Multi objective optimization for humanitarian logistics operations through the use of mobile technologies

Sets

I

Set of commodities to be distributed

J

Set of CPs

K

Set of LDCs

T

Planning horizon

M

Set of available vehicles

Collecting parameters

$QijA$

Capacity at CP j∈J, for commodity i∈I (m³)

$FiA$

Volume factor for commodity i∈I

$GiA$

Weight factor for commodity i∈I

$IijtA$

Inventory level for commodity i∈I at the beginning of period t=0 at CP j∈J

A_ij

Amount of commodity i∈I obtained at CP j∈J, after performing an expense D_jt to promote donations

$ICijt A$

Inventory cost per unit of commodity i∈I at CP j∈J in period t∈T

Routing parameters

$FmB$

Volume capacity of vehicle m∈M

$GmB$

Weight capacity of vehicle m∈M

$AjkmtB$

${1, ifarc(j, k)canbeusedbyvehiclem ∈M,inperiodt∈T 0, otherwise$

$CjkmB$

Cost of using arc (j, k), with vehicle m∈M

Demand parameters

M_i

Multiplying factor to determine the amount of commodity i∈I required to satisfy the average demand of one habitant per period

P_kt

Number of people attended at LDC k∈K

N_ikt

Demand of commodity i∈I, at LDC k∈K $(Nikt=Mi*Pkt )$

$QikC$

Capacity at LDC k∈K to storage the commodity i∈I (m³)

$CiktC$

Penalty cost per unit of commodity i∈I, not delivered at LDC k∈K in period t∈T

$ICikt C$

Inventory cost per unit of commodity i∈I, at LDC k∈K, in period t∈T

Decision variables

D_jt

Investment at CP j∈J, in period t∈T ($)

(D_jt×a_ij)

Amount of commodity i∈I, collected at CP j∈J, in period t∈T

X_ijkmt

Amount of commodity i∈I, from CP j∈J, to LDC k∈K, in period t∈T

$Iiktc$

Inventory of commodity i∈I, at the beginning of period t∈T, at LDC k∈K

U_ikt

Amount of commodity i∈I, unsatisfied at CP j∈J, in period t∈T

The management of crisis situations through humanitarian aid operations has historically been identified as a critical issue. Extreme and unexpected events such as natural disasters, industrial accidents, infectious diseases, epidemic phenomena and terrorist attacks, among others, pose major challenges to the agencies, companies and volunteer organizations involved in the delivery of critical supplies to the impacted site. Such situations generate extreme and unexpected fluctuations in demand for goods and services, which affect the local and external ability for satisfying such needs.

Given these scenarios, humanitarian organizations face different challenges to deliver the right goods and services to the right people at the right time and under the required conditions (Van Wassenhove, 2006). To achieve such objective, effective communication and decision making among relief organizations is crucial (Palomo-Gonzalez and Rahm, 2008). Such situation is critical, since the availability of supplies, vehicles, personnel, roads, among others, is limited due to the damage caused by the disaster (Barbarosoglu et al., 2002).

Humanitarian logistics operations represent a critical issue in Latin America. Among all disasters that took place worldwide throughout 2010, the earthquake in Haiti represented more than 222,000 casualties, about 39.1 percent of the total population of this country. Another case is the earthquake that took place in Chile in the same year, which generated an economic loss above 30 million USD. On a regional analysis, it can be identified that natural disasters have affected more than 50,319,927 people in Latin America and the Caribbean from 2000 to 2009 (CEPAL, 2011). Also, 75.93 percent of the deaths caused by natural disasters in 2010 took place in Latin America, generating an economic impact above 55 billion USD (Guha-Sapir et al., 2011).

Unfortunately, disaster relief will continue to expand market not only in Latin America but worldwide, as it is forecasted that over the next 50 years, both natural and man-made disasters will increase fivefold (Thomas and Kopczak, 2005). On top of this, and as stated by Oloruntoba and Gray (2006), the amount of research conducted on humanitarian logistics is extremely small and not commensurate with the importance of the subject. The disparity between the level of development on commercial and humanitarian logistics has led researchers and practitioners to adapt analytical formulations originally developed for commercial logistics to the humanitarian context. But most analytical formulations still fail to consider the key features of humanitarian logistics.

