relief operation entails achieving the three conditions (the 3Rs) simultaneously. It follows that a relief supply chain responding to a disaster can fail in many ways, when at least one of the three criteria is not met. More specifically, there are C(3,2)+C(3,1)+C(3,0)=3+3+1=7 ways a supply chain can fail, with regard to the right product, right place and right time criterion, where C(n, p) “n choose p” denotes the combinations of n objects taken p at a time, (pn). The first term, C(3,2), corresponds to the responses which fulfill two of the three conditions, e.g. right time, right place and wrong material, whereas the second term C(3,1) corresponds to cases where only one condition is fulfilled, e.g. right time, wrong place, and wrong material, and the last term, C(3,0)=1, represents the case where none of the three criteria is satisfied.

Each humanitarian supply chain, e.g. Red Cross, Red Crescent, Oxfam, CARE, etc. has idiosyncratic or intrinsic characteristics that may determine its ability to successfully respond to disaster, beyond the particular circumstances surrounding each relief operation. To account for this, we adopt a fixed effects logistic modeling approach in a Bayesian framework. Letting y_i,k denote the outcome of the kth intervention of supply chain i on a binary scale success=1, failure=0, we assume that:

(Equation 1) 

where p_i,k represents the expected probability of successful response by humanitarian supply chain i at occasion k. The total number of relief occasions is not necessarily the same for all supply chains under study as discussed below. The expected failure probability of supply chain i at the kth relief occasion is q_i,k=1−p_{i, k}. In order to relate the success probability to potential environmental factors while accounting for supply chain idiosyncrasies, we consider a fixed effects linear model on the logit of p_{i, k}. That is:

(Equation 2) 

where (Equation 3) for 0< u<1, X_i,k is the value of the explanatory variable X during the kth relief occasion for supply chain i(i=1, ..., N), and X is an environmental variable such as the infrastructure quality or any other external factor that may affect the success of a relief operation with regard to the 3R criterion. We consider a single predictor for simplicity, but the model can be extended to include as many predictors as necessary, both discrete and continuous.

The fixed effect δ_i captures the ith supply-chain’s proneness to success. Thus, conditionally on δ_i, the success probability of supply chain i when the predictor X takes the value 0 is (Equation 4). The regression parameter β determines how a shift in X from 0 (the baseline value) to 1 affects the success probability of a relief operation for the ith supply chain. More specifically, exp(β) is the factor by which the odds of success vs failure are multiplied as X switches from 0 to 1. For a categorical predictor, X with r>2 categories, r−1 dummy variables are required to represent each category but one set to be the baseline. In this case, exp(β_j) is the factor by which the odds for success vs failure are multiplied as X switches from the baseline category to the jth category, for j=2, ..., r−1, assuming that the first category has been selected as baseline. If the predictor X is continuous, then exp(β) is the factor by which the odds of success vs failure are multiplied when X increases by one unit. Note that, depending on the data at hand and the question being addressed, a model can involve a mixture of categorical and continuous predictors. In any case, care is warranted in interpreting the regression coefficients. For more details, we refer to Gelman and Hill (2007).

To fully account for uncertainty in parameter estimates and propagate it into predictions, we adopt a Bayesian approach (Gelman et al., 2003). Antai and Mutshinda (2010) pointed out the promises of the Bayesian approach in supply chain management and logistics. We place non-informative N(0,100) priors independently on α and β, and independent N(0,1) priors on the supply chain specific (fixed) effects δ_i. The supply chain effects δ_i could be treated as random (random effects) if the relief supply chains under study can be reasonably considered as a random sample from a larger population of similar supply chains. An advantage of such an approach is that the results can be generalized to the larger population. However, random effects estimation requires rich data. Independent variables in regression analysis and ANOVA are generally assumed to be fixed.

The model can be fitted to the data by Markov chain Monte Carlo (MCMC) simulation methods (Gilks et al., 1996) using Bayesian freeware such as WinBUGS (Spiegelhalter et al., 2003) or Open-BUGS (Thomas et al., 2006). Writing a BUGS code is relatively easy (e.g. Mutshinda et al., 2008). Having estimated the model parameters, the probability of a successful response by supply chain i given the state, X, of infrastructure can be evaluated through the inverse-logit function as (Equation 5), where (Equation 6), and (Equation 7), (Equation 8), and (Equation 9) are posterior estimates of α, β, and δ_i, respectively.

By using draws from the joint posterior p(α,β,δ_i∣Data) and repeatedly evaluating p_i, one obtains a posterior distribution of p_i involving posterior uncertainty in the parameter estimates. As we discuss further in this paper, this uncertainty is straightforwardly propagated into predictions.

