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A Model for Humanitarian Supply Chain: An Operation Research Approach
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7th International Conference on Building Resilience; Using scientific knowledge to inform policy and practice in disaster risk reduction, ICBR2017, 27 – 29 November 2017, Bangkok, Thailand 7th International Conference on Building Resilience; Using scientific knowledge to inform policy and practice in disaster risk reduction, ICBR2017, 27 – 29 November 2017, Bangkok, Thailand
A Model for Humanitarian Supply Chain: An Operation Research Approach A Model for Humanitarian Supply Chain: An Operation Research ab Approach Ma.Teodora E.Gutierrez* , Jose Edgar S.Mutucb a
ab bb Philippines Industrial Engineering Department, Technological Institute of the Philippines, Quezon City, ab b Industrial Engineering Department, De La Salle University, Manila, Philippines
a a
Industrial Industrial Engineering Engineering Department, Department, Technological Technological Institute Institute of of the the Philippines, Philippines, Quezon Quezon City, City, Philippines Philippines b b Industrial Engineering Department, De La Salle University, Manila, Philippines Industrial Engineering Department, De La Salle University, Manila, Philippines
Ma.Teodora E.Gutierrez* , Jose Edgar S.Mutuc
Abstract Abstract The study presents a mathematical model for identification of the optimum location of a temporary or fixed facility in a certain Abstract geographic area being studied. Particularly, it is applied to Humanitarian Supply Chain where it seeks to identify the best location The presents aa mathematical identification of location of temporary or facility certain of temporary center operations inmodel order for to optimize the delivery of relief goods to the The study study relief presents mathematical model for identification of the the optimum optimum location of aarandomly temporarydispersed or fixed fixed evacuation facility in in aacenters. certain geographic area being being studied. Particularly, itofis isrelief applied to Supply Chain where seeks identify the location The paper seeks to optimize theParticularly, movement it goods by minimizing the total transportation costto Operation geographic area studied. applied to Humanitarian Humanitarian Supply Chain where it it seeks tousing identify the best bestResearch location of temporary temporary relief center operations operations in of order to optimize optimize theThe delivery ofofrelief relief goods to the the aims randomly dispersed evacuation approach withrelief the integration of Center Gravity method. centerof gravity approach to locate a facility where it centers. reflects of center in order to the delivery goods to randomly dispersed evacuation centers. The paper paper seeks to optimize optimize the movement movement of relief goods goods by minimizing minimizing the total total transportation transportation cost cost using using Operation Operation Research Research equality of seeks distances and demand volume in of a network of customers’ locations. The to the relief by the approach with thewas integration of Center ofmodel. GravityThe method. The center the of gravity gravity approach aims to to locate locate facility where where it reflects A casewith study applied of to Center use theof resultsThe revealed geographic coordinates of the aaoptimum location of the approach the integration Gravity method. center of approach aims facility it reflects equality The of distances distances and demandlocation volume will in aa network network of customers’ customers’ locations. facility. identified optimum have a total savings of locations. 40% in the total transportation cost. Hence, by a significant equality of and demand volume in of A was use the model. results the coordinates of optimum of reduction the transportation cost will meanThe a significant reduction response time and delivery time of relief location goods because A case caseofstudy study was applied applied to to use thealso model. The results revealed revealed theofgeographic geographic coordinates of the the optimum location of the the facility. The identified identified optimum location will have aaoftotal total savings location of 40% 40% in in thea total total transportation Hence, aa significant these transportation cost are functions of will distances customers andthe function of volume cost. of customers’ The facility. The optimum location have savings of transportation cost. Hence, by bydemand. significant reduction of of the transportation transportation cost will will alsoalso mean significant reduction of response response time and deliverythe time of relief relief goods because identified optimum facility location could beaaasignificant prepositioned location of relief time goodsand covering affected areas in the city. reduction the cost also mean reduction of delivery time of goods because theseproposed transportation cost are functions of distances distances ofeasy customers location and simple function of to volume of customers’ customers’ demand. The The modelcost for are disaster facility location isof to use location and require tasks implement. The model is readily these transportation functions of customers and aa function of volume of demand. The identified optimum optimum facility location could could alsobebe beused prepositioned location of accessible to managers and planners so it can in their planning. identified facility location also aa prepositioned location of relief relief goods goods covering covering the the affected affected areas areas in in the the city. city. The proposed model Published for disaster disasterbyfacility facility location is easy easy to to use use and and require require simple simple tasks © 2017 The Authors. Elsevierlocation Ltd. is The proposed model for tasks to to implement. implement. The The model model is is readily readily Peer-review responsibility of the committee the 7th International Conference on Building Resilience. accessible tounder managers and planners planners so scientific