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

Anily, Shoshana; Bramel, Julien

doi:10.1002/nav.20031

Cited by 13 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the popularity of vendor-managed inventory (VMI), more and more companies have recognized that significant cost reductions can be achieved by integrating inventory control and vehicle routing into a cost-effective strategy, as illustrated in Chan et al (2002), Kleywegt et al (2002), Anily and Bramel (2004a), Campbell and Savelsbergh (2004), Li et al (2007) and Savelsbergh and Song (2007). Determining such a costeffective distribution strategy is known as Inventory Routing Problem (IRP).…”

Section: Introductionmentioning

confidence: 97%

Effectiveness evaluation on direct shipping strategy

Chen

2008

2008 IEEE International Conference on Systems, Man and Cybernetics

View full text Add to dashboard Cite

This paper considers the infinite horizon inventory routing problem for one-warehouse multi-retailer distribution systems. We focus on developing an analytic approach for evaluating the effectiveness of direct shipping strategy where each vehicle serves only one retailer in one delivery at its optimal replenishment rate. Explicit formula is obtained in terms of a few of easily measurable parameters. The formula allows the effectiveness of direct shipping strategy to be evaluated quickly using even a hand calculator. We demonstrate that the effectiveness of direct shipping is at least the square root of the smallest utilization ratio of vehicle capacity. This implies that direct shipping is 100% (respectively 94.86%) effective whenever the smallest utilization ratio is 100% (respectively 90%). This insight can help a firm answer questions such as: under what conditions does direct shipping perform well, and why? How well does direct shipping perform in a specific situation.

show abstract

Section: Introductionmentioning

confidence: 97%

Effectiveness evaluation on direct shipping strategy

Chen

2008

2008 IEEE International Conference on Systems, Man and Cybernetics

View full text Add to dashboard Cite

show abstract

“…We can observe that most of the earlier works concentrate on an infinite planning horizon (see for example Aghezzaf et al [9], Anily and Bramel [10] and Campbell and Savelsbergh [11]). …”

Section: Introductionmentioning

confidence: 98%

Ant Colony Optimization For Split Delivery Inventory Routing Problem

Wong

Moin

2017

MJCS

View full text Add to dashboard Cite

A one-to-many inventory routing problem (IRP) network comprising of a warehouse and geographically dispersed customers is studied in this paper. A fleet of a homogeneous vehicle located at the warehouse transports multi products from the warehouse to meet customer's demand on time in a finite planning horizon. We allow the customers to be visited more than once in a given period (split delivery) and the demand for each product is deterministic and time varying. Backordering is not allowed. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (the best integer solution) for each problem considered. We propose a modified ant colony optimization (ACO) which takes into account not only the distance but also the inventory that is vital in the IRP. We also carried the sensitivity analysis on important parameters that influence decision policy in ACO in order to choose the appropriate parameter settings. The computational results show that ACO performs better on large instances compared to the upper bound and performs equally well for small and medium instances. The modified ACO requires relatively short computational time.Keywords: Ant Colony Optimization, Inventory, Routing INTRODUCTIONSupply chain management is the control of supply chain to manage the flow of commodity both within and among the companies. Inventory routing problem (IRP) is a challenging NP hard problem in supply chain management which combines the vehicle routing problem where the route to visit the customers is decided and inventory management which concerns on the amount to be delivered to the customers. The main objective of IRP is to minimize both the total transportation and inventory cost over the planning horizon.Generally, IRP can be divided by different criteria such as the type of demand, single or multi period, planning horizon, and inventory policy (order-up-to level or maximum level Coelho and Laporte [1] recently proposed a branch-and-cut algorithm to solve the multi-product multi-vehicle IRP with deterministic demand and stock out cost is not allowed. In their paper, Coelho and Laporte [1] implemented a solution improvement algorithm after branch-and-cut identifies a new best solution. The purpose of solution improvement algorithm is to approximate the cost of a new solution resulting from the vertex removal and reinsertions. In this paper, the authors also considered additional two features: the driver partial consistency and the visiting space consistency. The results show that the visiting space helps in reducing the search space while providing a meaningful solution. This is the first paper that solves the problem with heterogeneous vehicles.The planning horizon of the problem also can be categorized into finite or infinite horizon. We can observe that most of the earlier works concentrate on an infinite planning horizon (see for example Aghezzaf et al. IRP with finite planning horizon can be categorized as a single or multi-period scenario. Feder...

show abstract

“…This article revisits a model first analyzed by Chan et al and subsequently by Anily and Bramel . A product has to be distributed from a central warehouse to a set of geographically dispersed retailers with vehicles of limited capacity.…”

Section: Introductionmentioning

confidence: 99%

“…They showed that the worst‐case asymptotic ratio between the best FPZIO and the best feasible policy is bounded by

\sqrt{2}

. Anily and Bramel focused on FP policies and on measuring the worst‐case asymptotic performance of specific FP policies with respect to the best policy of the class. In Anily and Bramel , a lower bound on the cost of the best possible FP policy was derived: it was shown to be asymptotically 98.5%‐effective.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic analysis of periodic policies for the inventory routing problem

Chan

Speranza

Bertazzi

2013

Naval Research Logistics

View full text Add to dashboard Cite

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

show abstract

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

Cited by 13 publications

References 18 publications

Effectiveness evaluation on direct shipping strategy

Effectiveness evaluation on direct shipping strategy

Ant Colony Optimization For Split Delivery Inventory Routing Problem

Asymptotic analysis of periodic policies for the inventory routing problem

Contact Info

Product

Resources

About