The main contribution of this research is to combine the design and development of a multiobjective optimization model with an information system based on the use of mobile technologies, to achieve an effective and timely coordination among governmental, non-profit and private organizations involved in disaster response. To support the decision-making process, the trade-off between economic and social costs faced by these organizations is studied through a Pareto frontier analysis. Also, special emphasis is placed in the context of developing economies through a particular case study considered under this research.

This paper is structured as follows. First, a conceptual background and literature review on humanitarian logistics is stated in Section 2, which includes an analysis of the differences between commercial and humanitarian logistics and the need for development of specific research in this field. Such section also includes a description of the critical role played by information systems in this context, as well as the suitability of mobile technologies for this kind of instances in developing economies. Based on this conceptual background, the multiobjective optimization model developed is presented in Section 3, including the definitions, notation, sets, parameters and decision variables considered. The characteristics, content and structure of the information system developed, and which is based on the use of mobile technology, is also presented. A case study in the Latin American context is presented in Section 4, including specific characteristics and challenges faced under this particular scenario. The main results obtained from the model developed and analytical analyses are outlined in Section 5, which includes a detailed discussion of the conclusions and managerial implications associated to this research. Finally, opportunities for future research based on this work are stated on Section 6.

After a disaster took place, infrastructures have been partially or totally destroyed and supply chains are inoperative. As stated by several authors (Beamon, 2004; Besiou et al., 2011; Dimitrova and Nichev, 2011; Thomas and Kopczak, 2005), humanitarian logistics is related to the collection and transportation of resources and items that provide humanitarian aid, from local distribution centers (LDC) to Points Of Distribution (PODs), including the final delivery to affected population. The aim of humanitarian logistics is to rapidly provide critical humanitarian relief supplies, in order to reduce human suffering and deprivation, as well as to efficiently use the typically scarce resources available (Holguin-Veras et al., 2010). Such activities include preparedness, response, mitigation and recovery after such disaster. Based on these characteristics, it has been identified that the dynamics, features and functioning of humanitarian logistics are significantly different from commercial logistics, where researchers have already developed highly sophisticated analytical models to optimize the various components of modern supply chains (Beamon and Balcik, 2008).

Such disasters can be localized or widespread, such as small tornadoes or floods that impact a small or large portion of a country, respectively. The magnitude of the logistical challenge in terms of the volume of cargo to be transported after a disaster is significant. Such situation presents significant challenges to all organizations involved in humanitarian relief: (1) the establishment of regulatory mechanisms for the coordination and cooperation of each actor involved in humanitarian logistics (Chandes and Pache, 2009; Kovacs and Spens, 2011); (2) the rapid estimation of supply needs once a disaster strikes, as well as the identification of the best ways to distribute the supplies according to the geographic, economic and political conditions of the disaster area (Thomas and Kopczak, 2005; Van Wassenhove, 2006); (3) the selection of distribution centers and their requirements in an emergency situation (Balcik et al., 2008; Beamon and Kotleba, 2006; Rawls and Turnquist, 2009); (4) the pre-establishment of specific locations to be used as warehouse and logistical centers (Chang et al., 2007; Garcia Arróliga, 2009; Sheu, 2007; Van Wyk and Yadavalli, 2011); and (5) the identification and administration of the PODs throughout the critical supply-provisioning stage (Gormez et al., 2011; Jaller and Holguín-Veras, 2012; Lin, 2010; Tejada, 2010).

Several authors have developed analytical models in this vein. Balcik et al. (2008) present a novel model to estimate the number and location of distribution centers, the amount of product to be stored and the necessary paths within the humanitarian logistics network. Salmeron and Apte (2010) proposed the a priori establishment of the capacity and resources needed in humanitarian logistics, through the development of a stochastic optimization model. In 2010, Lin formulated a multiobjective integer programming model that considers distribution centers that provide the location of temporary storage, in order to satisfy known demand points in an attempt to maximize the overall performance. In the same vein, Tejada (2010) proposes a metamodel for the localization and allocation of support operations in response to hurricanes whose occurrence is modeled as a Markov chain, identifying the location of the PODs and the a priori allocation of humanitarian aid supplies.