it can can be be used used in their theirofplanning. planning. accessible to managers and so it in © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2018 The Authors. Published by Elsevier Ltd. Keywords: Humanitarian Supply Chain, Operation Research, Centerof of the Gravity Method, Facility Location Planning Peer-review under responsibility of the scientific committee 7th International Conference on Building Resilience. Peer-review under responsibility of the scientific committee of the 7th International International Conference on Building Building Resilience. Resilience. Peer-review under responsibility of the scientific committee of the 7th Conference on Keywords: Humanitarian Supply Supply Chain, Chain, Operation Operation Research, Research, Center Center of of Gravity Gravity Method, Method, Facility Facility Location Location Planning Planning Keywords: Humanitarian 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility ofthe scientific committee of the 7th International Conference on Building Resilience. 1877-7058 1877-7058 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. * Corresponding author. Tel.: +63-02-9110964; Cell phoneof +63-02-9228989150 Peer-review under responsibility ofthe the International Peer-review under responsibility ofthe scientific scientific committee committee ofNo.: the 7th 7th International Conference Conference on on Building Building Resilience. Resilience. E-mail address:[email protected] * * Corresponding Corresponding author. author. Tel.: Tel.: +63-02-9110964; +63-02-9110964; Cell Cell phone phone No.: No.: +63-02-9228989150 +63-02-9228989150 E-mail E-mail address:[email protected] address:[email protected]
1877-7058 © 2018 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 7th International Conference on Building Resilience 10.1016/j.proeng.2018.01.085
Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666 Ma.Teodora E.Gutierrez , Jose Edgar S. Mutuc / Procedia Engineering00 (2017) 000–000
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1. Introduction Disaster is a serious disruption of the functioning of a community or society due to hazardous events [1]. The inevitable occurrence of disasters makes everyone to be prepared and resilient. For the past 20 years, humanitarian supply chain concept has been evolving and the current literatures have been addressing the questions of preparation and response phase of the disasters. In the recent year, a government agency in the Philippines named Commission of Audit pointed out some problems in disaster relief operations such as lack of storage facility for the procured supplies [2] and also could serve as repacking facilities for relief goods. The location of fixed or temporary facilities throughout the supply chain network is an important decision problem because it gives form, structure and shape to the entire supply chain system [3]. Actions and decisions within 72 hours to the areas affected are crucial to ensure effective and timely response to the victims of disaster in order to reduce mortality, life threatening morbidity and disability [4]. In order to have a quick response to the victim of disaster is to identify the best location of drop off points of relief goods which where it is closest to the most in need. The facility location should be in Center of Gravity, meaning that that location is the point where it reflects balance and equal weight to all customers’ location and demand. This weight is function of two variables namely, customers’ distances from the facility location and the customers’ demand. This study was taken to know the best location of drop off points of relief items that will increase responsiveness and decrease logistics cost. 2. Related Literature and Studies Facility location problems have been studied in the field of humanitarian supply chain, in the study of [5]where they surveyed more than 40 journal articles about optimization models for facility problems in emergency humanitarian logistics, it was found out that the major objectives are responsiveness, risks and cost efficiency. The use of temporary storage for emergency relief items is proven to improve the responsiveness, efficiency and effectiveness of humanitarian supply chain [6]. Where to locate a temporary or fixed local relief operation center facility is a strategic decision because it dictates the movement of relief goods and it determines quicker response to the needs of the victims. Adding regional distributional center to manage the delivery of relief goods would be cost efficient with an average cost reduction of 21% in several demand scenarios considered [7]. Several mathematical models have been presented in the literature to identify the appropriate facility locations for efficient supply network [8].Providing decision support systems for humanitarian logistics managers is important [9]. Other applications of facility location models is on the study to locate health care facilities in Hongkong [10], they consider four objectives and solve the problem using Multiple Objective Optimization and Genetic Algorithm. They generate 100 iterations for each generation of chromosomes and yield optimum location. The operation research technique with center of gravity approach was not yet applied in the disaster logistics. Looking at the previous studies, it requires high skills to execute the solutions but the paper’s proposed approached in disaster logistics is easy to use and requires simple tasks to implement.
3. Methodology 3.1 Operation Research Technique Operations research is the scientific study of operations for the purpose of better decision making and management [11]. The paper used Operation Research technique to identify an optimum solution by calculating the total transportation cost of the location of the new facility. It seeks to minimize transportation cost which is the sum of the product of customer’s volume of demand (vi) multiplied by the transportation rate to customer’s location i (ri) and multiplied by the distances of each customer location i from the facility location(di) as seen in equation (1).