The number of disaster-relief operations will definitely differ among supply chains. Data unbalance can be handled by adopting the data structure illustrated in Table III, where SC, standing for supply chain, takes values 1 through 4 assuming, without loss of generality, that four supply chains are involved. Letting the categorical predictor X indicating the infrastructure status take the value 1 for good quality infrastructure and 0 for bad quality infrastructure (the baseline), the model can be simply written as:

(Equation 10) 

where (Equation 11), whereas SC_n and X_n are, respectively, the nth values of the vectors SC and that of the predictor X, corresponding to the nth element of the response vector y, and the number of observations is not necessarily the same for different supply chains.

This model can be easily fitted by MCMC through WinBUGS or OpenBUGS as illustrated in the following simulation study.

We use computer-simulated data to illustrate the model implementation. We simulated data for N=3 supply chains, with β set to 1.5 without loss of generality, and the fixed effects for supply chains 1, 2, 3 set to 0.30, 0.10 and −0.50, respectively. Note that in simulation studies, parameter values are assigned arbitrarily. We have chosen positive and negative values whose magnitudes range from relatively small (0.10) to moderate (0.30) to large (0.50), in order to evaluate the ability of our model to identify the signs and magnitudes of the effects. The data involved 55 observations. In order to exemplify the model’s ability to handle unbalanced data, we simulated 26 observations for supply chain 1, 16 for supply chain 2, and 12 for supply chain 3. The vector of infrastructure qualities was simulated from a Binomial(55, 0.5) distribution, which resulted in 29 ones and 26 zeroes. For a given supply chain, say supply chain i, we simulated each response, y, from Bernoulli(p_i), with (Equation 12), and η_i=α+βX+δ_i, based on the assumed values of β and δ_i, for i=1,2,3.

We used MCMC in OpenBUGS to sample from the joint posterior of the model parameters, We ran 10,000 burn-in iterations of three parallel Markov chains starting from dispersed initial values, followed by a further 50,000 iterations, and thinned the post burn-in draws to each 25th sample to reduce the sample autocorrelation.

Figure 2 displays the posterior means (filled circles) and the error-bars (posterior mean ±1SD) of the supply chain fixed effects, with the true values (open circles) overlaid.

The marginal posteriors of the model parameters α and β are summarized in Table IV, and Figure 2 shows the posterior means and the error-bars (posterior mean±1posterior SD) of the supply chain fixed effects, with their “true” values (open circles) overlaid.

Providing posterior means and credible intervals is the best way of presenting the results of a Bayesian analysis since it gives not only point estimates (the posterior means), but also measures of posterior uncertainty around the posterior estimates. Moreover, this way of presenting Bayesian results allows for direct assessment of the statistical importance of the effects by considering as statistically important any effect whose credible interval excludes zero and vice versa.

The results shown in Table IV and Figure 2 demonstrate the model effectiveness at retrieving the “true” parameter values (i.e. the values assumed in the data simulation process).

The posteriors of the fixed effects, δ_i, are a posteriori bell-shaped and essentially centered at true values in all cases, the “true” values are well within one standard deviation from the posterior mean. Despite the relatively large posterior uncertainty in the supply chain effects, δ_i, their posterior means are very close to the true values. The proposed model can be used for a predictive analysis intended for example, to select the best-suited relief supply chain for a pacific disaster. For a particular supply chain, supply chain i say, the posterior predictive distribution of the relief outcome (success/failure) in a specific environment characterized by the value of the predictor variable X can be simulated from by drawing n samples (α,β,δ_i)(j) (j=1, …, n) from the joint posterior p(α,β,δ_i∣Data) and, for each j, generating a binary outcome (Equation 13) with (Equation 14), and η_i=α+βX+δ_i. This produces a sample (Equation 15) from the posterior predictive distributions of interest on which failure analysis can be based. This predictive distribution involves the posterior uncertainty in model parameters, and differential supply chain proneness to success/failure through the fixed effects δ. Note that although failure is our event of interest, we have defined our model so that the success outcome “1” corresponds to a successful response, to avoid confusion.

This study contributes to research and practice in a number of ways. First, based on the perspectives and overall results presented herein, this paper implicitly signifies the coming of age of performance and performance measurement within the discipline of humanitarian logistics and supply chain management. While broad techniques for performance measurement within logistics and supply chain management have been discussed and proposed in literature (e.g. Abidi et al., 2014; Schiffling and Piecyk, 2014; Beamon and Balcik, 2008; Beamon, 1999; Gunasekaran et al., 2004; Giannakis, 2007), this research implies that more specific techniques for measuring performance within humanitarian logistics as well as techniques and methods to identify and collect appropriate data are and will continue to be challenging issues within the supply chain context (Ghadge et al., 2013) and therefore requiring further research. As such, a major contribution of this model lies in the fact that it reduces the number of failure scenarios from 127 within the 7Rs to just seven within the revised 3Rs. This provides humanitarian organizations, as well as government agencies, a parsimonious set of failure scenarios with which they could actually work and control in order to estimate failure in their operations. The implication of this for humanitarian organizations and government agencies suggests that less time and money are expended on such vital estimations as these kinds of estimations for the relief supply chain have been known to be quite tedious and time-consuming. Consequently, the decision-making process for such organizations can be more reliable and transparent, as the data collection within the model, which is binomial and easy, is a continuous process over the entire operation. These basis can serve as useful avenues that may be used to update donors on areas of success and areas where more work needs to be done.

