Cooperation between multiple news-vendors with transshipments

Slikker, Marco; Fransoo, JC Jan; Wouters, Marc

doi:10.1016/j.ejor.2004.03.014

Cited by 122 publications

(73 citation statements)

References 19 publications

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“…Therefore, from (21), in order to find a core allocation (β i : i ∈ N ), we only need to find a vector (θ i : i ∈ N ) that satisfies conditions (19) and (20).…”

Section: Now For Any S ⊆ N We Havementioning

confidence: 99%

Cost Allocation for Joint Replenishment Models

Zhang

2009

Operations Research

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We consider the one-warehouse multiple retailer inventory model with a submodular joint setup cost function. The objective of this model is to determine an inventory replenishment policy that minimizes the long-run average system cost over an infinite time horizon. Although the optimal policy for this problem is still unknown, a class of easy-to-implement power-of-two policies are 98% effective. This paper focuses on how the cost, under an optimal power-of-two policy, should be allocated to the retailers. This question generates an interesting cooperative game. We prove that this cooperative game has a non-empty core. The key to our result is a strong duality theorem for the one-warehouse multiple retailer problem under power-of-two policies.

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“…Therefore, from (21), in order to find a core allocation (β i : i ∈ N ), we only need to find a vector (θ i : i ∈ N ) that satisfies conditions (19) and (20).…”

Section: Now For Any S ⊆ N We Havementioning

confidence: 99%

Cost Allocation for Joint Replenishment Models

Zhang

2009

Operations Research

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“…We envision contracts that will specify both aspects a-priori. Some of these issues were previously analyzed for risk neutral firms with symmetric (i.e., equal across firms) costs in a cooperative setting [12, 13 and references therein] and for unequal shortage costs [18,1]. But none of these authors considered endogenously determined "entitlements" within a cooperative bargaining setting or unequal production costs or risk aversion.…”

Section: Introductionmentioning

confidence: 99%

Nash bargaining over allocations in inventory pooling contracts

Hanany

Gerchak

2008

Naval Research Logistics

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When facing uncertain demand, several firms may consider pooling their inventories leading to the emergence of two key contractual issues. How much should each produce or purchase for inventory purposes? How should inventory be allocated when shortages occur to some of the firms? Previously, if the allocations issue was considered, it was undertaken through evaluation of the consequences of an arbitrary priority scheme. We consider both these issues within a Nash bargaining solution (NBS) cooperative framework. The firms may not be risk neutral, hence a nontransferable utility bargaining game is defined. Thus the physical pooling mechanism itself must benefit the firms, even without any monetary transfers. The firms may be asymmetric in the sense of having different unit production costs and unit revenues. Our assumption with respect to shortage allocation is that a firm not suffering from a shortfall, will not be affected by any of the other firms' shortages. For two risk neutral firms, the NBS is shown to award priority on all inventory produced to the firm with higher ratio of unit revenue to unit production cost. Nevertheless, the arrangement is also beneficial for the other firm contributing to the total production. We provide examples of Uniform and Bernoulli demand distributions, for which the problem can be solved analytically. For firms with constant absolute risk aversion, the agreement may not award priority to any firm. Analytically solvable examples allow additional insights, e.g. that higher risk aversion can, for some problem parameters, cause an increase in the sum of quantities produced, which is not the case in a single newsvendor setting. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

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“…These are core non-emptiness, computational ease and justifiability. The core concept, a measure of stability, has also received special interest by several other papers and the core non-emptiness has been shown for different newsvendor settings: newsvendors with a common pool of inventory (Hartman et al, 2000;Müller et al, 2002;Slikker et al, 2001), and newsvendors with lateral transshipment or multiple channels of supply (Slikker et al, 2005;Özen et al, 2008;Chen and Zhang, 2009). All of these studies assume complete pooling of inventory, i.e., inventory can be diverted to satisfy demand that creates the highest profit from any stock point.…”

Section: Introductionmentioning

confidence: 99%

“…We are first interested in the stability of this type of cooperation and focus on the core concept as many papers in the literature (see Hartman et al, 2000;Müller et al, 2002;Slikker et al, 2001;Slikker et al, 2005;Özen et al, 2008). The core concept considers a natural criterion for stability that is each retailer should do better in the coalition than pursuing any of their alternatives, i.e., working alone or forming another coalition.…”

Section: Introductionmentioning

confidence: 99%

Stability and monotonicity in newsvendor situations

Özen¹,

Erkip

Slikker

2012

European Journal of Operational Research

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a b s t r a c tThis study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers' dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.

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Cooperation between multiple news-vendors with transshipments

Cited by 122 publications

References 19 publications

Cost Allocation for Joint Replenishment Models

Cost Allocation for Joint Replenishment Models

Nash bargaining over allocations in inventory pooling contracts

Stability and monotonicity in newsvendor situations

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