Min TC =
& '()
vi ∗ ri ∗ di
(1)
Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666 Ma.Teodora E.Gutierrez , Jose Edgar S.Mutuc / Procedia Engineering 00 (2017) 000–000
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3.2 Center of Gravity Method The paper seeks first to compute for the geographic coordinates of the location of the new facilities within the network of customers’ locations using Center of Gravity Method. The center of gravity methods in facilities location analysis is a quantitative model that seeks to compute for the geographic coordinates for a new facilities that will have minimum cost. The main variables in the study are the customer’s location, volume of goods shipped and the shipping or transportation rates. The facility to be located is determined by the solution process of the center of gravity method [12] and as follows: The first step is to find the latitude and longitude of the location of customers. Second step is to convert these latitude and longitude into x and y coordinates by identifying one point of reference in any location in the geographic area being investigated. This point of reference is also called point of origin which will have a value of 0, 0 in the x and y coordinates grid. The third step is to determine the quantity of volume or demands required in each customer’s location and the transportation rates. Fourth step is to approximate the initial location of the facilities using Center of Gravity formulas in equation (2) and equation (3), omitting initially the distance of each customer’s location. Where the x bar is the x coordinate of the new facility to be located and y bar is the y coordinate of the new facility to be located. Fifth step is to calculate the di, applying the equation (4) using the resulted x bar and y bar coordinates from step four. Sixth step is to substitute the value of di into the equations (5) and equation (6) and solve for the revised X bar and Y bar coordinates. Seventh step is to recalculate di, based on the revised x bar and y bar coordinates. Eight steps is to repeat steps five and step six, until the x bar and y bar coordinates does not change for successive iterations or there is little changes in the x and y coordinates that continuing the iterations is not productive. Ninth step is to calculate the total cost of the identified optimum locations using equation (1).
x bar = (Vi ∗ Ri ∗ Xi)/ (Vi ∗ Ri)
y bar = (Vi ∗ Ri ∗ Yi)/ (Vi ∗ Ri) 𝑑𝑑𝑑𝑑 = (𝑥𝑥𝑥𝑥 − 𝑥𝑥)^2 − (𝑦𝑦𝑦𝑦 − 𝑦𝑦)^2 x bar = [(Vi ∗ Ri ∗ Xi)/di]/ (Vi ∗ Ri)/di y bar = [(Vi ∗ Ri ∗ Yi)/di]/ (Vi ∗ Ri)/di
(2) (3) (4) (5) (6)
4. Case Study -Results and Analysis
A case study was applied to test the proposed approach, we consider Marikina City which has a population of 450, 741 people and an area of 22.64 Km2 as shown in Figure 1. It is one of the cities in the Philippines that often experiences sudden and slow on set of floods. The flood in the city is due to Marikina River that frequently overflowed when heavy rains occurred. The frequency of occurrence of floods in this city due to typhoons ranges from two times to three times per year. Public Schools in Marikina are usually opened up as temporary evacuation shelters for the victims of disaster. Marikina City has twenty one evacuation centers spread within the area. One of these Public Schools could be a candidate facility for a temporary relief operation centers.
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Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666 Ma.Teodora E.Gutierrez , Jose Edgar S. Mutuc / Procedia Engineering00 (2017) 000–000
Fig. 1. Geographic Area of Marikina City The objective is to seek for the optimum location of a temporary facility of relief operation center in order to deliver the total demands of relief items to the affected families within 72 hours after disaster strikes. Figure 2 shows the different locations of the evacuation centers in Marikina City as shown by the blue circles. The bigger circle reflects larger volume of demand in that particular evacuation centers. Using the previously mentioned approach in the methods section, three variables were considered, which are the location of evacuation centers, and is expressed as geometric coordinate point in the latitude and longitude in the geographic map, the demand per families of the relief goods as measured in kilograms and the shipping cost or transportation rate for each demand location. The existing facility of relief center operation is near the City Municipal Hall. This center is a drop off point of the family food pack relief goods, supplied by the National Relief Operation Center which is 20 km away and is the starting point of shipment of relief goods to all evacuation centers. The City Municipal Hall has a latitude and longitude of 14.6330277 and 121.09898129999999 and it is the origin of the x and y coordinates in the solution iterations, which has a value of 0, 0.
