A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints

2006 ◽  
Vol 6 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Pablo A. Miranda ◽  
Rodrigo A. Garrido
Keyword(s):  
Facility Location ◽  
Inventory Control ◽  
Capacity Constraints ◽  
Location Model ◽  
Stochastic Capacity

scholarly journals Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-27 ◽  
Author(s):  
Claudio Araya-Sassi ◽  
Pablo A. Miranda ◽  
Germán Paredes-Belmar
Keyword(s):  
Inventory Control ◽  
Lagrangian Relaxation ◽  
Location Problem ◽  
Subgradient Method ◽  
Capacity Constraints ◽  
Mixed Integer ◽  
Total System ◽  
Periodic Review ◽  
Decomposition Approach ◽  
Stochastic Capacity

We studied a joint inventory location problem assuming a periodic review for inventory control. A single plant supplies a set of products to multiple warehouses and they serve a set of customers or retailers. The problem consists in determining which potential warehouses should be opened and which retailers should be served by the selected warehouses as well as their reorder points and order sizes while minimizing the total costs. The problem is a Mixed Integer Nonlinear Programming (MINLP) model, which is nonconvex in terms of stochastic capacity constraints and the objective function. We propose a solution approach based on a Lagrangian relaxation and the subgradient method. The decomposition approach considers the relaxation of different sets of constraints, including customer assignment, warehouse demand, and variance constraints. In addition, we develop a Lagrangian heuristic to determine a feasible solution at each iteration of the subgradient method. The proposed Lagrangian relaxation algorithm provides low duality gaps and near-optimal solutions with competitive computational times. It also shows significant impacts of the selected inventory control policy into total system costs and network configuration, when it is compared with different review period values.

scholarly journals A Facility Location Model for Air Pollution Detection

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
G. Lancia ◽  
F. Rinaldi ◽  
P. Serafini
Keyword(s):  
Genetic Algorithm ◽  
Air Pollution ◽  
Air Quality ◽  
Mathematical Models ◽  
Facility Location ◽  
Large City ◽  
Location Model ◽  
Practical Algorithms ◽  
Pollution Detection ◽  
The City

We describe mathematical models and practical algorithms for a problem concerned with monitoring the air pollution in a large city. We have worked on this problem within a project for assessing the air quality in the city of Rome by placing a certain number of sensors on some of the city buses. We cast the problem as a facility location model. By reducing the large number of data variables and constraints, we were able to solve to optimality the resulting MILP model within minutes. Furthermore, we designed a genetic algorithm whose solutions were on average very close to the optimal ones. In our computational experiments we studied the placement of sensors on 187 candidate bus routes. We considered the coverage provided by 10 up to 60 sensors.

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