Pre-positioning relief supplies in Brazil through location decisions

Transcription

1 Pre-postonng relef supples n Brazl through locaton decsons Irneu de Brto Junor Department of Producton Engneerng, Unversty of Sao Paulo Department of Logstcs, FATEC Jessen Vdal S J Campos, Adrana Leras Department of Industral Engneerng, Pontfcal Catholc Unversty of Ro de Janero Hugo Tsugunobu Yoshda Yoshzak (hugo@usp.br) Department of Producton Engneerng, Unversty of Sao Paulo Graduate Program n Logstcs Systems Engneerng, Unversty of Sao Paulo Abstract In humantaran logstcs, specfc goals not only mnmzng costs should be consdered. Consderng eght dsaster scenaros, ths work ams to defne locatons for pre-postonng dsaster relef supples through a two-stage stochastc model wth coverage constrants based on dstrbuton costs, penaltes for unattended demand, dsruptons n hghways, and meda nfluence. Keywords: humantaran logstcs, faclty locaton, stochastc optmzaton Introducton Clmate change has caused several natural dsasters n recent years and forecasts estmate that over the next 50 years, natural and man-made dsasters wll ncrease fvefold n number and severty (Thomas and Kopczak 2005). Many recent events have demonstrated the vulnerablty of socetes, such as the tsunam and the earthquake n the Indan Ocean n 2004 and n Japan n 2011, hurrcanes n the Carbbean, earthquakes n Pakstan n 2005, n Hat and Chle n 2010 and a typhoon n the Phlppnes n These events and ther consequences llustrate how challengng the response to extreme events s (Holguín-Veras et al. 2007). The large number of vctms and the unpredctable nature of such events make humantaran operatons crtcal for dsaster management, and one of the man ways to mprove the tme, cost, and qualty of relef operatons (Blecken et al. 2009). The agle and effectve moblzaton and utlzaton of resources s essental to assst vctms. (Bozorg-Amr et al. 2013). The shortage of materals or neffcent resource management can compromse the emergency response ncreasng sufferng (Holgun-Veras et al. 2013). It s hence mportant to develop strateges for preparedness and response. Operatons n many humantaran crses stll have ther management models establshed on prncples of mltary and governmental organzatons, based on the "just n case" phlosophy, due to the lack of alternatve supply n tmes of crss (Natarajarathnam et al. 2009). The ncrease n the number of people affected by natural (hurrcanes, floods, earthquakes, tsunams) 1