Ma.Teodora E.Gutierrez , Jose Edgar S.Mutuc / Procedia Engineering 00 (2017) 000–000 Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666
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Fig. 2. Spatial Arrangement of Evacuation Centers in Marikina City Applying the proposed approach, the optimum location is at geographic coordinates, 723.99 for x coordinates and 1876.29 for y coordinates. This computed value is at iteration 5, where it has the lowest transportation cost of 1, 693.497.80 Philippine Pesos. Table 1 shows the solution iterations , We stop at the 15th iteration because the previous successive iterations yields little changes on the x and y coordinates and the total cost have little changes also. To locate the computed x and y coordinates into the world map, it is then converted to latitude and longitude, the results is is14.649987 and 121.105701 respectively. In the world map, it has the following address: 26 Candazo St, Marikina, 1800 Metro Manila, Philippines. Evaluating the feasibility of this location as temporary relief operation center facility, it is noted that this is a residential area, so we use the concept of greedy heuristic approach to move the points with minimum deviation from the computed optimum location. This greedy heuristic approach is a process of looking to the nearest neighbourhood point. The nearest neighbourhood point is Marikina High School which is 450 meters away from the computed geographic location. Marikina High School is the optimum location to housed or built the temporary relief center operations as seen in figure 3, this will served as drop off points of bulk of relief goods supplied by the National Relief Operation Center and drop off points for relief goods donated by individual and organizations which needs repacking to form family food pack relief goods which consists of similar items released
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by National Relief Operation Center. Marikina High School is a secondary public school in the city and also usually opened up as temporary evacuation center for the victims of disasters. Table 1. Summary of Solution Algorithm Iteration X coordinate Y coordinate 0 540.6238 1544.823 1 484.41 1,560.97 2 472.42 1,562.01 3 469.86 1,560.31 4 884.75 2,285.86 5 723.99 1,876.29 6 647.61 1,545.32 7 523.39 1,567.17 8 482.47 1,571.07 9 474.07 1,569.33 10 471.78 1,566.29 11 470.61 1,563.46 12 469.75 1,561.05 13 469.05 1,559.01 14 468.47 1,557.31 15 467.99 1,555.88
Total Cost 2,231,822.47 2,227,890.6 2,227,704.92 3,036,470.34 2,416,711.63 1,693,497.80 2,245,423.75 2,229,924.73 2,227,856.62 2,227,750.91 2,227,723.20 2,227,704.73 2,227,691.72 2,227,682.57 2,227,676.13 2,227,671.60
To validate the effectiveness of the computed geographical location, we use equation (1) to compute for the total transportation cost of existing facility which is in City Municipal Hall and the computed optimum location of facility. Marikina High School is a 2 km away from the existing relief center facility which is in the City Municipal Hall. To compute for the total transportation cost from the optimum facility location to all evacuation centers, we use the transportation rate which is $ 0.44 per kilograms per kilometre ($/kg/km). This transportation rate is the cost of moving the relief goods from the relief center facility to all evacuation centers. The existing location of facility has a total transportation cost of 2, 850,278.79 Philippines Pesos (Php) and the computed optimum location of facility has a total transportation cost 1,693,497.80 Philippine Pesos (Php). Hence, the difference of the total transportation cost is Php1, 156,780.99, which mean a savings of more than 40% when the relief operation centre is placed to the computed optimum location, which is the Marikina High School.
Ma.Teodora E.Gutierrez , Jose Edgar S.Mutuc / Procedia Engineering 00 (2017) 000–000 Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666
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Fig. 3. Geographic location of the optimum location of facility 5. Conclusions With the use of the proposed approach, it is possible to determine the minimum time and cost to locate the optimum site for a temporary relief center operations facility, which will immediately provide for the needs of the disasters victims. The costs are functions of distances of evacuation centers, volume of demand needed for each evacuation centers and the shipping cost. Applying Center of Gravity method resulted in finding the optimum location of a single facility as it reflects minimum cost which was shown in the study and as compared to any different locations in geographic area being studied. Positioning the facilities in the optimum location will result to a significant saving of 40% of the total transportation cost. It also validate that the location of facilities affects the movement of the relief goods. The better positioned of the facilities, the quicker the movement of relief goods which will meet the standards of 72 hours of response time for delivery of relief goods and the lower the transportation cost as well. The results show that the identified facility is accessible which are closer to the most in need and reflects accessibility to all evacuation centers. Quicker response to the needs of disaster victims could mean helping to build resilience in to their daily lives.By determining the optimum facility locations, it will help the policy makers and the emergency managers on planning the operations of the relief centers. This proposed solution approach is also applicable to any facilities to be built in the geographic area being studied, either a temporary healthcare facilities or temporary water supply facilities considering two major parameters the distances of the victims’ locations and volume of demand of each victim’s locations. The identified optimum facility location could also be served as prepositioned locations of relief goods covering the affected areas
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in the city. For the future direction of research, the proponents are developing a decision support system of mobile application for the facility location planning to aid the decision makers in identifying an optimum location of their facilities given the customers’ locations and volume of demand. References [1]