Another advantage of the model presented herein has to do with its lack of normativity. This character of the model allows organizations and institutions the freedom to decide how failure may be defined from, for example, the 7Rs. The ability to modify failure variables to be measured according to current demands, circumstances or requirements demonstrates the flexibility of the model. However, in this paper, the three most important failure variables have been stated as right time, right product and right place. This emphasizes the idea that different failure variables might be important for different humanitarian organizations, agencies and even donors, at different stages and time periods of an operation. The flexibility of the model presented implies that failure can be quickly estimated at different stages of an operation while also continuously changing the failure variables over the entire lifetime of the relief operation. It should also be noted that donors might be interested in specific performance variables within one round of funding, and an entirely different set of variables in a different round.

From a managerial perspective, this research implies that failure in relief supply chains’ response to disaster events signal the potentials and caveats to humanitarian organizations if not properly addressed. These organizations need to show that they are capable of delivering on points upon which funds or support had been sought and received. As the allocation of funds by donor organizations may increasingly depend on the performance of relief agencies, managers should be aware of how such failures may be estimated, monitored and interpreted in order to avoid losing customers.

Finally, this research deals with the task of defining and estimating failure in humanitarian relief supply chains including lives and property, which are issues most typically discussed at all levels of government given the increasing numbers of disasters and affected populations. This work can therefore be useful for policy makers that focus on preparedness for and mitigation of some of these more devastating natural disasters.

However, the model may be criticized for not being totally inclusive as it does not offer any direct implications for donors. The model is directed at relief agencies, government organizations and other NGOs that have a fiduciary responsibility to higher governing bodies or sponsors to act for and on behalf of such sponsors and patrons in a particular matter interest to them. The methodology is intended to make the process of identifying failure within humanitarian relief supply chain operations easy enough for managers and operators within relief organizations to fulfill their obligations to their customers, on both sides of the aisle. Hence, in this vain, based on historical data on supply chain performances in relief operations, the model can go on to help managers and operators of such relief supply chains identify supply chain data that may be best applied to particular circumstances. The Bayesian rule provides a machinery for updating knowledge about supply chain performances in light of new data allowing for real time estimations of failure. And as such, Bayesian inference can be seen as a learning process, where previous posteriors are used as new priors and updated as new data becomes available. In this way, decision making within this setting can always be based on updated information.

In conclusion, failure analysis, here based on the idea of customerization for and within humanitarian/relief supply chains, is critical not only in terms of improving the overall reliability and competitiveness of relief supply chains, but also in terms of securing donor support for subsequent relief activities. In this paper we have operationalized failure in humanitarian supply chains by defining the success of a relief operation following a disaster as the ability to respond to locations of current disaster at the right time, to the right place and with the right product. The addition of “the customer” within this operationalization introduces the consideration of customer service within supply chain management and logistics to the further streamlining of the popular 7Rs logistics principle to a more manageable 3Rs to an already complex process of humanitarian relief via the relief supply chain. We designed a Bayesian fixed effects logistic model that can be used to evaluate the probability of a failed response by a humanitarian supply chain, based on historical records. The model is designed to accommodate environmental covariates that may affect the relief operation. The supply chain specific fixed effects, δ, are introduced to accommodate all latent features that uniquely determine a supply chain’s propensity to fail in its response to a natural disaster, with regard to our 3R principle, while controlling for the physical conditions of the relief operation. We demonstrated the implementation of our model with computer-simulated data, using MCMC simulation through OpenBUGS to sample from the joint posterior of the model parameters. The model proved effective at recovering the true parameter values. The inclusion of supply chain fixed effects provides the ability to account for differential effectiveness across supply chains, which is valuable in predictive analysis for selecting the best-suited relief supply chains in a specific context. The modeling approach proposed here also exploits the fact that considerable information regarding the last-mile operations of the humanitarian/relief chain can be readily applied for failure analysis in humanitarian/relief supply chains, for which attempts have so far been inconspicuous.

A customer orientation had long been implicit in humanitarian supply chains, yet no emphasis and connection to customers had been previously made and operationalized in the humanitarian supply chain literature. The customer focus of non-profit organizations is an emerging field within marketing. The approach presented in this paper may provide insights to managers, operators of humanitarian supply chains, as well as relief organizations on how to mitigate failure and improve their success metrics by focussing on their donors as well as beneficiaries as customers who require certain needs and wants fulfilled by the humanitarian and relief supply chain.

While the model presented is yet to be evaluated with real-world humanitarian supply chains, the methodology and results presented in this paper thus only has an illustrative character, therefore future research work should be directed at methods and techniques with which operators of humanitarian supply chains may go about gathering customer data, both upstream as well as downstream, for use in such analyzes as presented in this paper.