Gormez et al. (2011) developed a model focused on the localization of centers and PODs in Istanbul, in response to future earthquakes to ultimately minimize the average distance traveled to provide supplies; while Jaller and Holguín-Veras (2012) propose a POD localization model that incorporates social costs such as the distance a victim travels to the proposed POD, the time or level of service during the distribution of humanitarian aid, and the simplicity of the parameters required for the execution of the POD localization model makes it attractive for decision-makers.

The infrastructure and communication systems represent a critical issue, since information is crucial to the performance of any logistics system. Disaster communication planning and timely decision making are activities undertaken by specialists, as they try to foresee operational problems that might occur during an unforeseeable crisis (Mordecai, 2008). However, while information technology is an essential element on the successful operation of humanitarian logistics, these systems by themselves are not enough to guarantee success in decision making. To tackle this issue, and as stated on “wireless technology for social change” (2008), mobile technologies can quickly and informally disseminate information among persons and organizations, since it is a good medium for information sharing both during and in the aftermath of a disaster.

Organizations create value through information sharing and exchange (Rollins et al., 2011). As stated by Setaputra et al. (2010), information technologies facilitate synchronization and integration of an entire supply chain, since information management has an impact on all targets of supply chain management. Even more, the supply chain’s success is dependent on the accuracy and velocity of the information provided by the supply chain members. These are of special importance in humanitarian logistics operations, since effective information systems are one of the backbones to have a successful quick-response program toward a disaster.

Mobile technologies play an important role in communication efforts during the various phases of a humanitarian catastrophe – from the early warning phase through the immediate disaster response and longer-term reconstruction efforts. Some crisis experts have argued that a crisis control center should be mobile or even virtual. A mobile center can be deployed anywhere. You do not have to worry if your facility is shut down, unless the mobile center was at the site of the crisis, which is not the case in most situations that have taken place in Latin America, as well as in other regions worldwide. Reliable communication among various sectors that intervene in relief and aid activities connecting the various places where these activities take place is imperative for the success of any operation.

The need for interoperability of communications systems in disaster response is a well-known problem. It has long been identified as a primary requirement for increasing performance among first-response agencies (Comfort, 2005). The transmission of data, the exchange of information, the confirmation of supply movements, the request for new deliveries and the safety of the teams on the ground − these are only a few of the needs that telecommunications can serve during logistical supply operations. Unfortunately, most efforts on the use of mobile technology in disaster situations have been focused on early warning systems, which is why this research is focused on the development of a decision support framework – represented by a multiobjective optimization model and its corresponding information system based on the use of mobile technologies – to increase the efficiency of humanitarian logistics operations toward disaster response.

The model developed considers specific characteristics in humanitarian logistics operations which are crucial in its decision-making process: the existing collecting points (CP) available outside the disaster site, local distributions centers at the disaster site, demand volume for different items required, available routes and vehicles to deliver items, capacity constraints on vehicles stated in volume and weight, transportation and inventory costs at origin and destination locations, the capacity to collect items to be transported and delivered at the disaster site, among others. A particular contribution of the model developed is that it also considers the so-called deprivation costs, which provide valuable insights for an economic valuation of the human suffering associated with a lack of access to a good or service by the affected population. The analysis includes the identification of an optimal solution under a multicriteria analysis, which provides valuable insights for decision-makers such as enabling efficient computation and ease of implementation.

The following bi-objective model considers two objective functions: first, operating costs, which include shipment costs from CP to LDC, collecting costs at CP, inventory costs at both CP and LDC, and shortage costs; while second, considers social (deprivation) costs incurred by not satisfying demand in a timely manner. Then Pareto front is formed by total operating costs vs deprivation volume which is a convex function and the (normalized) weighted sum method can be used.

Some additional assumptions considered in the model are:

• all of the units that work for civil protection are equipped with mobile devices, mainly laptop computers with satellite connections;

• the data used to run the model is collected onsite by the local devices or the on-the-ground units; and

• the model considers only available data and no uncertainty.

The following concepts, notation, sets, parameters and decision variables are used to formulate the proposed multiobjective optimization model. The definitions presented include assumptions considered on its development.