2 and anthropogenc dsasters (terrorst attack, technologcal or nuclear accdent) has requred major management efforts from relef organzatons and emergency operaton teams. Several studes under a global perspectve have been developed to mprove ths response, demonstratng the mportance of humantaran logstcs (Beamon and Kotleba 2006, Thomas 2004, Van Wassenhove 2006). In Brazl, floods occurred n the Itaja valley n 2008, São Luz do Paratnga n early 2011 and n Esprto Santo n 2013, n addton to catastrophc landsldes n Ro de Janero n 2011, and caused thousands of vctms. In southeastern Brazl, there are also predctons of ncreased frequency as a result of global warmng (Fapesp 2011). Therefore, takng preventve measures s necessary, ncludng locaton and pre-postonng of relef supples. In the network confguraton, the strategy for locatng, along wth the humantaran logstcs supply chan, s characterstcally relevant to the response tme of a dsaster (Balck and Beamon 2008). Faclty locaton decsons affect the performance of the emergency relef operatons n dsaster, snce the number, locaton of dstrbuton centers and the amount of supply relefs theren drectly affect the response tme and costs observed along the supply chan. Relef supples are basc elements for affected people to have access to food and hygene products n the frst moments after the dsaster. The aglty and readness n the dstrbuton of these tems are necessary, especally n the frst 72 hours after the event (Salmerón and Apte 2010), so that rescue teams begn the actvtes and the vctms can thus stablze ther lves. Also ncluded are materals requred for relef teams (response) to act mmedately after the event. Ths paper proposes a methodology to support the decson on where to locate relef supples facltes. An applcaton n Brazl llustrates the effectveness of the proposed approach. Addtonally, as a result, an analyss of the Brazlan Cvl Defense strategy and the current nfrastructure for dsaster response s made. Through a two-stage stochastc optmzaton model (Dantzg 1955), stes are evaluated for nstallng dstrbuton centers (depots) for these materals. Ths optmzaton process results n proposng locatons that mnmze the operatonal total cost through openng or not relef supply depots consderng openng costs, and penaltes for unmet demand. Constrants can be grouped as capacty (storage and transport), avalable materals (nventory, donatons and purchases) and mnmum level servce (mnmum met demand and coverage. Uncertanty s a characterstc of dsasters and s ntroduced n the model through scenaros based on dsaster severty and magntude whch affect the demand of relef supples, meda coverage that nduce the amount of donatons sent by the populaton n general and accessblty ruptures n some hghways. Specfc characterstcs of humantaran logstcs operatons, such as product allocaton that may be purchased under contracts prevously negotated and establshment of constrants for ruptures n the transportaton pathways that restrcts capacty are presented. A detaled analyss on how to assgn penaltes for unmet demand based on the behavor of the model s also presented. To mplement the model, demand for humantaran ad supples s defned accordng to nternatonally agreed concepts, usng hstorcal data of Agences and also based on the rsk mappng conducted by muncpaltes; freght rates accordng to the dstance from the ste; and penaltes for noncomplance demand. Seventeen relef supply materals for the vctms and rescue workers were consdered. These materals are necessary for rescue and relef n the frst hours after a dsaster and are avalable at the locatons defned by the model for storage. Fnally, the Brazlan Cvl Defense strategy for the current dsaster response nfrastructure s analyzed to verfy the capactes and the coordnaton systems. 2

3 The mathematcal model The goal of the model proposed s establsh the locaton of one or more permanent dstrbuton centers for storng relef supples for the vctms of dsasters that may occur n a regon. The problem s modeled as a two-stage stochastc optmzaton model and s based on papers by Mete and Zabnsky (2010) and Rawls and Turnqust (2011). Uncertanty s ntroduced through scenaros. Specfc characterstcs of humantaran logstc operatons - such as purchases of relef supples prevously negotated, places for materals screenng and warehousng used only n cases of dsasters (ncdental), dsruptons n route access - are ncluded. Fgure 1 llustrates the structure of the model: Fgure 1 - Model structure The ndex sets employed are I: canddate dstrbuton centers ( Є I), K: relef supples (k Є K), J: demand ponts (j Є J) and C: scenaros (c Є C). The frst stage decsons are represented by varable X, whch equals 1 f the dstrbuton center s opened, 0 otherwse, and the decson varable S k that s the average nventory level of supply relef k at dstrbuton center (kg). The parameters are the annual cost of nstallaton and operaton of dstrbuton center - g (BRL$ - Brazlan Real); the amount avalable of supply k - e k (kg); maxmum regular storage capacty of k n dstrbuton center - l k (kg); mnmum annual nventory of k n dstrbuton center - ne k (kg); qd max and qd mn ; maxmum and mnmum number of dstrbuton centers to be opened and the bnary that assumes 0 f the dstance s greater than the maxmum dstance, and 1 otherwse (coverage matrx) a j. The frst stage of the model s: mn [ ( )] (1) Subject to: k (2) (3) 3

