An asymptotic 98.5%-effective lower bound on fixed partition policies for the inventory-routing problem

Anily, Shoshana; Bramel, Julien

doi:10.1016/j.dam.2003.09.005

Cited by 34 publications

(28 citation statements)

References 10 publications

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“…For j ʦ {1, 2, 3}, let d j denote the retailer's average distance from the depot in the ring A j . The next theorem is from [3]. THEOREM 1: Under the assumptions of our probabilistic model:…”

Section: Preliminariesmentioning

confidence: 98%

“…Note that the vehicle leaves the depot carrying Wt* Յ Q units of product. Anily and Bramel [3] provide deterministic and probabilistic lower bounds on the cost of any FPP. The rest of this section presents some of those results which are needed for the current analysis.…”

Section: Preliminariesmentioning

confidence: 99%

“…The analysis of the proposed heuristic is based on the following probabilistic model which is the same as in [3,9] and similar to [1,5,7]. Each retailer is characterized by two random variables: its location and its demand rate which are assumed independent.…”

Section: Preliminariesmentioning

confidence: 99%

“…The main reason for the relatively slow progress in this direction is due to the lack of a good lower bound on the optimal cost in the FPP class. In [3], the authors develop a lower bound on the optimal cost within the FPP class, which is shown to be asymptotically at least 98.5% of the optimal cost.…”

Section: Introductionmentioning

confidence: 98%

“…In this paper we present a procedure which is based on a region partitioning scheme (RP) called the Circular Fixed Partitioning scheme (CFP) and we investigate its effectiveness relative to the lower bound on the FPP class that was derived in [3]. The scheme works as follows.…”

Section: Introductionmentioning

confidence: 99%

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A probabilistic analysis of a fixed partition policy for the inventory‐routing problem

Anily

Bramel

2004

Naval Research Logistics

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Abstract:We consider the Inventory-Routing Problem (IRP) where n geographically dispersed retailers must be supplied by a central facility. The retailers experience demand for the product at a deterministic rate, and incur holding costs for keeping inventory. Distribution is performed by a fleet of capacitated vehicles. The objective is to minimize the average transportation and inventory costs per unit time over the infinite horizon. We focus on the set of Fixed Partition Policies (FPP). In an FPP, the retailers are partitioned into disjoint and collectively exhaustive sets. Each set of retailers is served independently of the others and at its optimal replenishment rate. Previous research has measured the effectiveness of an FPP solution relative to a lower bound over all policies. We propose an additional measure that is relative to the optimal FPP. In this paper we construct a polynomial-time partitioning scheme that is shown to yield an FPP whose cost is asymptotically within 1.5% ϩ ⑀ of the cost of an optimal FPP, for arbitrary ⑀ Ͼ 0. In addition, in some cases, our polynomial-time scheme yields an FPP whose cost is asymptotically within 1.5% ϩ ⑀ of the minimal policy's cost (over all feasible policies).

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Section: Preliminariesmentioning

confidence: 98%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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A probabilistic analysis of a fixed partition policy for the inventory‐routing problem

Anily

Bramel

2004

Naval Research Logistics

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Asymptotic analysis of periodic policies for the inventory routing problem

Chan

Speranza

Bertazzi

2013

Naval Research Logistics

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In this article, a distribution system is studied where the sum of transportation and inventory costs is to be minimized. The inventory holding cost is assumed to be the same for all retailers. A fixed partition (FP) periodic policy is proposed with tight asymptotic worst‐case performance of 3/2 with respect to the best possible policy. This bound cannot be improved in the class of FP periodic policies. In partition‐based PB policies, the retailers are first partitioned into sets and then the sets are grouped in such a way that sets of retailers within a group are served together at selected times. A PB periodic, policy is presented with tight worst‐case asymptotic performance of 11−46≈1.202 with respect to the best possible policy. This latter performance improves the worst‐case asymptotic performance of 2 of the previously best known policy for this problem. We also show that the proposed PB periodic policy has the best worst‐case asymptotic performance within the class of PB policies. Finally, practical heuristics inspired by the analyzed policies are designed and tested. The asymptotic worst–case performances of the heuristics are shown to be the same of those of the analyzed policies. Computational results show that the heuristics suggested are less than 6.4% on average from a lower bound on the optimal cost when 50 or more retailers are involved. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013

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