A dynamic lot-sizing model with multi-mode replenishments: polynomial algorithms for special cases with dual and multiple modes

Jaruphongsa, Wikrom; Çetinkaya, Sıla; Lee, Chung Yee

doi:10.1080/07408170590918218

Cited by 43 publications

(44 citation statements)

References 30 publications

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“…The warehouse orders incur a fixed cost and the outbound transportation cost function consists of a fixed cost per delivery plus a cost per vehicle dispatched. Jaruphongsa et al [12] consider a similar model with two available outbound shipment modes: one with a fixed setup cost structure and the other with a multiple setup cost structure. Diaby and Martel [10] develop a Lagrangian relaxation based procedure to solve a more general problem for multiechelon distribution systems (each facility has a single predecessor) with general piece-wise linear ordering and transportation cost functions.…”

Section: Introductionmentioning

confidence: 98%

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Jin¹,

Muriel

2009

Naval Research Logistics

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Abstract:We consider a multi-stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118-138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T 2 ) algorithm for the single-stage dynamic lot sizing problem; (2) an O(T 3 ) algorithm for the case of a single-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal.

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Section: Introductionmentioning

confidence: 98%

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Jin¹,

Muriel

2009

Naval Research Logistics

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“…This problem is extensively studied (Veinott 1969, Atkins andIyogun 1988) and is sometimes referred to as the coordinated replenishment problem (Kao 1979, Chung et al 1996, Robinson and Gao 1996, Robinson and Lawrence 2004 or the joint replenishment problem (Joneja 1990, Federgruen andTzur 1994). In the case where the orders can be shipped via multiple modes, there is a different set up structure associated with each mode (Jaruphongsa et al 2005). Production planning models without set ups have also been considered.…”

Section: Extension On the Set Upsmentioning

confidence: 99%

Modeling industrial lot sizing problems: a review

Jans¹,

Degraeve²

2008

International Journal of Production Research

295

120

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“…Their focus is to find the optimal replenishment quantities to minimize the sum of transportation and inventory related costs. See, for example, Aucamp (1982), Lee (1986), Lee (1989), Tersine and Barman (1994), Çetinkaya and Lee (2002), Jaruphongsa et al (2005), Mendoza and Ventura (2008). The papers in the latter body of research, study the pricing of transportation services within the context of fleet management.…”

Section: Introductionmentioning

confidence: 99%

“…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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A dynamic lot-sizing model with multi-mode replenishments: polynomial algorithms for special cases with dual and multiple modes

Cited by 43 publications

References 30 publications

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Modeling industrial lot sizing problems: a review

Transportation pricing of a truckload carrier

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