The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Baller, Annelieke C.; Dabia, Said; Dullaert, Wout; Vigo, Daniele

doi:10.1016/j.ejor.2019.01.070

Cited by 19 publications

(11 citation statements)

References 49 publications

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“…This variant of the IRP is interesting to investigate theoretically, given the discussion on the PSP in Section 2.2, but also has a practical application . For the tour length approximation, we use a result of Beardwood et al who show that the tour length is asymptotically equal to

ϕ \sqrt{A \cdot N}

for large N , where ϕ is a constant and A is the surface of the area in which the N points can be placed uniformly at random.…”

Section: Inventory Routing In the Euclidean Planementioning

confidence: 99%

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Complexity of inventory routing problems when routing is easy

Baller

Hoogeboom

et al. 2019

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In the inventory routing problem (IRP) inventory management and route optimization are combined. The traveling salesman problem (TSP) is a special case of the IRP, hence the IRP is NP-hard. We investigate how other aspects than routing influence the complexity of a variant of the IRP. We first study problem variants on a point and on the half-line. The problems differ in the number of vehicles, the number of days in the planning horizon and the service times of the customers. Our main result is a polynomial time dynamic programming algorithm for the variant on the half-line with uniform service times and a planning horizon of 2 days. Second, for nearly any problem in the class with nonfixed planning horizon, we show that the complexity is dictated by the complexity of the pinwheel scheduling problem, for which the complexity is a long-standing open research question. Third, NP-hardness is shown for problem variants with nonuniform servicing times. Finally, we prove strong NP-hardness of a Euclidean variant with uniform service times and an easily computable routing cost approximation, avoiding immediate NP-hardness via the TSP. KEYWORDSapproximation, computational complexity, dynamic programming, inventory routing, periodic replenishment, pinwheel schedulingThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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ϕ \sqrt{A \cdot N}

for large N , where ϕ is a constant and A is the surface of the area in which the N points can be placed uniformly at random.…”

Section: Inventory Routing In the Euclidean Planementioning

confidence: 99%

“…In many vehicle routing problems (VRP) the vehicles are capacitated in terms of load, however, in the ATM replenishment problem, the time spent by a vehicle is often more binding . Time is also more binding than load in, for example, online ordered package delivery and blood product distribution .…”

Section: Introductionmentioning

confidence: 99%

Complexity of inventory routing problems when routing is easy

Baller

Hoogeboom

et al. 2019

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“…Nevertheless, we need to set the cardinality of customers of set  , in order to compute the assignment cost t sc in (1). In this experimentation, | | is determined as a percentage of ||.…”

Section: Experimentationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In addition, they provide additional services, such as the preparation of shipping and export documents, cargo insurance, and filling of insurance claims. For example, forwarders are very common in the field of intermodal freight transportation [8], aircargo services [15] and cash distribution for ATMs [1]. This paper is motivated by the role of a forwarder without vehicles in dealing with the planning of delivery shipments in a seaport, where a fleet of inbound containers from the sea is filled with pallets, which have different destinations in the land-side.…”

Section: Introductionmentioning

confidence: 99%

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The forwarder planning problem in a two‐echelon network

et al. 2019

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This paper is motivated by the case of a forwarder dealing with inland transportation planning, from a seaport, of inbound containers filled with pallets having different destinations in the land‐side. Although the forwarder is not the owner nor controls any vehicle, he is required to plan both the assignment of containers to intermediate depots, where the pallets are unpacked, and the assignment of pallets to the vehicles used for the distribution from depots to consignees. We present a mathematical model supporting the forwarder in this two‐echelon network to minimize assignment costs, while accounting for a balanced workload among all carriers involved in this distribution scheme. We discuss a tailor‐made implementation of the model in a realistic context and present a heuristic method to solve realistic‐sized instances. Our computational experiments confirm the viability of this method.

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