Rahman Khorramfar edited section_A_Stochastic_Optimization_Model__.tex  almost 8 years ago

Commit id: 5c68c805e81df9219c6b61dc9e3e098489f1e06a

deletions | additions      

       

\section{A Stochastic Optimization Model for Designing Last Mile Relief Networks}  distribution + locating + allocation \\ Noyan et. al \cite{NoyanEtal2015} mention the importance of the relief items distribution in the last mile, i.e., where the items are delivered to the affected people. They state that, although a lot of donations and relief items are often collected once any disaster occurs, the challenge is how to deliver the items where it is needed and to the amount that is needed. They focus on the so-called ``last mile'' relief network, which is depicted as a two-echelon network with the following structure: 1) a local distribution center (LDC), which is a large warehouses storing relief items, and 2) multiple points of distribution (PODs), where the relief items are delivered demand points (i.e., to the affected people). Recognizing the need to design the relief network rather than focusing only on the distribution problems, the authors suggest a mathematical program to determine the locations and capacities of PODs as well as the flow of a single package supply from LDC to PODs and the assignment of demand points to PODs. To help formulating a real-world problem, they incorporate the inherent uncertainty in the demand as well as in the transportation network through post-disaster link capacities. Hence, they formulate the problem as a two-stage stochastic optimization with finite number of scenarios, where the locations and capacities of PODs are determined in the first stage, while the flow of supply from LDC to PODs and the assignment of demand points to PODs is computed in the second stage. In particular, the authors define ``accessibility'' (as ease of access to POD for its demand points) and ``equity'' (e.g., in the supply allocation) and incorporate them into their model. To solve the model, the authors develop a branch-and-cut algorithm, which is based on the so-called ``Integer L-shaped Method'', and suggest valid feasibility and optimality cuts. To implement their algorithm, the authors employs ``Lazy Constraint Callback'' feature of IBM ILOG CPLEX, which increases the performance of the algorithm by avoiding the evaluation of the same integer solution more than once during the course of the algorithm. To help their model catch a real-world case, the authors collect and process the data obtained from the earthquake hit Van province in Turkey in 2011 and compare multiple policies to ensure ``accessibility and equity'' of their model.