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Modelling and solving the multiperiod inventory routing problem with stochastic stationary demand rates

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Abstract
The inventory-routing problem (IRP) is a typical logistics optimisation problem that supply chains, implementing vendor managed inventory (VMI), are confronted with. It combines inventory control and vehicle routing. The main objective of the IRP is to jointly determine optimal quantities of the product to be delivered to the retailers, delivery periods and optimal vehicle routes for the shipment of these quantities. This paper considers a multiperiod inventory-routing problem with stochastic stationary demand rates (MP-SIRP). The problem is first formulated as a linear mixed-integer stochastic program for which we propose a deterministic equivalent approximation model (MP-DAIRP(alpha)). This latter model can be decomposed into two well-know subproblems: an inventory allocation subproblem and a vehicle routing subproblem. The stochastic aspect of the demand is accounted for in the inventory allocation subproblem. The vehicle routing subproblem is solved as a deterministic mixed-integer problem. Lagrangian relaxation is used to determine close to optimal feasible solutions for the MP-DAIRP(alpha). Results of the proposed Lagrangian relaxation approach on some numerical examples are reported and thoroughly discussed.
Keywords
DELIVERIES, INTEGRATED PRODUCTION, Lagrangian relaxation, ALGORITHM, MANAGEMENT, DESIGN, mixed-integer programming, stochastic demand rate, multiperiod inventory routing, PRODUCTS, ALLOCATION

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Chicago
Abdul Rahim, Mohd Kamarul Irwan, Yiqing Zhong, El-Houssaine Aghezzaf, and Tarik Aouam. 2014. “Modelling and Solving the Multiperiod Inventory Routing Problem with Stochastic Stationary Demand Rates.” International Journal of Production Research 52 (14): 4351–4363.
APA
Abdul Rahim, M. K. I., Zhong, Y., Aghezzaf, E.-H., & Aouam, T. (2014). Modelling and solving the multiperiod inventory routing problem with stochastic stationary demand rates. INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH, 52(14), 4351–4363.
Vancouver
1.
Abdul Rahim MKI, Zhong Y, Aghezzaf E-H, Aouam T. Modelling and solving the multiperiod inventory routing problem with stochastic stationary demand rates. INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH. 2014;52(14):4351–63.
MLA
Abdul Rahim, Mohd Kamarul Irwan, Yiqing Zhong, El-Houssaine Aghezzaf, et al. “Modelling and Solving the Multiperiod Inventory Routing Problem with Stochastic Stationary Demand Rates.” INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 52.14 (2014): 4351–4363. Print.
@article{5675075,
  abstract     = {The inventory-routing problem (IRP) is a typical logistics optimisation problem that supply chains, implementing vendor managed inventory (VMI), are confronted with. It combines inventory control and vehicle routing. The main objective of the IRP is to jointly determine optimal quantities of the product to be delivered to the retailers, delivery periods and optimal vehicle routes for the shipment of these quantities. This paper considers a multiperiod inventory-routing problem with stochastic stationary demand rates (MP-SIRP). The problem is first formulated as a linear mixed-integer stochastic program for which we propose a deterministic equivalent approximation model (MP-DAIRP(alpha)). This latter model can be decomposed into two well-know subproblems: an inventory allocation subproblem and a vehicle routing subproblem. The stochastic aspect of the demand is accounted for in the inventory allocation subproblem. The vehicle routing subproblem is solved as a deterministic mixed-integer problem. Lagrangian relaxation is used to determine close to optimal feasible solutions for the MP-DAIRP(alpha). Results of the proposed Lagrangian relaxation approach on some numerical examples are reported and thoroughly discussed.},
  author       = {Abdul Rahim, Mohd Kamarul Irwan and Zhong, Yiqing and Aghezzaf, El-Houssaine and Aouam, Tarik},
  issn         = {0020-7543},
  journal      = {INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH},
  keywords     = {DELIVERIES,INTEGRATED PRODUCTION,Lagrangian relaxation,ALGORITHM,MANAGEMENT,DESIGN,mixed-integer programming,stochastic demand rate,multiperiod inventory routing,PRODUCTS,ALLOCATION},
  language     = {eng},
  number       = {14},
  pages        = {4351--4363},
  title        = {Modelling and solving the multiperiod inventory routing problem with stochastic stationary demand rates},
  url          = {http://dx.doi.org/10.1080/00207543.2014.883470},
  volume       = {52},
  year         = {2014},
}

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