UNISDR (2016). United Nations Office for Disaster Risk reduciton. Retrieved October 12, 2016, from http://www.unisdr.org/we/inform/terminology#letter-d [2] Cabigao, F., Jr. Disaster Aid, the Money Trail, January 2015. Relief protocols & rules http://pcij.org/stories/relief-protocols-rules/. [3] Charles, A. L. (2016). Designing an efficient humanitarian supply network. Journal of Operations Management, 1-13. [4] Federal Emergency Management Agency (2017) Disaster Planning is up to you. Retrieved June 9, 2017.https://www.fema.gov/newsrelease/2007/03/30/disaster-planning-you. [5] Boonmee, C. A. (2017). Facility location optimization model for emergency humanitarian logistics. International Journal of Disaster Risk Reduction [6] Maharjan, R. ((2017)). Warehouse location determination for humanitarian relief distribution in Nepal. Transportation Research Procedia , 1115-1163. [7] Dufour, É., Laporte, G., Paquette, J., & Rancourt, M. (2017). Logistics service network design for humanitarian response in South Africa. Omega . [8] Charles, A. L. (2016). Designing an efficient humanitarian supply network. Journal of Operations Management , 1-13 [9] Gosling, H. G. (( 2014 )). A framework to compare OR models. Procedia Engineering , 22-28. [10] Wenting Zhang, K. C. (2016). A multi-objective optimization approach in Health Care Facility Location allocation Problems in Highly Developed Cities such as Hongkong. Computers, Environment and Urban Systems , 220-230. [11] Stilianakis, Nikolaos;Consoli,Sergio. (2013). Operations Research in disaster preparedness and response: A Public Health Perspective. JRC Technical Report, European Commissions . [12] Decisions, F. L. (n.d.). Retrieved June 9, 2017, from Facility Location Decisions: http://courses.washington.edu/cee587/Readings/Chapter%2013%20Facility%20Location%20Decisions.pdf
Available Available online online at at www.sciencedirect.com www.sciencedirect.com
Available online at www.sciencedirect.com Procedia Procedia Engineering00 Engineering00 (2017) (2017) 000–000 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 212 (2018) 659–666
7th International Conference on Building Resilience; Using scientific knowledge to inform policy and practice in disaster risk reduction, ICBR2017, 27 – 29 November 2017, Bangkok, Thailand 7th International Conference on Building Resilience; Using scientific knowledge to inform policy and practice in disaster risk reduction, ICBR2017, 27 – 29 November 2017, Bangkok, Thailand
A Model for Humanitarian Supply Chain: An Operation Research Approach A Model for Humanitarian Supply Chain: An Operation Research ab Approach Ma.Teodora E.Gutierrez* , Jose Edgar S.Mutucb a
ab bb Philippines Industrial Engineering Department, Technological Institute of the Philippines, Quezon City, ab b Industrial Engineering Department, De La Salle University, Manila, Philippines
a a
Industrial Industrial Engineering Engineering Department, Department, Technological Technological Institute Institute of of the the Philippines, Philippines, Quezon Quezon City, City, Philippines Philippines b b Industrial Engineering Department, De La Salle University, Manila, Philippines Industrial Engineering Department, De La Salle University, Manila, Philippines
Ma.Teodora E.Gutierrez* , Jose Edgar S.Mutuc
Abstract Abstract The study presents a mathematical model for identification of the optimum location of a temporary or fixed facility in a certain Abstract geographic area being studied. Particularly, it is applied to Humanitarian Supply Chain where it seeks to identify the best location The presents aa mathematical identification of location of temporary or facility certain of temporary center operations inmodel order for to optimize the delivery of relief goods to the The study study relief presents mathematical model for identification of the the optimum optimum location of aarandomly temporarydispersed or fixed fixed evacuation facility in in aacenters. certain geographic area being being studied. Particularly, itofis isrelief applied to Supply Chain where seeks identify the location The paper seeks to optimize theParticularly, movement it goods by minimizing the total transportation costto Operation geographic area studied. applied to Humanitarian Humanitarian Supply Chain where it it seeks tousing identify the best bestResearch location of temporary temporary relief center operations operations in of order to optimize optimize theThe delivery ofofrelief relief goods to the the aims randomly dispersed evacuation approach withrelief the integration of Center Gravity method. centerof gravity approach to locate a facility where it centers. reflects of center in order to the delivery goods to randomly dispersed evacuation centers. The paper paper seeks to optimize optimize the movement movement of relief goods goods by minimizing minimizing the total total transportation transportation cost cost using using Operation Operation Research Research equality of seeks distances and demand volume in of a network of customers’ locations. The to the relief by the approach with thewas integration of Center ofmodel. GravityThe method. The center the of gravity gravity approach aims to to locate locate facility where where it reflects A casewith study applied of to Center use theof resultsThe revealed geographic coordinates of the aaoptimum location of the approach the integration Gravity method. center of approach aims facility it reflects equality The of distances distances and demandlocation volume will in aa network network of customers’ customers’ locations. facility. identified optimum have a total savings of locations. 40% in the total transportation cost. Hence, by a significant equality of and demand volume in of A was use the model. results the coordinates of optimum of reduction the transportation cost will meanThe a significant reduction response time and delivery time of relief location goods because A case caseofstudy study was applied applied to to use thealso model. The results revealed revealed theofgeographic geographic coordinates of the the optimum location of the the facility. The identified identified optimum location will have aaoftotal total savings location of 40% 40% in in thea total total transportation Hence, aa significant these transportation cost are functions of will distances customers andthe function of volume cost. of customers’ The facility. The optimum location have savings of transportation cost. Hence, by bydemand. significant reduction of of the transportation transportation cost will will alsoalso mean significant reduction of response response time and deliverythe time of relief relief goods because identified optimum facility location could beaaasignificant prepositioned location of relief time goodsand covering affected areas in the city. reduction the cost also mean reduction of delivery time of goods because