A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment

•A fixed-charge transportation problem with transshipment and backordering under stochastic and dynamic demand is studied.•A mixed integer stochastic programming formulation is proposed.•Complexity results for this problem are presented.•A rolling horizon approach is proposed to solve the problem.•N...

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Published in:European journal of operational research Vol. 301; no. 3; pp. 912 - 922
Main Authors: Cavagnini, Rossana, Bertazzi, Luca, Maggioni, Francesca
Format: Journal Article
Language:English
Published: Elsevier B.V 16-09-2022
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Abstract •A fixed-charge transportation problem with transshipment and backordering under stochastic and dynamic demand is studied.•A mixed integer stochastic programming formulation is proposed.•Complexity results for this problem are presented.•A rolling horizon approach is proposed to solve the problem.•Numerical results show that the rolling horizon approach provides effective solutions in short computational time. We study a fixed-charge transportation problem under stochastic and dynamic demand. We propose a multi-stage mixed integer stochastic programming formulation, where the first-stage decision is the delivery from the supplier to the retailers, while transshipment is used, in addition to classical backordering as recourse decision. The objective is the minimization of the total expected cost. We prove that this problem is NP-hard and, through a worst-case analysis, that transshipment can provide significant cost savings. Extensive computational studies are carried out to evaluate the performance of a rolling horizon approach with respect to the optimal cost. Numerical results show that this heuristic provides effective solutions in short computational time. Managerial insights are finally drawn.
AbstractList •A fixed-charge transportation problem with transshipment and backordering under stochastic and dynamic demand is studied.•A mixed integer stochastic programming formulation is proposed.•Complexity results for this problem are presented.•A rolling horizon approach is proposed to solve the problem.•Numerical results show that the rolling horizon approach provides effective solutions in short computational time. We study a fixed-charge transportation problem under stochastic and dynamic demand. We propose a multi-stage mixed integer stochastic programming formulation, where the first-stage decision is the delivery from the supplier to the retailers, while transshipment is used, in addition to classical backordering as recourse decision. The objective is the minimization of the total expected cost. We prove that this problem is NP-hard and, through a worst-case analysis, that transshipment can provide significant cost savings. Extensive computational studies are carried out to evaluate the performance of a rolling horizon approach with respect to the optimal cost. Numerical results show that this heuristic provides effective solutions in short computational time. Managerial insights are finally drawn.
Author Maggioni, Francesca
Cavagnini, Rossana
Bertazzi, Luca
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  givenname: Rossana
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  surname: Cavagnini
  fullname: Cavagnini, Rossana
  email: cavagnini@dpo.rwth-aachen.de
  organization: Deutsche Post Chair – Optimization of Distribution Networks, RWTH Aachen University, Kackertstr. 7B, Aachen 52072, Germany
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  givenname: Luca
  surname: Bertazzi
  fullname: Bertazzi, Luca
  email: luca.bertazzi@unibs.it
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  givenname: Francesca
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  fullname: Maggioni, Francesca
  email: francesca.maggioni@unibg.it
  organization: Department of Management, Information and Production Engineering, University of Bergamo, Viale Marconi 5, Dalmine (BG) 24044, Italy
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Keywords Multi-stage stochastic programming
Rolling horizon approach
Fixed-charge transportation problem
Transshipment
Logistics
Language English
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Snippet •A fixed-charge transportation problem with transshipment and backordering under stochastic and dynamic demand is studied.•A mixed integer stochastic...
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SubjectTerms Fixed-charge transportation problem
Logistics
Multi-stage stochastic programming
Rolling horizon approach
Transshipment
Title A rolling horizon approach for a multi-stage stochastic fixed-charge transportation problem with transshipment
URI https://dx.doi.org/10.1016/j.ejor.2021.11.037
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