Locations off the ground, where items donated by society, nongovernmental organizations (NGOs) and government – among others – are collected. Such items will be sent to the place where the disaster took place.

Locations on the ground (at the disaster site) that will be used to receive items sent from CPs and that will be distributed among affected population. It is assumed that the number, location and capacity for both CPs and LCDs are known, which is commensurate with the strategies defined by government agencies as part of the preparation stage toward a future disaster.

In order to estimate demand, it is assumed that a multiplying factor is defined for each kind of item (commodity) considered. It is assumed that such multiplying factor determines the demand per habitant and per period for such commodity. This is also commensurate with current practices developed by organizations involved in humanitarian relief organizations, since the average daily demand required per habitant for such kind of items is estimated and known a priori.

The length of time considered to collect and distribute items to the affected site. Such length is usually defined by the main government office in charge of overall disaster relief operations and depends on the kind of event, location and volume of affected population.

The set of available connections between CPs and LDCs; i.e., the set of available routes that connect locations considered on both sets. Such connections may be available or not, depending on the impact of the disaster over communication infrastructure.

The capability to collect items at a particular CP if an economic expenditure is made to promote donations among the local community, where such CP is located. It represents the capability to receive items donated per each dollar invested to promote donations among the population. Such assumption is also commensurate with practices usually performed by ONGs, local, regional and federal government offices, which invest money to promote significant donations among population located off the ground.

Let costs and deprivation be computed as follows:

The model formulation is as follows:

min (Costs, Deprivation).

Subject to:

The objective function is based on (1) and (2), which consider two objectives to be minimized: (1) considers all operating costs, which include shipment costs from CPs to LCDs, collecting costs at CPs, inventory costs at both CPs and LCDs, and shortage costs; while (2) considers social (deprivation) costs incurred by not satisfying demand in a timely manner. Constraint set (3) keeps track of capacity restrictions at each CP for all commodities obtained from collecting efforts performed. Constraint set (4) presents a balance between: commodities collected at a CP; commodities held on inventory; and commodities sent from each CP to all LDCs. In the same vein, constraint sets (5) and (6) state volume and weight restrictions – respectively – on the vehicles considered. Constraint set (7) computes shortages for commodities not delivered at LDCs, while constraint set (8) guarantees that only available connections between CPs and LDCs are used. Constraint set (9) maintains a balance between units sent and units collected. Constraint sets (10) and (11) keep track of inventory levels according to existing capacity. Finally, constraint sets (12)-(15) correspond to nonnegativity constraints.

As stated in the conceptual background section, an essential part of the planning process toward a disaster includes the deployment and effective use of the best means of communication. In the absence of timely, valid communications, organizations cannot function effectively under the urgent stress of disaster. Individuals are left to make their best guesses about risk and safety, rumors spread wildly, and available skills and resources are overlooked as personnel search hurriedly for workable strategies of action.

The multiobjective optimization model presented takes advantage of data generated and shared through the humanitarian logistics information system (HLIS) described in this section. Table I shows all the information considered under such HLIS, which is commensurate with data required by governmental and NGOs involved in humanitarian response toward a disaster. The data considered was developed in accordance with the Red Cross office in Mexico and Center for National Disaster Prevention in Mexico (CENAPRED) and is also in accordance with data considered by international organizations like the Pan-American Health Organization. Such information system provides the data required by the multiobjective optimization model described above.

The HLIS takes advantage of mobile technologies to generate and share information in a more efficient manner. As shown in Figures 1 and 2, the conceptual design is developed on a platform that allows users and decision-makers to share and consult information through mobile devices. In particular, Figure 1 shows some of the initialization screens, while Figure 2 shows examples of the screens created to capture and consult the information described on Table I.

In the same vein, Figure 3 illustrates the links for communication generated among all actors and parties involved in humanitarian relief. One of the main advantages arises on the fact that such communication can be performed in a timely manner through the use of the best means of communication at disposal. Once the information is generated, the system exports such data to spreadsheets, in order to be used on a program developed on GAMS© as part of this research. Such program performs a Pareto analysis that can be used by stakeholders involved in the decision-making process toward humanitarian logistics operations.