4 (4) (5) (6) (7) The objectve functon (1) mnmzes the (operatng cost of dstrbuton centers) + (expected value of the soluton of the second stage functon). Constrant (2) establshes that, for an tem k, the amount stored at every dstrbuton center cannot exceed the maxmum amount avalable, (3) lmts the nventory level by the capacty of dstrbuton center, (4) lmts the mnmum nventory of tem k to open a dstrbuton center. Constrants (5) and (6) lmt the number of dstrbuton centers to be opened and (7) ensures the mnmum dstance from the pont of demand to, at least, one dstrbuton center. In the second stage, decson varables are the amount (kg) of k to transport from dstrbuton center to pont of demand j, under scenaro c ( ); the unmet demand (kg) of k, at pont j under scenaro c ( ); amount of k (kg) purchased, allocated n dstrbuton center, under scenaro c ( ) and an auxlary bnary varable to make purchases only f k s necessary ( ) The parameters are: transportaton cost (BRL$/kg) from dstrbuton center to demand pont j under scenaro c ( ); penalty per unt of k (BRL$/ kg) not suppled to demand pont j under scenaro c ( ); amount of donatons of k (kg) receved n dstrbuton center under scenaro c ( ); demand of k (kg) n demand pont j under scenaro c ( ); bnary parameter regardng the accessblty of dstrbuton center (1 - accessble, 0 not accessble) under scenaro c ( ), ncdental storage capacty of k n dstrbuton center under scenaro c ( ); transportaton capacty by weght ( ) and by volume (m 3 ) ( ) from dstrbuton center to demand pont j under scenaro c; mnmum demand (kg) of k to be suppled at demand pont j, under scenaro c ( ) and contractual lmt (kg) establshed for purchases of k, under scenaro c ( ). Other parameters are the weght x volume (m 3 /kg) converson factor ( ) and a large number to make purchases of supples k only f necessary ( ). The second stage of the model s formulated as: ( ) ( ) (8) j Subject to: (9) (10) 4

5 ( ) (11) (12) k (13) k (14) b ( ) (15) b (16) b ( ) (17) (18) (20) (19) (21) { } (22) The objectve functon (8) mnmzes the (transportaton cost under scenaro c + penalty for unmet demand under scenaro c). Constrant (9) ensures that relef supply k be transported from to demand pont j s avalable at. Constrant (10) calculates the unmet demand of k n j under scenaro c. (11) ensures that relef supply k be transported from to demand pont j s at the dstrbuton center opened by x wth suffcent capacty (regular + ncdental). Constrants (12) (13) ensure the transport capacty by weght and volume of supply k, (14) ensures that a mnmum demand of k at demand pont j s met. Constrants (15) to (20) are employed for the purchase process: (15) establshes a condton for purchasng relef supples k f Demand - Inventory Donatons > 0 (CO_AUX = 0) and (16) defnes when no purchase s requested f Inventory + Donatons Demand > 0 (CO_AUX = 1). Constrant (17) defnes purchase of relef supply k only f CO_AUX = 0. (18) ensures that the purchase of supples k s allocated to the dstrbuton center opened by x. (19) ensures that the total purchase of supply k allocated to each dstrbuton center does not exceed the contractual total amount under scenaro c and (20) ensures that the purchase of supples k s performed only after the consumpton of the nventory and the donaton receved n. Constrants (21) and (22) defne non-negatvty and bnary varables, respectvely. Case study The optmzaton model proposed s appled to the Paraba Valley case (Sao Paulo State - Brazl) to evaluate the technques used and the results. Ths regon of two mllon nhabtants was chosen manly because t s a regon prone to natural dsasters and also because of the hstorcal data and geographc nformaton avalable. 5

6 Fve local canddates to dstrbuton center locaton are consdered: São Paulo, Caçapava, São José dos Campos, Taubaté, and Tremembé. These stes were chosen because they already have Cvl Defense operatons and are stuated n locatons wth a few accdents hstory, thus less lkely to rupture. Fgure 2 llustrates the regon: Fgure 2 - Paraba Valley Map The scenaros: The scenaros were establshed accordng to the severty and magntude of dsasters (medum, large, and catastrophe). Small dsasters were not consdered because the communty tself overcomes ts consequences, thus not requrng relef supples. In addton, the dsclosure n the meda was consdered at two levels: low or large. The meda plays a key role, especally n moblzng volunteers and donatons snce the meda representaton nfluences people's percepton of the urgency and people, n natural dsasters, are more wllng to donate than n man-made dsasters (Zagefka et al., 2011). However, meda s organzed as for-proft enterprses and carefully choose the most proftable topcs (Coronel, 2010) and needs could go unnotced when the meda fals to expose them because of competng headlnes. Another consderaton s dsrupton possbltes whch may affect the accessblty of supply channels to affected stes, changng the costs of transport and supples. To establsh scenaros, probabltes were estmated based on experts panels (Salmerón and Apte 2010). The probabltes were estmated usng the Delph method manly due to anonymty, because among specalsts there was functonal herarchy, whch could nfluence opnons. Experts n Cvl Defense, Dsasters, Geology, Meteorology, Archtecture, and Journalsm took part of the panel. Table 1 shows the probablty of scenaros Dsclosure Table 1 - Probablty of scenaros Dsaster magntude Medum Large Catastrophe Low dssemnaton by meda 24.00% 8.11% 1.00% Hgh dssemnaton by meda 26.44% 15.33% 7.33% Hgh dssemnaton by meda and ruptures 0.00% 13.56% 4.22% 6

