Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

Chan, Lap Mui Ann; Muriel, Ana; Shen, Zuo‐Jun Max; Simchi‐Levi, David; Teo, Chung‐Piaw

doi:10.1287/mnsc.48.11.1446.267

Cited by 125 publications

(82 citation statements)

References 4 publications

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“…Chan et al (2000) have considered a variant of OWMR, in which the ordering costs are piecewise-linear functions, and the holding cost is linear and additive. They considered the class of zero-inventory ordering (ZIO) policies, in which the warehouse and retailers order if and only if their current on hand inventory is 0.…”

Section: Introductionmentioning

confidence: 99%

“…They established the effectiveness of these policies, showing that the cost of the optimal ZIO policy is at most 4 3 times the cost of the optimal policy. In Chan et al (2000) and in a subsequent paper by Shen et al (2002), they have proposed an integer program to find the optimal ZIO policy, which is NP-hard. Next they have developed heuristics to round the optimal solution of the LP relaxation to get an approximation algorithm for finding the best ZIO policy.…”

Section: Introductionmentioning

confidence: 99%

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A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

et al. 2008

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Deterministic inventory theory provides streamlined optimization models that attempt to capture tradeoffs in managing the flow of goods through a supply chain. We will consider two well-studied deterministic inventory models, called the one-warehouse multi-retailer problem (OWMR) and its special case the joint replenishment problem (JRP), and give approximation algorithms with worst-case performance guarantees.That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8-approximation algorithm. Our results are based on an LP-rounding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP problem.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

et al. 2008

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“…Becchetti et al (2006) and Khanna et al (2002) have considered special cases of the tree JRP with assumptions on the holding cost structure. Chan et al (2002) show that zero-inventory policies are near-optimal for joint replenishment problems with piecewise linear costs, however their conditions do not imply submodularity.…”

Section: Literature Reviewmentioning

confidence: 94%

The submodular joint replenishment problem

et al. 2015

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The joint replenishment problem is a fundamental model in supply chain management theory that has applications in inventory management, logistics, and maintenance scheduling. In this problem, there are multiple item types, each having a given time-dependent sequence of demands that need to be satisfied. In order to satisfy demand, orders of the item types must be placed in advance of the due dates for each demand. Every time an order of item types is placed, there is an associated joint setup cost depending on the subset of item types ordered. This ordering cost can be due to machine, transportation, or labor costs, for example. In addition, there is a cost to holding inventory for demand that has yet to be served. The overall goal is to minimize the total ordering costs plus inventory holding costs.In this paper, the cost of an order, also known as a joint setup cost, is a monotonically increasing, submodular function over the item types. For this general problem, we show that a greedy approach provides an approximation guarantee that is logarithmic in the number of demands. Then we consider three special cases of submodular functions which we call the laminar, tree, and cardinality cases, each of which can model real world scenarios that previously have not been captured. For each of these cases, we provide a constant factor

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“…While many of the papers in this area consider the problem in a single echelon setting (e.g., Aucamp, 1982;Lee, 1986;Tersine and Barman, 1994;Shinn et al, 1996;Burwell et al, 1997;Hwang et al, 1990;Jaruphongsa et al, 2005;Mendoza and Ventura, 2008;Rieksts and Ventura, 2008;Toptal, 2009), relatively recent papers model and solve the replenishment problems of multiple echelons under transportation considerations (see Hoque and Goyal, 2000;Çetinkaya and Lee, 2002;Chan et al, 2002;Toptal et al, 2003;Toptal and Çetinkaya, 2006;Rieksts and Ventura, 2010).…”

Section: Introductionmentioning

confidence: 99%

Transportation pricing of a truckload carrier

Toptal

Bingöl

2011

European Journal of Operational Research

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a b s t r a c tFreight transportation is a major component of logistical operations. Due to the increase in global trade, fierce competition among shippers and raising concerns about energy, companies are putting more emphasis on effective management and usage of transportation services. This paper studies the transportation pricing problem of a truckload carrier in a setting that consists of a retailer, a truckload carrier and a less than truckload carrier. In this setting, the truckload carrier makes his/her pricing decision based on previous knowledge on the less than truckload carrier's price schedule and the retailer's ordering behavior. The retailer then makes a determination of his/her order quantity through an integrated model that explicitly considers the transportation alternatives, and the related costs (i.e., bimodal transportation costs) and capacities. In the paper, the retailer's replenishment problem and the truckload carrier's pricing problem are modeled and solved based on a detailed analysis. Numerical evidence shows that the truckload carrier may increase his/her gainings significantly through better pricing and there is further opportunity of savings if the truckload carrier and the retailer coordinate their decisions.

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Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

Cited by 125 publications

References 4 publications

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

The submodular joint replenishment problem

Transportation pricing of a truckload carrier

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