The system has been designed to be used by governmental entities, mainly local Civil Protection. Regarding that time in case of disasters is crucial, the model elaborated is not time consuming, considering that an natural made, sudden onset hydrometeorological disaster is in the order of days, it can be run in the computers on-site and updated to a main server located at Civil Protection Base in 30 minutes on average. For the study case presented, the planning horizon is three days, then we consider that 30 mins in a HP ProBook 6470b with Intel i5 (3.1 GHz) processor featuring vPro technology, a 500 GB hard disk and 4 GB working memory is appropriate.

In Section 4, a case study in the Latin American context is described, where the multiobjective optimization model and HLIS developed were validated on an instance provided by governmental organizations involved in humanitarian logistics response.

The application of the developed model was to a town located in the Acambay de Ruiz Castañeda municipality in the State at Mexico. This town has 4,422 inhabitants and is located at 2,456 meters above sea level. The presented situation is the case of flood, the instance was real and consequence of a natural disaster. The characteristics of this instance are outlined below.

Five CPs are considered, which collect and sent commodities required at two LDCs at the disaster site. All CPs can perform shipments through road, except for CP(2) – which is not reachable by land because of a damaged bridge that connects to the disaster site – and CP(5) – which cannot reach the disaster site by land because a mountain separates it from the disaster site. Three different kind of land vehicles are considered, as well as one kind of aircraft. Capacities in volume and weight are known for all vehicles and the aircraft considered, while two of the roads (connections) considered can only be traversed by one specific kind of vehicle.

Predefined LDCs have information about daily requirements of the commodities considered for the affected population in their corresponding areas (defined during the preparation stage toward a disaster), which are used as a basis to compute the estimated daily demand at each area. In particular, three kind of commodities are considered on this instance, which correspond to basic kits for: first, food and water; second, personal hygiene; and third, medicines. Commodities are grouped into these kits, such that each one provides the average daily requirements for an entire family at the disaster site.

Given the kind of event considered, deliveries are performed every three days during a 15 days term, during which information is generated and shared through the HLIS developed. Figure 4 shows an illustration of the instance considered.

The weighted objectives method it used to solve the bi-objective model presented in Section 3.1 with the goal of vary the assigned weight to each objective and find the solution curve of the model:

• Step 1. The model is evaluated for one of the objectives, obtaining the optimal value, in this case the objective “Deprivation” represented by (F₁) and at the same time the lower bound of the objective “Costs” (F₂) is obtained.

• Step 2. The procedure is repeated, but now the objective of the model is the “Costs” function.

• Step 3. The results are entered in a spreadsheet and the parameters showed in Table II are obtained.

The right section of the table indicates the notation to he used to express the structure of the new objective function. The instance considered is analyzed under a weighted multiobjective criteria, with a starting value β=0.5 for the objective function considered:

The parameters I_i are the resulting optimal solutions of evaluating the model based on the function F_i; what is done the considered optimal value is subtracted to the F_i function, i.e. the distance from 0 to the minimum found for that function and is divided between the real path of the feasible solutions through the division times (AI₁−I₁). With this the weight affects the solution that has as a base the optimal result or the goal result of the model.

Where β is the weighting factor that can have a value from [0, 1], subsequently the mathematical model is evaluated with the variation of this factor and the optimal solutions curve for that particular scenario.

Under a β=0.5 value, total cost is 66,752.98 USD, and the deprivation volume accounts for 34 percent of total demand; i.e., 1,777 kits out of 5,162 required. Figure 5 shows the behavior for the total operating cost and deprivation functions, for 0⩽β⩽1, which allow decision-makers to identify the changes on such costs under different preferences among both objectives.

In the same vein, the ranges for the weight assigned to each objective where the best results are obtained are identified. Figure 6 shows the results obtained for the deprivation cost function, where the best values are obtained in the range [0.4, 0.7] for its weight. Under the range [0, 0.4] the model does not achieve a significant improvement; however, a stable value is observed above 0.7, which corresponds to the best (minimum) shortage reported on the demand required to be satisfied.