theseproposed transportation cost are functions of distances distances ofeasy customers location and simple function of to volume of customers’ customers’ demand. The The modelcost for are disaster facility location isof to use location and require tasks implement. The model is readily these transportation functions of customers and aa function of volume of demand. The identified optimum optimum facility location could could alsobebe beused prepositioned location of accessible to managers and planners so it can in their planning. identified facility location also aa prepositioned location of relief relief goods goods covering covering the the affected affected areas areas in in the the city. city. The proposed model Published for disaster disasterbyfacility facility location is easy easy to to use use and and require require simple simple tasks © 2017 The Authors. Elsevierlocation Ltd. is The proposed model for tasks to to implement. implement. The The model model is is readily readily Peer-review responsibility of the committee the 7th International Conference on Building Resilience. accessible tounder managers and planners planners so scientific it can can be be used used in their theirofplanning. planning. accessible to managers and so it in © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2018 The Authors. Published by Elsevier Ltd. Keywords: Humanitarian Supply Chain, Operation Research, Centerof of the Gravity Method, Facility Location Planning Peer-review under responsibility of the scientific committee 7th International Conference on Building Resilience. Peer-review under responsibility of the scientific committee of the 7th International International Conference on Building Building Resilience. Resilience. Peer-review under responsibility of the scientific committee of the 7th Conference on Keywords: Humanitarian Supply Supply Chain, Chain, Operation Operation Research, Research, Center Center of of Gravity Gravity Method, Method, Facility Facility Location Location Planning Planning Keywords: Humanitarian 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility ofthe scientific committee of the 7th International Conference on Building Resilience. 1877-7058 1877-7058 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. * Corresponding author. Tel.: +63-02-9110964; Cell phoneof +63-02-9228989150 Peer-review under responsibility ofthe the International Peer-review under responsibility ofthe scientific scientific committee committee ofNo.: the 7th 7th International Conference Conference on on Building Building Resilience. Resilience. E-mail address:[email protected] * * Corresponding Corresponding author. author. Tel.: Tel.: +63-02-9110964; +63-02-9110964; Cell Cell phone phone No.: No.: +63-02-9228989150 +63-02-9228989150 E-mail E-mail address:[email protected] address:[email protected]
1877-7058 © 2018 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 7th International Conference on Building Resilience 10.1016/j.proeng.2018.01.085
Ma.Teodora E. Gutierrez et al. / Procedia Engineering 212 (2018) 659–666 Ma.Teodora E.Gutierrez , Jose Edgar S. Mutuc / Procedia Engineering00 (2017) 000–000
660 2
1. Introduction Disaster is a serious disruption of the functioning of a community or society due to hazardous events [1]. The inevitable occurrence of disasters makes everyone to be prepared and resilient. For the past 20 years, humanitarian supply chain concept has been evolving and the current literatures have been addressing the questions of preparation and response phase of the disasters. In the recent year, a government agency in the Philippines named Commission of Audit pointed out some problems in disaster relief operations such as lack of storage facility for the procured supplies [2] and also could serve as repacking facilities for relief goods. The location of fixed or temporary facilities throughout the supply chain network is an important decision problem because it gives form, structure and shape to the entire supply chain system [3]. Actions and decisions within 72 hours to the areas affected are crucial to ensure effective and timely response to the victims of disaster in order to reduce mortality, life threatening morbidity and disability [4]. In order to have a quick response to the victim of disaster is to identify the best location of drop off points of relief goods which where it is closest to the most in need. The facility location should be in Center of Gravity, meaning that that location is the point where it reflects balance and equal weight to all customers’ location and demand. This weight is function of two variables namely, customers’ distances from the facility location and the customers’ demand. This study was taken to know the best location of drop off points of relief items that will increase responsiveness and decrease logistics cost. 2. Related Literature and Studies Facility location problems have been studied in the field of humanitarian supply chain, in the study of [5]where they surveyed more than 40 journal articles about optimization models for facility problems in emergency humanitarian logistics, it was found out that the major objectives are responsiveness, risks and cost efficiency. The use of temporary storage for emergency relief items is proven to improve the responsiveness, efficiency and effectiveness of humanitarian supply chain [6]. Where to locate a temporary or fixed local relief operation center facility is a strategic decision because it dictates the movement of relief goods and it determines quicker response to the needs of the victims. Adding regional distributional center to manage the delivery of relief goods would be cost efficient with an average cost reduction of 21% in several demand scenarios considered [7]. Several mathematical models have been presented in the literature to identify the appropriate facility locations for efficient supply network [8].Providing decision support systems for humanitarian logistics managers is important [9]. Other applications of facility location models is on the study to locate health care facilities in Hongkong [10], they consider four objectives and solve the problem using Multiple Objective Optimization and Genetic Algorithm. They generate 100 iterations for each generation of chromosomes and yield optimum location. The operation research technique with center of gravity approach was not yet applied in the disaster logistics. Looking at the previous studies, it requires high skills to execute the solutions but the paper’s proposed approached in disaster logistics is easy to use and requires simple tasks to implement.
