Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity

2008 ◽  
Vol 44 (1) ◽  
pp. 47-65 ◽  
Author(s):  
Pablo A. Miranda ◽  
Rodrigo A. Garrido
Keyword(s):  
Lagrangian Relaxation ◽  
Location Problem ◽  
Valid Inequalities ◽  
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.

A new extended formulation with valid inequalities for the Capacitated Concentrator Location Problem

2021 ◽  
Vol 289 (3) ◽  
pp. 975-986
Author(s):  
Massimo Di Francesco ◽  
Manlio Gaudioso ◽  
Enrico Gorgone ◽  
Ishwar Murthy
Keyword(s):  
Location Problem ◽  
Valid Inequalities ◽  
Extended Formulation ◽  
Concentrator Location

scholarly journals New valid inequalities and facets for the Simple Plant Location Problem

2018 ◽  
Vol 269 (3) ◽  
pp. 824-833 ◽  
Author(s):  
Laura Galli ◽  
Adam N. Letchford ◽  
Sebastian J. Miller
Keyword(s):  
Location Problem ◽  
Valid Inequalities ◽  
Plant Location

scholarly journals A lagrangian relaxation approach for a machinery location problem in forest harvesting

2003 ◽  
Vol 23 (1) ◽  
pp. 111-128 ◽  
Author(s):  
Jorge R. Vera ◽  
Andrés Weintraub ◽  
Manfred Koenig ◽  
Gaston Bravo ◽  
Monique Guignard ◽  
...  
Keyword(s):  
Lagrangian Relaxation ◽  
Location Problem ◽  
Forest Harvesting
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