7 Results and dscusson Settng the penaltes A careful analyss of penaltes was conducted. Penaltes for unmet demand s establshed through calbraton of the model (Mete and Zabnsky 2010 to verfy the mpact of ths parameter on the results. In ths work, the man goal of ths calbraton s to assure that shortages wll only occur due to the constrants of the model, preventng vable non-supply. In ths work penaltes are consdered the same for all products, and the transportaton cost was chosen as the ntal reference. The hgher cost of transportaton between locatons, the lower the lmt ntally establshed, because below ths value, the model can allow shortages n the locaton, snce the cost of supply s lower than the transportaton cost. Based on growng values, the model was verfed and the results behavor was observed from 1 to 10,000 tmes the hghest transportaton cost. Smlar analyss was conducted by Barbarosoglu and Arda (2004), especally regardng unmet demand and values of EVPI and VSS. Fgure 3 llustrates the model behavor for the number of deposts opened and the shortages due penaltes. Fgure 3 Opened depots and penaltes Note that even n the range 1-3 tmes the hghest transportaton cost, the model enables shortages due to the fxed cost. The coverage constrant requres openng at least 2 locatons; however, relef supples were not dstrbuted. In an analyss of the shortages behavor, low values for penaltes n scenaros wth hgher demand, more dstant locatons were not suppled. In scenaros wth lower demand, dfferences n allocaton occurred, but the total shortage level dd not change. Consequently, 3 tmes hgher transportaton cost was the lower lmt set for penaltes. From ths value, the unmet demand remans stable untl one more depot s opened, whch occurs between 500 and 600 tmes. These fndngs ndcate that even at ths level there were constrants preventng avalable materals from beng used. Noyan (2012) hghlghts that the EVPI - Expected Value of Perfect Informaton and the VSS - Value of the Stochastc Soluton (Brge and Louveaux 1997) are the two best-known performance measures of stochastc soluton. Observng the behavor of EVPI and VSS allows verfyng that the EVPI, from 95 tmes the hghest transportaton cost, has an upward trend and then falls agan. Ths result s due the WS (wat-and-see) soluton used for calculatng the EVPI opens depots by scenaros. From penalty equal to 95 tmes the hghest transportaton cost, openng depots n some scenaros s started, ncreasng the dfference of fxed costs between the soluton obtaned under uncertanty (recourse problem - RP ) and the WS soluton Ths openng of deposts ncreases untl the thrd depot s opened by stochastc soluton (RP). From ths pont, 7

