“ An Approach of Modeling for Humanitarian Supplies” Presented By: Devendra Kumar Dewangan

1. “An Approach of Modeling for Humanitarian Supplies” Presented By: Devendra Kumar Dewangan Research Scholar Department of Management Studies Indian Institute of Technology Roorkee

2. 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.

3. 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

4. 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.

5. The Humanitarian Supply Chain Figure 1.1 A typical humanitarian supply chain International Agency Government Donor International NGOs Beneficiary Community based organization (local partner) Govt. Control

6. Objective Functions Under Disaster Relief Operations • Minimization of total cost • Maximization of travel reliability • Minimize latest arrival

7. 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.

8. 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.

9. 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.

10. 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:

11. 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

12. 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.

13. 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.

14. Constraint (7) states that entering and exit route node is same. Constraint (8) states that a route can operate out of only one facility.

15. 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 (Zijv) and the assignment variables (Yij).

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

17. 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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