3. Methodology 3.1 Operation Research Technique Operations research is the scientific study of operations for the purpose of better decision making and management [11]. The paper used Operation Research technique to identify an optimum solution by calculating the total transportation cost of the location of the new facility. It seeks to minimize transportation cost which is the sum of the product of customer’s volume of demand (vi) multiplied by the transportation rate to customer’s location i (ri) and multiplied by the distances of each customer location i from the facility location(di) as seen in equation (1).
Min TC =
& '()
vi ∗ ri ∗ di
(1)
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3.2 Center of Gravity Method The paper seeks first to compute for the geographic coordinates of the location of the new facilities within the network of customers’ locations using Center of Gravity Method. The center of gravity methods in facilities location analysis is a quantitative model that seeks to compute for the geographic coordinates for a new facilities that will have minimum cost. The main variables in the study are the customer’s location, volume of goods shipped and the shipping or transportation rates. The facility to be located is determined by the solution process of the center of gravity method [12] and as follows: The first step is to find the latitude and longitude of the location of customers. Second step is to convert these latitude and longitude into x and y coordinates by identifying one point of reference in any location in the geographic area being investigated. This point of reference is also called point of origin which will have a value of 0, 0 in the x and y coordinates grid. The third step is to determine the quantity of volume or demands required in each customer’s location and the transportation rates. Fourth step is to approximate the initial location of the facilities using Center of Gravity formulas in equation (2) and equation (3), omitting initially the distance of each customer’s location. Where the x bar is the x coordinate of the new facility to be located and y bar is the y coordinate of the new facility to be located. Fifth step is to calculate the di, applying the equation (4) using the resulted x bar and y bar coordinates from step four. Sixth step is to substitute the value of di into the equations (5) and equation (6) and solve for the revised X bar and Y bar coordinates. Seventh step is to recalculate di, based on the revised x bar and y bar coordinates. Eight steps is to repeat steps five and step six, until the x bar and y bar coordinates does not change for successive iterations or there is little changes in the x and y coordinates that continuing the iterations is not productive. Ninth step is to calculate the total cost of the identified optimum locations using equation (1).
x bar = (Vi ∗ Ri ∗ Xi)/ (Vi ∗ Ri)
y bar = (Vi ∗ Ri ∗ Yi)/ (Vi ∗ Ri) 𝑑𝑑𝑑𝑑 = (𝑥𝑥𝑥𝑥 − 𝑥𝑥)^2 − (𝑦𝑦𝑦𝑦 − 𝑦𝑦)^2 x bar = [(Vi ∗ Ri ∗ Xi)/di]/ (Vi ∗ Ri)/di y bar = [(Vi ∗ Ri ∗ Yi)/di]/ (Vi ∗ Ri)/di
(2) (3) (4) (5) (6)
4. Case Study -Results and Analysis
A case study was applied to test the proposed approach, we consider Marikina City which has a population of 450, 741 people and an area of 22.64 Km2 as shown in Figure 1. It is one of the cities in the Philippines that often experiences sudden and slow on set of floods. The flood in the city is due to Marikina River that frequently overflowed when heavy rains occurred. The frequency of occurrence of floods in this city due to typhoons ranges from two times to three times per year. Public Schools in Marikina are usually opened up as temporary evacuation shelters for the victims of disaster. Marikina City has twenty one evacuation centers spread within the area. One of these Public Schools could be a candidate facility for a temporary relief operation centers.
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Fig. 1. Geographic Area of Marikina City The objective is to seek for the optimum location of a temporary facility of relief operation center in order to deliver the total demands of relief items to the affected families within 72 hours after disaster strikes. Figure 2 shows the different locations of the evacuation centers in Marikina City as shown by the blue circles. The bigger circle reflects larger volume of demand in that particular evacuation centers. Using the previously mentioned approach in the methods section, three variables were considered, which are the location of evacuation centers, and is expressed as geometric coordinate point in the latitude and longitude in the geographic map, the demand per families of the relief goods as measured in kilograms and the shipping cost or transportation rate for each demand location. The existing facility of relief center operation is near the City Municipal Hall. This center is a drop off point of the family food pack relief goods, supplied by the National Relief Operation Center which is 20 km away and is the starting point of shipment of relief goods to all evacuation centers. The City Municipal Hall has a latitude and longitude of 14.6330277 and 121.09898129999999 and it is the origin of the x and y coordinates in the solution iterations, which has a value of 0, 0.