8 the declne of percentage value of EVPI (absolute value remans) s observed. The VSS has a logarthmc trend wth varatons n ths trend n the ponts of open depots. Ths s because n all the cases the determnstc soluton opens only 2 deposts. Fgure 4 shows the behavor of total open deposts (RP soluton) and EVPI and VSS. Fgure 4 VSS and EVPI and open depots It s possble to assume that the penalty between 3 and 95 tmes the maxmum value of the transportaton cost produces equvalent results. For further analyss, we set ths value at 95. Changng ths value as well as the pattern used s evaluated n senstvty analyss. Results The model was mplemented usng the software AIMMS 3.13, CPLEX solver 12.5 Intel Core Core 2 Quad Q9650 CPU 3GHz, 4 Gb RAM, 32-bt operatonal system Wndows7. and spent 39s to solve all nstances (stochastc, wat-and-se, determnstc, and modfed stochastc). The determnstc soluton was obtaned usng the weghted average of the parameters to a 5-year horzon. Dfferently from the determnstc soluton, the stochastc soluton shows the values obtaned and that the penaltes (95 tmes the transportaton cost) strongly nfluence the results due to the shortage of materals. Ways of mprovng the results are possble, manly through adjustments and relefs n the constrants, especally n warehouse capacty; however these results are therefore closer to the real case, especally n the occurrence of a catastrophe. Table 2 shows the results of determnstc and stochastc models. Table 2 - Results of the determnstc and stochastc models Determnstc (BRL$) Stochastc (BRL$) Fxed Cost to open depot 80, , Transportaton costs 17, , Penaltes costs 4, , Total cost 102, , Dstrbuton centers opened São Paulo Tremembé São Paulo Tremembé 8

9 Shortages occurred n all the scenaros. In some scenaros, albet pre-postoned, the purchased materals and donatons were enough to supply, yet they were not completely used specally due to constrants of capacty of deposts. The lowest relatve cost s the transportaton, whch justfes the mnmum openng depots. Performance measures of stochastc soluton The result for EVPI was 0.01% the VSS 4.23% for penaltes equal to 95 tmes the hghest transportaton cost. In the worst case, when penalty s 600 tmes the hghest transportaton cost, EVPI was 3.07%. Takng nto consderaton n whch the smaller the EVPI value, the better the soluton s, and the hgher the VSS value, the better the soluton, based on these values, EVPI can be concluded to provde good results n accommodaton of the uncertantes and, the behavor of VSS s compatble wth the humantaran logstcs lterature because the VSS value depends and ncreases n functon of the value of the penaltes. Smlar behavor of VSS was also obtaned by Noyan (2012) who acheved 54.05% to for EVPI and 0.84% to 5.41% for VSS and Salmerón and Apte (2010) who obtaned EVPI between 24% and 25% and 47% for VSS. The percentage values are relatve to the WS soluton. Unmet demand analyss For each scenaro, the reasons for shortages were evaluated. The materals were analyzed accordng to the user type (vctms or rescue teams), because there were no donatons of the tems for the rescue teams. The results show that for small dsasters and medum dsasters wth meda dsclosure scenaros, shortages happened only n rescue teams relef supples due to nsuffcent amount of materals. In such cases, purchases were made untl the upper lmt, but were not enough to meet the demand. In medum dsasters wth low meda dsclosure scenaros, shortages occurred for all users not only due to the amount of materals avalable but, n some cases, even wth materals n suffcent quantty or able to be bought, constrants on storage capacty dd not allow these materals to be used for assstance. In catastrophe scenaros, shortages occurred specally due to constrants n storage capacty. Donatons reduce the materals shortages for the populaton, but these relef supples were not used for assstance. Conclusons Based on papers by Mete and Zabnsky (2010) and Rawls and Turnqust (2011), ths work presented a model to support pre-postonng dsaster relef supply decsons n Brazl through stochastc mathemathcal modelng. Specfc features of the humantaran operatons, such as emergency purchases and route dsruptons were added to the model. The model performance was evaluated accordng to EVPI and VSS measures. An approach to assgn penaltes based on the behavor of the model through EVPI and VSS ndcators was also performed. The results show that as the magntude of the dsaster ncreases, not only the materals avalablty but coordnated actons and decson-makng should be more effectve. Transportaton plannng and locatons that allow logstcs actvtes, such as screenng and storage of materals to respond to a dsaster, are necessary. Consderatons about human sufferng (Holgun-Veras et al. 2013) and varaton of parameters (Balck and Beamon 2008) were performed to analyze the behavor of the model n these stuatons. The fndngs also provded analyss of the Brazlan Cvl Defense (Brazl, 2012) whch s structured based on the muncpal level wthout a regonal approach. The preparedness 9

