“An Approach of Modeling for Humanitarian Supplies”

Presented By:Devendra Kumar Dewangan

Research Scholar

Department of Management Studies

Indian Institute of Technology Roorkee

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Abstract

This paper addresses the nature of the humanitarian aid supply

chain and Location Routing Problems to minimize the total

cost with respect to disaster areas and propose a

comprehensive model for Location Routing Problems.

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Agenda IntroductionThe Humanitarian Supply ChainObjective Functions Under Disaster Relief OperationsReliable Transportation During Disaster Relief OperationsLocation Routing Problems Location Routing Model Integrated Location Routing ModelsConclusionReferences

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Introduction In today’s scenario, disasters seem to be prominent all corners

of the globe, the importance of disaster management is undeniable.

No country and no community are protected from the risk of disasters.

A large amount of human losses and unnecessary demolition of infrastructure can be avoided with very responsive Supply Chain Management.

The related activities are usually classified as four phases of Preparedness, Response, Recovery, and Mitigation.

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The Humanitarian Supply Chain

Figure 1.1 A typical humanitarian supply chain

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Govt. Control

Community based

organization (local

partner)

Beneficiary

Government Donor

International Agency

International NGOs

Objective Functions Under Disaster Relief Operations

Minimization of total cost

Maximization of travel reliability

Minimize latest arrival

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Reliable Transportation During Disaster Relief Operations

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Planning for humanitarian supplies and response operations

have largely been the concern of emergency management

agencies.

As per the recent research in the humanitarian relief and

development have put great prominence on issues providing a

more reliable, efficient logistic and information infrastructure

that are best addressed through increased inter-agency

collaboration.

Location Routing ProblemsTo solve Routing Problems with the facility location problems to minimize the total cost by selecting a set of facilities and constructing delivery routes with constraints such as:

Customer demands

Vehicle and facility capacities

Number of vehicles

Route lengths or route durations (specified time limit)

Tour constraint: each vehicle has to start and end at the same facility.

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Location Routing Model

Notations,

fi = Cost of fixed facility i

cir = Cost of route r associated with facility, i

xi = 1 if facility i is selected, 0 otherwise

yir = 1 if route r associated with facility i is selected, 0 otherwise

avir = 1 if route r associated with facility i visits client v, 0

otherwise.

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This objective function minimizes both the fixed costs and the

routing costs.

The Integer Programming formulation for the problem is:

Minimization

minimizes the fixed cost and route costs

Subject to:

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i i ir ir

i L i L r Fr

f x c y

i

i

ir

ir

1 , ........(1)

x y , , ...........(2)

x , y {0,1}

vir ir

i r

a y v

i r

Integrated Location Routing ModelsNotations:

Zijv = vehicle route

Ps = set of points = I J∪Nd = distance between node i Ps and j Ps. ∈ ∈Vcj = variable cost per unit processed by a facility at candidate facility site j J.∈Yij = maximum throughput for a facility at candidate facility site j J. ∈hi = variable facility

S = set of supply points (analogous to plants in the Geoffrion and Graves model),

indexed by s

Csj = unit cost of shipping from supply point s S to candidate facility site j J. ∈ ∈V = set of candidate vehicles, indexed by v

σv = capacity of vehicle v V ∈τv = maximum allowable length of a route served by vehicle v V ∈αv = cost per unit distance for delivery on route v V∈

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Objective Function: 

Zijv = {1, if vehicle v V goes directly from point j Ps.∈ ∈ 0, if not }

Decision Variables:

Qsj = quantity shipped from supply source s S to facility site j J∈ ∈

Minimize

Objective function:(3) minimizes the sum of the fixed facility location costs,

the shipment costs from the origin points (plants) to the facilities, the variable

facility throughput costs and the routing costs to the customers. 12

i. . h .Yi i sj sj j ij

j J s S j J j J i I

f x C Q Vc

ijv. Z ........(3)v d

v V j Ps i Ps

N

Constraint (4) requires each customer to be on exactly one route.

Constraint (5) imposes a capacity restriction for each vehicle.

Constraint (6) limits the length of each route.

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ijvZ 1 .............(4)i I

v V j Ps

i. ijvh Z ............(5)v v V

i I j Ps

ijvZ ............(6)d v v V

j Ps i Ps

N

Constraint (7) states that entering and exit route node is same.

Constraint (8) states that a route can operate out of only one

facility.

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ijv ijv ;Z Z 0 .........(7)i Ps v V

j Ps j Ps

ijvZ 1 ............(8)v V

j J i I

Constraint (9) implies the flow into a facility from the origin points in

terms of the total order or demand that is served by the facility.

Constraint (10) shows that if route k K leaves customer node i I and ∈ ∈also leaves facility j J, then customer i I must be assigned to facility ∈ ∈j J . This constraint associates the vehicle routing variables (Z∈ ijv) and

the assignment variables (Yij).

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ih .Y 0 ............(9)sj ij j J

s S i I

Q

; ;1 ........(10)imr jhv ij j J i I v V

m Ps h Ps

Z Z Y

Constraints (11)-(14) are standard integrality and non-negativity

constraints.

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0,1 ............(11)j j JX

ij 0,1 ;Y ............(12)i I j J

ijv 0,1 ; ;Z .........(13)i Ps j Ps v V

;0 ............(14)sj s S j JQ

Conclusions

In this paper, we focused on a methodology that incorporates the idea of the most trustworthy path in a facility location problem or location routing problems for humanitarian supply chains.

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