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Fig. 2. Spatial Arrangement of Evacuation Centers in Marikina City Applying the proposed approach, the optimum location is at geographic coordinates, 723.99 for x coordinates and 1876.29 for y coordinates. This computed value is at iteration 5, where it has the lowest transportation cost of 1, 693.497.80 Philippine Pesos. Table 1 shows the solution iterations , We stop at the 15th iteration because the previous successive iterations yields little changes on the x and y coordinates and the total cost have little changes also. To locate the computed x and y coordinates into the world map, it is then converted to latitude and longitude, the results is is14.649987 and 121.105701 respectively. In the world map, it has the following address: 26 Candazo St, Marikina, 1800 Metro Manila, Philippines. Evaluating the feasibility of this location as temporary relief operation center facility, it is noted that this is a residential area, so we use the concept of greedy heuristic approach to move the points with minimum deviation from the computed optimum location. This greedy heuristic approach is a process of looking to the nearest neighbourhood point. The nearest neighbourhood point is Marikina High School which is 450 meters away from the computed geographic location. Marikina High School is the optimum location to housed or built the temporary relief center operations as seen in figure 3, this will served as drop off points of bulk of relief goods supplied by the National Relief Operation Center and drop off points for relief goods donated by individual and organizations which needs repacking to form family food pack relief goods which consists of similar items released
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by National Relief Operation Center. Marikina High School is a secondary public school in the city and also usually opened up as temporary evacuation center for the victims of disasters. Table 1. Summary of Solution Algorithm Iteration X coordinate Y coordinate 0 540.6238 1544.823 1 484.41 1,560.97 2 472.42 1,562.01 3 469.86 1,560.31 4 884.75 2,285.86 5 723.99 1,876.29 6 647.61 1,545.32 7 523.39 1,567.17 8 482.47 1,571.07 9 474.07 1,569.33 10 471.78 1,566.29 11 470.61 1,563.46 12 469.75 1,561.05 13 469.05 1,559.01 14 468.47 1,557.31 15 467.99 1,555.88
Total Cost 2,231,822.47 2,227,890.6 2,227,704.92 3,036,470.34 2,416,711.63 1,693,497.80 2,245,423.75 2,229,924.73 2,227,856.62 2,227,750.91 2,227,723.20 2,227,704.73 2,227,691.72 2,227,682.57 2,227,676.13 2,227,671.60
To validate the effectiveness of the computed geographical location, we use equation (1) to compute for the total transportation cost of existing facility which is in City Municipal Hall and the computed optimum location of facility. Marikina High School is a 2 km away from the existing relief center facility which is in the City Municipal Hall. To compute for the total transportation cost from the optimum facility location to all evacuation centers, we use the transportation rate which is $ 0.44 per kilograms per kilometre ($/kg/km). This transportation rate is the cost of moving the relief goods from the relief center facility to all evacuation centers. The existing location of facility has a total transportation cost of 2, 850,278.79 Philippines Pesos (Php) and the computed optimum location of facility has a total transportation cost 1,693,497.80 Philippine Pesos (Php). Hence, the difference of the total transportation cost is Php1, 156,780.99, which mean a savings of more than 40% when the relief operation centre is placed to the computed optimum location, which is the Marikina High School.
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Fig. 3. Geographic location of the optimum location of facility 5. Conclusions With the use of the proposed approach, it is possible to determine the minimum time and cost to locate the optimum site for a temporary relief center operations facility, which will immediately provide for the needs of the disasters victims. The costs are functions of distances of evacuation centers, volume of demand needed for each evacuation centers and the shipping cost. Applying Center of Gravity method resulted in finding the optimum location of a single facility as it reflects minimum cost which was shown in the study and as compared to any different locations in geographic area being studied. Positioning the facilities in the optimum location will result to a significant saving of 40% of the total transportation cost. It also validate that the location of facilities affects the movement of the relief goods. The better positioned of the facilities, the quicker the movement of relief goods which will meet the standards of 72 hours of response time for delivery of relief goods and the lower the transportation cost as well. The results show that the identified facility is accessible which are closer to the most in need and reflects accessibility to all evacuation centers. Quicker response to the needs of disaster victims could mean helping to build resilience in to their daily lives.By determining the optimum facility locations, it will help the policy makers and the emergency managers on planning the operations of the relief centers. This proposed solution approach is also applicable to any facilities to be built in the geographic area being studied, either a temporary healthcare facilities or temporary water supply facilities considering two major parameters the distances of the victims’ locations and volume of demand of each victim’s locations. The identified optimum facility location could also be served as prepositioned locations of relief goods covering the affected areas
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in the city. For the future direction of research, the proponents are developing a decision support system of mobile application for the facility location planning to aid the decision makers in identifying an optimum location of their facilities given the customers’ locations and volume of demand. References [1]
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