10 and response plans are arranged by the ctes; however, as assessed by the model, n major dsasters and catastrophes, physcal structures n affected ctes could be dsrupteda regonalzed approach to the strategc plans for dsasters preparaton and response, encompassng more alternatves of supply ponts and mutual assstance between ctes, s recommended. Acknowledgments The authors would lke to thank CAPES, Mnstry of Educaton of Brazl, Brasíla, and the Vanzoln Foundaton, São Paulo, Brazl. References Balck, B., B. M Beamon Faclty locaton n humantaran relef. Internatonal Journal of Logstcs: Research and Applcatons 11 (2): Barbarosoglu, G., Y. Arda A two-stage stochastc programmng framework for transportaton plannng n dsaster response. Journal of the Operatonal Research Socety 55 (1): Beamon, B. M., S. A. Kotleba Inventory management support systems for emergency humantaran relef operatons n South Sudan. The Internatonal Journal of Logstcs Management 17 (2): Brge, J., F. Louveaux Introducton to Stochastc Programmng. Sprnger-Verlag, New York. Blecken, A., B. Hellngrath, W. Dangelmaer, S. F. Schulz A humantaran supply chan process reference model. Internatonal Journal of Servces Technology and Management, 12 (4): Bozorg-Amr, A., M. S. Jabalamel,, S. M. J. Mrzapour Al-e-Hashem A mult-objectve robust stochastc programmng model for dsaster relef logstcs under uncertanty. OR Spectrum. 35 (4): Brazl, Le nº , de 10 de abrl de Polítca Naconal de Defesa Cvl (Cvl Defense Natonal Polcy). Brasíla. Coronel, S. S Corrupton and the Watchdog Role of the News Meda. Norrs, P. (ed) Publc sentnel: news meda & governance reform. The Internatonal Bank for Reconstructon and Development / The World Bank. Washngton, DC, Dantzg, G Lnear Programmng under Uncertanty. Management Scence 50 (12) Supplement: Fapesp Sudeste terá mas tempestades. Agênca de notícas da Fundação de Amparo a Pesqusa de São Paulo. Avalable at (accessed date August 10, 2011). Holguín-Veras, J., N. Pérez S. Ukkusur, T. Wachtendorf, B. Brown Emergency logstcs ssues mpactng the Response to Katrna: a synthess and prelmnary Suggestons for mprovement. Transportaton Research Record 2022: Holguín-Veras, J., N. Pérez, M. Jaller, L. N. Van Wassenhove, F. Aros-Vera On the approprate objectve functon for post-dsaster humantaran logstcs models. Journal of Operatons Management 31(5): Mete, H. O., Z. B. Zabnsky Stochastc optmzaton of medcal supply locaton and dstrbuton n dsaster management. Internatonal Journal of Producton Economcs 126 (1): Natarajarathnam, M., I. Capar, A. Narayanan Managng supply chans n tmes of crss: a revew of lterature and nsghts. Internatonal Journal of Physcal Dstrbuton & Logstcs Management 39 (7): Noyan, N Rsk-averse two-stage stochastc programmng wth an applcaton to dsaster management. Computers & Operatons Research 39 (3): Salmerón, J., A. Apte Stochastc Optmzaton for Natural Dsaster Asset Prepostonng. Producton and Operatons Management 19 (5): Thomas, A Leveragng prvate expertse for humantaran supply chans. Forced Mgraton Revew 21: Thomas, A.S., L.R. Kopczak, From logstcs to supply chan management: The path forward n the humantaran sector. Frtz Insttute, San Francsco CA, Avalable at (accessed date August 03, 2011). Van Wassenhove, L.N Humantaran ad logstcs: supply chan management n hgh gear. Journal of the Operatonal Research Socety 57 (5): Zagefka, H., M. Noor, R. Brown, G. R. de Moura, T. Hopthrow Donatng to dsaster vctms: Responses to natural and humanly caused events. European Journal of Socal Psychology 41: do: /ejsp