“An Approach of Modeling for Humanitarian Supplies”
Presented By:
Devendra Kumar Dewangan
Research Scholar
Department of Management Studies
Indian Institute of Technology Roorkee
1
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.
2
Agenda
 Introduction
 The Humanitarian Supply Chain
 Objective Functions Under Disaster Relief Operations
 Reliable Transportation During Disaster Relief Operations
 Location Routing Problems
 Location Routing Model
 Integrated Location Routing Models
 Conclusion
 References
3
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.
4
The Humanitarian Supply Chain
Government
Donor
Beneficiary
International
Agency
Community
based
organization
(local partner)
International
NGOs
Govt. Control
Figure 1.1 A typical humanitarian supply chain
5
Objective Functions Under Disaster Relief
Operations
 Minimization of total cost
 Maximization of travel reliability
 Minimize latest arrival
6
Reliable Transportation During Disaster
Relief Operations
 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.
7
Location Routing Problems
To 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.
8
Location Routing Model
Notations,
fi =
cir =
xi =
yir =
avir =
Cost of fixed facility i
Cost of route r associated with facility, i
1 if facility i is selected, 0 otherwise
1 if route r associated with facility i is selected, 0 otherwise
1 if route r associated with facility i visits client v, 0
otherwise.
9
This objective function minimizes both the fixed costs and the
routing costs.
The Integer Programming formulation for the problem is:
Minimization
f x   c
i
i
ir
i L
yir
iL r Fr
minimizes the fixed cost and route costs
Subject to:
 a
vir
i
yir 1
, v ........(1)
r
xi  yir
, i, r...........(2)
xi , yir  {0,1}
10
Integrated Location Routing Models
Notations:
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
11
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
 fx 
i
j J
i
s S




  Csj.Qsj    Vcj .   hi . Y ij 
j J
 jJ

 i I



   v.    Nd Zijv  ........(3)
v V
 j Ps i Ps

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
 Z
ijv
1
i  I .............(4)
vV j Ps
Constraint (4) requires each customer to be on exactly one route.


hi.   Zijv    v

iI
 j Ps

v V ............(5)
Constraint (5) imposes a capacity restriction for each vehicle.
 N Z
d
ijv
 v
vV ............(6)
j Ps i Ps
Constraint (6) limits the length of each route.
13
Z Z
ijv
j Ps
ijv
0
i Ps ; vV .........(7)
j Ps
Constraint (7) states that entering and exit route node is same.
 Z
ijv
jJ
1
vV ............(8)
iI
Constraint (8) states that a route can operate out of only one
facility.
14
Q   h .Y
sj
sS
i
ij
0
j J ............(9)
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.
Z
imr
mPs
  Zjhv  Yij 1 j J ;i  I ;vV ........(10)
hPs
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 (Zijv) and
the assignment variables (Yij).
15
Xj  0,1
j J ............(11)
Yij  0,1
i  I ; j J ............(12)
Zijv  0,1
i Ps ; j  Ps ; vV .........(13)
Qsj  0
s  S ; j J ............(14)
Constraints (11)-(14) are standard integrality and non-negativity
constraints.
16
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.
17
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