Newsvendor equations for optimal reorder levels of serial inventory systems with fixed batch sizes

Doğru, Mustafa K.; Houtum, Geert‐Jan van; Kok, A.G. de

doi:10.1016/j.orl.2008.06.003

Cited by 7 publications

(10 citation statements)

References 10 publications

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“…In other words, the y * k u are those values, such that the first-passage time k has cdf h. (A similar but more complex relation holds for integer demand; see Dogru et al 2008.) This connection will be useful later.…”

Section: First-passage Times and Stockout Probabilitiesmentioning

confidence: 98%

Supply Streams

Song

Zipkin

2013

M&SOM

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A supply stream is a continuous version of a supply chain. It is like a series inventory system, but stock can be held at any point along a continuum, not just at discrete stages. We assume stationary parameters and aim to minimize the long-run average total cost. We show that a stationary continuous-stage echelon base-stock policy is optimal. That is, at each geographic point along the supply stream, there is a target echelon inventory level, and the optimal policy at all times is to order and dispatch material so as to move the echelon inventory position as close as possible to this target. We establish this result by showing that the solutions to certain discrete-stage systems converge monotonically to a limit, as the distances between the stages become small, and this limit solves the continuous-stage system. With demand approximated by a Brownian motion, we show that, in the continuous-stage limit, the supply stream model is equivalent to one describing first-passage times. This linkage leads to some interesting and useful results. Specifically, we obtain a partial differential equation that characterizes the optimal cost function, and we find a closed-form expression for the optimal echelon basestock levels in a certain special case, the first in the inventory literature. These expressions demonstrate that the well-known square-root law for safety stock does not apply in this context.

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Section: First-passage Times and Stockout Probabilitiesmentioning

confidence: 98%

Supply Streams

Song

Zipkin

2013

M&SOM

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“…The optimal policy for the inventory control of a one-warehouse multi-retailer inventory system is unknown, and expected to be complex; Dogru (2006) provides numerical analysis of the optimal policy for a few instances that supports the claim. However, an assumption, known as the balance assumption, leads to the decomposition property and the full characterization of the optimal policy.…”

Section: Introductionmentioning

confidence: 91%

“…Using the convexity of the expected cycle cost function G cyc (•, z * ), it can be shown that a base stock policy (y 0 , z * ) with y 0 ∈ Y * 0 minimizes the average expected cost of a one-warehouse multi-retailer inventory system in an infinite horizon under the balance assumption (see Federgruen and Zipkin 1984b;Dogru 2006).…”

Section: Single Cycle Analysismentioning

confidence: 99%

“…For serial systems where materials flow from one stock point to another in fixed batches (which is a generalization of Clark and Scarf model where fixed batch quantities equal to one at each stock point), echelon (R, Q) policies have been proven to be optimal by Chen (2000). Dogru et al (2008) identified that the optimal reorder levels satisfy newsvendor characterizations. Diks and de Kok (1998) showed that the optimal base stock levels in a one-warehouse multi-retailer inventory system with continuous demands satisfy newsvendor equations.…”

Section: Introductionmentioning

confidence: 99%

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Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption

Dogru¹,

Kok

Houtum

2012

Cent Eur J Oper Res

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“…Seo et al [22] defined the order risk policy to decide reorder time to develop the optimal reorder policy for a distribution system with one-warehouse and multiple retailers. Dogru et al [23] used echelon stock newsvendor equations to optimize the reorder policy in an N-echelon stochastic serial inventory system with a given fixed batch size and linear penalty costs. Leng and Parlar [24] developed a simple profit-sharing contract to achieve supply chain coordination where the retailer manages the inventory system using reorder policy.…”

Section: Literature Reviewmentioning

confidence: 99%

Coordination of a Supply Chain with Advertising Investment and Allowing the Second Ordering

Xiao¹,

Xin-xin²,

Zhao³

2010

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This paper develops a game theoretic model of a one-manufacturer and one-retailer supply chain allowing the second ordering to investigate how to coordinate the order quantity and advertising investment via a markdown money-cooperative advertising contract. We focus on the effects of allowing the second ordering on equilibrium outcome and coordination mechanism. We find: the relationship between the unit wholesale prices and the chargeback rate depends on whether allowing the second ordering; the coordination mechanism is robust to demand uncertainty; the unit wholesale price in period 2 increases with the unit production cost in period 2, the unit delayed delivery cost and unit salvage value if and only if the chargeback rate is sufficiently small while that in period 1 is independent of them. In addition, we study the Pareto condition of coordination mechanism under which both manufacturer and retailer are better off using the coordination mechanism and find that the unit production costs in different periods may have contrary effects on the bounds of Pareto range

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Newsvendor equations for optimal reorder levels of serial inventory systems with fixed batch sizes

Cited by 7 publications

References 10 publications

Supply Streams

Supply Streams

Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption

Coordination of a Supply Chain with Advertising Investment and Allowing the Second Ordering

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