Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands

Federgruen, Awi; Groenevelt, Harry; Tijms, Henk

doi:10.1287/mnsc.30.3.344

Cited by 129 publications

(88 citation statements)

References 20 publications

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“…For such cases, however, Zheng [36] proves that a modified (s, S) policy, so-called (s, c, S) policy, is optimal in the decentralized system. Federgruen et al [12] provide an iterative procedure to repeatedly update the (s, c, S) values for each item until the optimum is reached.…”

Section: Propositionmentioning

confidence: 99%

Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing

Netessine

Savin

Xiao

2006

Operations Research

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We consider the problem of dynamically cross-selling products (e.g., books) or services (e.g., travel reservations) in the e-commerce setting. In particular, we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product, what we call a "packaging complement. " Given consumer preferences and product inventories, we analyze two issues: (1) how to select packaging complements, and (2) how to price product packages to maximize profits.We formulate the cross-selling problem as a stochastic dynamic program blended with combinatorial optimization. We demonstrate the state-dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem. In particular, we focus on two practical business settings: with (the Emergency Replenishment Model) and without (the Lost-Sales Model) the possibility of inventory replenishment in the case of a product stockout. For the Emergency Replenishment Model, we establish that the problem is separable in the initial inventory of all products, and hence the dimensionality of the dynamic program can be significantly reduced. For both models, we suggest several packaging/pricing heuristics and test their effectiveness numerically. AbstractWe consider the problem of dynamically cross-selling products (e.g., books) or services (e.g., travel reservations) in the e-commerce setting. In particular, we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product, "packaging complement". Given consumer preferences and product inventories, two issues are analyzed: (1) how to select packaging complements and (2) how to price product packages to maximize profits.We formulate the cross-selling problem as a stochastic dynamic program blended with combinatorial optimization. We demonstrate the state-dependent and dynamic nature of the optimal package selection problem and derive structural properties of the dynamic pricing problem. In particular, we focus on two practical business settings: with (the Emergency Replenishment model) and without (the Lost Sales model) the possibility of inventory replenishment in the case of a product stock-out. For the Emergency Replenishment model, we establish that the problem is separable in the initial inventory of all products and hence the dimensionality of the dynamic program can be significantly reduced. For both models several packaging/pricing heuristics are suggested and their effectiveness is tested numerically.

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Section: Propositionmentioning

confidence: 99%

Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing

Netessine

Savin

Xiao

2006

Operations Research

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“…The same decomposition technique has later been extended to compound Poisson demand by Thompson and Silver [31] and Silver [28]. Using a similar decomposition approach, Federgruen, Greoenvelt, and Tijms [9] propose a semi-Markov decision model and use a policy-iteration algorithm to solve for the optimal values of the control policy parameters. We denote this policy by (s, c, S) F .…”

Section: Can-order Policiesmentioning

confidence: 99%

“…We let AC* ᏼ denote the optimal cost rate of a given policy ᏼ where ᏼ can be one of the following: Our proposed (Q, S, T) policy; P(s, S) in [33]; (Q, S) in [21] (and [22]; the can-order policies, (s, c, S) F and (s, c, S) M , as calculated in [9] and [18], resp. ; and, Q(s, S) in [20].…”

Section: Comparison With Existing Policiesmentioning

confidence: 99%

The stochastic joint replenishment problem: A new policy, analysis, and insights

Özkaya

Gürler

Berk

2006

Naval Research Logistics

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Abstract:In this study, we propose a new parsimonious policy for the stochastic joint replenishment problem in a singlelocation, N-item setting. The replenishment decisions are based on both group reorder point-group order quantity and the time since the last decision epoch. We derive the expressions for the key operating characteristics of the inventory system for both unit and compound Poisson demands. In a comprehensive numerical study, we compare the performance of the proposed policy with that of existing ones over a standard test bed. Our numerical results indicate that the proposed policy dominates the existing ones in 100 of 139 instances with comparably significant savings for unit demands. With batch demands, the savings increase as the stochasticity of demand size gets larger. We also observe that it performs well in environments with low demand diversity across items. The inventory system herein also models a two-echelon setting with a single item, multiple retailers, and cross docking at the upper echelon.

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“…For any other items, j, whose inventory levels are less than their respective can-order levels, c j , orders will also be placed so that inventory levels of items j are raised to S j . Federgruen et al (1984) modeled a can-order policy as a semi-Markov decision problem with compound Poisson demands and positive lead-times. They showed that a can-order policy is considerably better than uncoordinated policies, often providing as much as a 20% savings.…”

Section: Introductionmentioning

confidence: 99%

Applying Genetic Algorithm for Can-Order Policies in the Joint Replenishment Problem

Nagasawa¹,

Irohara²,

Matoba³

et al. 2015

Industrial Engineering and Management Systems

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In this paper, we consider multi-item inventory management. When managing a multi-item inventory, we coordinate replenishment orders of items supplied by the same supplier. The associated problem is called the joint replenishment problem (JRP). One often-used approach to the JRP is to apply a can-order policy. Under a can-order policy, some items are re-ordered when their inventory level drops to or below their re-order level, and any other item with an inventory level at or below its can-order level can be included in this order. In the present paper, we propose a method for finding the optimal parameter of a can-order policy, the can-order level, for each item in a lost-sales model. The main objectives in our model are minimizing the number of ordering, inventory, and shortage (i.e., lost-sales) respectively, compared with the conventional JRP, in which the objective is to minimize total cost. In order to solve this multi-objective optimization problem, we apply a genetic algorithm. In a numerical experiment using actual shipment data, we simulate the proposed model and compare the results with those of other methods.

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Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands

Cited by 129 publications

References 20 publications

Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing

Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing

The stochastic joint replenishment problem: A new policy, analysis, and insights

Applying Genetic Algorithm for Can-Order Policies in the Joint Replenishment Problem

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