Figure 7 presents the same analysis for the total operating costs. Based on both graphs, it can be said that the best behavior can be found above 0.3 and 0.4, respectively. Both graphs present satisfactory results on the [0.3, 0.6] range. Above 0.7, none of the graphs present significant improvements on their respective objectives. Based on this kind of analysis and the weights assigned to each objective – which will depend on the kind of event and the impact generated – organizations involved can support its decision-making process toward humanitarian logistics operations.

In the lines below, a sensitivity analysis is performed on the case study considered. Such analysis includes: changes on transportation costs and the corresponding impact on the efficient solutions curve; where each curve is created through 20 points which correspond to results obtained under variations for such values; and changes on penalizations incurred for unsatisfied demand (deprivation cost), where three different functions are considered: a constant value for such penalization; a linear increase under a 1.2 value; and an exponential increase for such penalization. Such scenarios were defined in accordance with CENAPRED.

Figures 8 and 9 present results for both scenarios, respectively. In particular, variations up to 10 percent (0.9, 0.93, 0.96, 1, 1.03, 1.6, 1.1) on transportation costs were considered to develop Figure 8, which shows the extreme values for such range (0.9 and 1.1) and which correspond to the greatest changes on total cost under this analysis. In the same vein, Figure 9 presents the corresponding study for the deprivation function under the three penalizations considered, while the optimal solutions curve is shown on Figure 10. Based on such graphs, decision-makers can identify the best scenario to support the logistics strategy for humanitarian relief.

Even though the field of commercial logistics is large and constantly growing, the need for humanitarian management is increasingly recurrent. However, commercial logistics has specific characteristics and needs that make it different from closely related disciplines. This investigation helped identify: the particularities of humanitarian logistics; the existence of specific analytical models for the coordination and distribution of critical supplies at an impacted site; the difference between the resource requirements and the availability of the resources as a constant in humanitarian work; the need for proper management of the humanitarian distribution chain both to mitigate human suffering and to optimize the available resources for the effective management of humanitarian supply chains; and the advantages on the use of mobile technologies to generate timely and reliable information to support multiobjective optimization models like the one presented on this research.

In particular, this study presents a multiobjective optimization model and its corresponding information system – based on the use of mobile technologies – to support humanitarian logistics operations toward disaster response. The model developed considers CP, distribution centers at the disaster site and the corresponding demand for several commodities, available routes, and a collection rate to collect items at locations off the ground. The model considers two objective functions: total operating costs, which include shipment costs from CP to LDC, collecting costs, inventory costs at both locations and shortage costs; while the second objective function considers social (deprivation) costs incurred by not satisfying demand in a timely manner. The model developed takes advantage of information generated through the use of mobile technologies.

Based on the above, the optimization model developed considers the particularities of humanitarian logistics, the deprivation costs associated to the timely delivery of critical supplies, the need to make optimal use of scarce resources, and the modeling of all possible scenarios at the stage of provisioning for the population affected by a disaster. The existence of an optimal distribution plan was outlined. A case study in the Latin American context was also presented, including specific characteristics and challenges faced under this particular scenario and managerial implications, ease of implementation and enabling efficient computation to support decision-makers involved in such operations.

This study has limitations that need to be addressed and which open avenues for further research. The first limitation is on the linear functions considered for deprivation functions, since there may be some instances where the deprivation cost may not be a linear function over time. The second limitation is on defining measures for the specific role played by stakeholders involved in humanitarian logistics operations, since this kind of activity – in comparison to commercial logistics – may have several organizations and people involved in humanitarian relief, which may take charge of specific activities that need to be measured and controlled on an overall basis.

The use of mobile technologies to generate timely information in humanitarian logistics operations is a key issue. Such information can support optimization models in humanitarian logistics operations in an effective manner, since such technologies play an important role in communication efforts during the various phases of humanitarian catastrophe. This is of special importance in developing economies like the ones in Latin America, since reliable communication among various sectors that intervene in relief and aid activities connecting the various places where these activities take place is imperative for the success of any operation. The transmission of data, the exchange of information, the confirmation of supply movements, the request for new deliveries, and the safety of the teams on the ground, these are only a few of the needs that telecommunications and optimization models can serve during humanitarian relief operations.