P Model & Location Model

8/10/2019 P Model & Location Model

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Tufingki presents an extensive reference model that visualizes andclassifies logistics related tasks in any disaster relief operationsinto superior functions and process steps.

Tufingkgis Reference Model of ERL


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Step 1: Region clustering and risk analysis

This step comprises the following three tasks: Profiles of the extent of each disaster type have to be drawn. Endangered regions and main threats have to be identified. Create profiles of resource needs depending on the region as well as the type

of disaster.

Step 2: Cluster-specific pre-assessment In this step, the disaster relief potential of each cluster is investigated,

structural as well as resource-related deficits are revealed The relief capacity is compared with the potential resource need of this cluster

so that structural bottlenecks become visible.Step 3: Planning and implementation of network structures This step focuses on the elimination of structural logistics deficits. This is achieved by improving existing, or creating additional structures and

logistics systems with the objective of permitting a faster ramp-up of logisticsoperations in the case of a disaster



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Step 4: Generic contingency supply management

This step deals with the anticipation of necessary supplies during a disasterand the execution of generic procurement. This leads to disaster-unspecific inventory that can be accessed in case of

need, whereby valuable response time can be saved.Step 5: Standardized ad-hoc mobilization of emergency supplies Standardized supplies which were pre-positioned for emergencies are

mobilized to the extent indicated as necessary by a rough pre-assessment. Time-saving has highest priority, and fast transportation modes are chosen to

bring the relief supplies to the beneficiaries.Step 6: Mobilization and procurement of supplies The delivery of supplies switches from a push-system to a pull-system based

on detailed and continuously improved assessment data.Step 7: Transport Consolidation of shipments Transshipment



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In the p-median problem we are interested in finding the location of p facilities

to serve demand nodes so that the transportation cost is minimized. We assume that the facilities are CDCs where the demand nodes are previously

located RDCs Following parameters are required:

CDC Set of central distribution center nodes. RDC - Set of regional distribution center nodes. Fi Available supplies of relief items in ith CDC. Hj Aequired quantity of relief items in jth RDC. CRij - Transportation costs for a unit of relief items between the ith CDC and the jth RDC.

The required variable for the P- Median problem are as follows: Xji Binary variable for allocating the demand of the jth RDC to ith CDC. Zi Binary variable for opening the ith CDC.

Location Model (P Median)


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iY

ji X

jiY X p X

j X

X d h

i

ji

i ji

j j

j ji

i j jiiji

allfor1,0

,allfor1,0

,allfor

allfor1subject to

min


Allocated demand of each RDC toexactly one CDC

Selects exactly p new CDC to be

opened.

Ensures that demand of RDC to beallocated only to CDC.


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A B C D

E F

G IH

J LK

15 22 18

12

18

22

22 25

19 21

1919

30

24

20

12

1624

25

1215

15 10 12 18

11 16

22 19 20

13

245



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Distance matrix for the network

Node i A B C D E F G H I J K LA 0 15 37 55 24 60 18 33 48 40 58 67B 15 0 22 40 38 52 33 48 42 55 61 61

C 37 22 0 18 16 30 41 28 20 58 39 39D 55 40 18 0 34 12 59 46 24 62 43 34E 24 38 16 34 0 36 25 12 24 47 37 43F 60 52 30 12 36 0 57 42 12 50 31 22G 18 33 41 59 25 57 0 15 45 22 40 61H 33 48 28 46 12 42 15 0 30 37 25 46I 48 42 20 24 24 12 45 30 0 38 19 19J 40 55 58 62 47 50 22 37 38 0 19 40K 58 61 39 43 37 31 40 25 19 19 0 21L 67 61 39 34 43 22 61 46 19 40 21 0

Site j



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Cost (demand x distance) matrix for the network

Demand Node i A B C D E F G H I J K L

A 0 225 555 825 360 900 270 495 720 600 870 1005B 150 0 220 400 380 520 330 480 420 550 610 610

C 444 264 0 216 192 360 492 336 240 696 468 468D 990 720 324 0 612 216 1062 828 432 1116 774 612E 120 190 80 170 0 180 125 60 120 235 185 215F 1440 1248 720 288 864 0 1368 1008 288 1200 744 528G 198 363 451 649 275 627 0 165 495 242 440 671H 528 768 448 736 192 672 240 0 480 592 400 736I 624 546 260 312 312 156 585 390 0 494 247 247J 880 1210 1276 1364 1034 1100 484 814 836 0 418 880K 1102 1159 741 817 703 589 760 475 361 361 0 399L 1340 1220 780 680 860 440 1220 920 380 800 420 0

Site j

h i x d ij



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A B C D E F G H I J K L

A 0 225 555 825 360 900 270 495 720 600 870 1005B 150 0 220 400 380 520 330 480 420 550 610 610C 444 264 0 216 192 360 492 336 240 696 468 468D 990 720 324 0 612 216 1062 828 432 1116 774 612E 120 190 80 170 0 180 125 60 120 235 185 215

F 1440 1248 720 288 864 0 1368 1008 288 1200 744 528G 198 363 451 649 275 627 0 165 495 242 440 671H 528 768 448 736 192 672 240 0 480 592 400 736I 624 546 260 312 312 156 585 390 0 494 247 247J 880 1210 1276 1364 1034 1100 484 814 836 0 418 880K 1102 1159 741 817 703 589 760 475 361 361 0 399L 1340 1220 780 680 860 440 1220 920 380 800 420 0

Total 7816 7913 5855 6457 5784 5760 6936 5971 4772 6886 5576 6371

serving all the demand from a facility at A



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To find the facility location of one quick response depot for HumanitarianLogistics the Weber facility location methodology can be used.

The aim of this method is to estimate an optimal facility location in plane for a setof customers by using Euclidean distance measurement

A facility location is searched on a surface of a the globe for a set of disasters withgiven coordinates on the surface of this ball.

Location Model


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Equation (1) shows the relation between the apex angle W in radian, the radius ofthe ball and the geo- coordinates of the points {, ; i, i} defining W:

B = r cos -1 (cos cos i cos ( - i) + sin sin i)

Average earth radius is r = 6,371 km. Set of customers as disasters with geo- coordinates (i, i) in radian. Demand bi of each customer as weight of first urgent supplies per capita times

number of people affected.

Location Model


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So the target function of the model is the following with the coordinates (, ) astarget coordinates of the centralized quick response depot.

This function minimizes the total transportation performance in tons kilometers

for all disasters depending on the localization of the quick response depot. Miehle developed an iterative method to estimate the optimal location. First the

partial derivatives of (2) with respect to and have to be estimated

Location Model


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Then (3) and (4) have to be solved for and for as far as possible and with thereceived equations (5) and (6) the Miehle -algorithm can be executed: It startswith an arbitrary chosen set of coordinates, insert as 0 and 0 and the results 1and 1 has to be set as 0 and 0 in the next iteration step as long as thedifference between 0 and 1 as well as 0 and 1 is smaller than a pre -definedboundary

Location Model

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P Model & Location Model