Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem

Agra, Agostinho; Cerveira, Adelaide; Requejo, Cristina

doi:10.1007/978-3-319-51469-7_20

Cited by 4 publications

(7 citation statements)

References 22 publications

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“…The mixed integer model is weak in the sense that the integrality gap is usually large . In order to tighten the model, we discuss families of valid inequalities and the use of an extended formulation.…”

Section: Model Tighteningmentioning

confidence: 99%

“…All tests were run using a computer with an Intel Core i7‐4750HQ 2.00 GHz processor and 8 GB of RAM, and were conducted using the Xpress‐Optimizer 28.01.04 solver with the default options. The performed experiments are based on the instances introduced in which are generated as follows.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Complex problems combining production, inventory and routing decisions have received much attention in recent years . For a survey on previous publications see .…”

Section: Introductionmentioning

confidence: 99%

“…Absi et al and Chitsaz et al propose two‐phase iterative methods where the original inventory‐routing problem is split into two subproblems, an inventory problem and a routing problem. Agra et al also propose the decomposition of the production‐inventory‐routing problem into a production‐inventory subproblem and a routing subproblem using a new Lagrangian decomposition enhanced with valid inequalities. Chitsaz et al formulate the problem as a MIP and propose a three‐phase decomposition matheuristic that relies on the iterative solution of different subproblems.…”

Section: Introductionmentioning

confidence: 99%

“…The quantities to deliver to each client in each time period as well as the inventory levels can be adjusted to the scenario (known as second-stage decisions). Such assumptions may hold for short planning horizons.Complex problems combining production, inventory and routing decisions have received much attention in recent years [6,9,11,14,16,17,19,20,25,29,33,38,40]. For a survey on previous publications see [4].…”

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confidence: 99%

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An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

2017

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We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first‐stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.

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Section: Model Tighteningmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

“…Complex problems combining production, inventory and routing decisions have received much attention in recent years . For a survey on previous publications see .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

2017

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Logistic Operations in a Hospital: A Multi-item Inventory Distribution Problem with Heterogeneous Fleet

Agra

Cerveira

Requejo

2019

Pharmaceutical Supply Chains - Medicines Shortages

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Stochastic inventory-routing problem with lateral transshipment for perishable product

Tanhatalab

2021

JM2

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Purpose This study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned. Design/methodology/approach Owing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds. Findings The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure. Practical implications This paper covers the modeling of some real-world problems in which demand is uncertain and managers face making some concurrent decisions related to supply chain management, transportation and logistics and inventory control issues. Furthermore, considering the perishability of product in modeling makes the problem more practically significant as these days there are many supply chains handling dairy and other fresh products. Originality/value Considering uncertainty, production, transshipment and perishable product in the inventory-routing problem makes a new variant that has not yet been studied. The proposed novel solution is based on the LR approach that is enhanced by some heuristics and some valid inequalities that make it different from the current version of the LR used by other studies.

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Lagrangian Relaxation Bounds for a Production-Inventory-Routing Problem

Cited by 4 publications

References 22 publications

An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

Logistic Operations in a Hospital: A Multi-item Inventory Distribution Problem with Heterogeneous Fleet

Stochastic inventory-routing problem with lateral transshipment for perishable product

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