A characterization of optimal base-stock levels for a multistage serial supply chain

Berling, Peter; Martínez‐de‐Albéniz, Victor

doi:10.1002/nav.21675

Cited by 9 publications

(6 citation statements)

References 29 publications

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“…To resolve the potential discontinuity at x = U we define J k U as the minimum of the solution of the HJB equation-i.e., lim x→U J k x -and the cost-togo of not moving the unit at U until more demand(s) has occurred, i.e., J N k U = J k−1 U / r + . This type of discontinuity is discussed in the appendix after the proof of Lemma 2 and is also encountered in Berling and Martínez-de-Albéniz (2011a).…”

Section: Application Of the Model: A Road Transport Case Studymentioning

confidence: 93%

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Dynamic Speed Optimization in Supply Chains with Stochastic Demand

Berling

Martínez‐de‐Albéniz

2016

Transportation Science

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I n this paper, we analyze how to continuously adjust the speed in a supply chain with stochastic demand. For each unit (e.g., truckload, shipping container) in the chain, one must decide at which speed it should be moved downstream, given the state of the system, to minimize total supply chain costs. We decompose the problem into a set of one-dimensional subproblems that can be easily solved and characterize the optimal variable speed policy: under some assumptions, we show that it is optimal to set a speed that is first increasing in the distance to the market, and then decreasing. As a result, at optimality a given unit will experience an accelerating speed and then it will be slowed down, unless a demand occurs, in which case, the speed will be adjusted upward. We finally provide a transportation case study where we estimate the benefits of a variable-speed compared to a fixed-speed policy and show them to be significant both financially and from a CO 2 -emissions perspective.

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Section: Application Of the Model: A Road Transport Case Studymentioning

confidence: 93%

“…With J k x 1 as the new border condition, the first part of the lemma applies for x 1 ≤ x < x 2 and so on. For further details and some examples on discontinuous costs, see Berling and Martínez-de-Albéniz (2011a).…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Dynamic Speed Optimization in Supply Chains with Stochastic Demand

Berling

Martínez‐de‐Albéniz

2016

Transportation Science

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“…Berling and Martínezde-Albéniz (2016a) extend the analysis by Muharremoglu and Tsitsiklis (2008) and allow for expediting but again do not allow order-crossing. Berling and Martínez-de-Albéniz (2016b) apply the results of Berling and Martínez-de-Albéniz (2016a) in the context of transportation within a supply chain.…”

Section: Unit-tracking Approachmentioning

confidence: 99%

Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach

Berling

Sonntag

2022

Production and Operations Management

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This paper considers a single-stage make-to-stock production-inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost-minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unittracking/decomposition approach, taking into account the possibility of order-crossing, which is new to the literature and relevant to other planning problems. The extended unit-tracking/decomposition approach allows us to determine the optimal base-stock level and to formulate the exact and an approximate expression of the per-period cost of a base-stock policy. The same approach is also used to develop a state-dependent ordering policy. The numerical study reveals that our state-dependent policy can reduce inventory-related costs compared to the base-stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory-related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality. K E Y W O R D Sbase-stock policy, inventory control, random yield, rework, unit-tracking approach INTRODUCTIONWe consider a single-stage make-to-stock productioninventory system under random demand and random yield, where defective units are reworked. Random yield refers to the number of items meeting the desired quality requirements, set either by a company itself or externally, for example, by the US Food and Drug Administration (FDA) for pharmaceutical products or the Federal Communications Commission (FCC) for electronic products. Our goal is to determine the ordering policy that minimizes the total average inventory-related cost per period, comprised of holding costs for all units on stock and backorder costs for all units that cannot be satisfied immediately from stock on hand.

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“…Those MSSPs can become intractable with increase in number of time periods and with increase in number of suppliers. Previous methods given in (Cheaitou and Van Delft, 2013), (Berling and Martínez-de Albéniz, 2015) and (Berling and Martínez-de Albéniz, 2016) consider demand distributions to be independent across time. In practice we often encounter dependent or correlated demand and distributions not following parametric distributions.…”

Section: Context and Motivationsmentioning

confidence: 99%

An Approximate Method for Integrated Stochastic Replenishment Planning with Supplier Selection

Sahu

Dhaenens

Veerapen

et al. 2020

Proceedings of the 9th International Conference on Operations Research and Enterprise Systems

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A practical methodology for integrated stochastic replenishment planning with supplier selection is proposed for the single item inventory system. A rolling horizon strategy is adopted to implement the ordering decisions. Our method works in two stages. The first stage is a general black box stage that gives the minimum expected "coverage period" cost. The second stage uses a dynamic programming approach to compute the minimum expected cost for the rolling horizon. The proposed method is applicable for both stationary and non-stationary demand distributions and even for problems with minimum order quantity constraints. We also propose to examine the benefits of a dynamic supplier selection approach in comparison to selecting a common supplier. We conduct extensive numerical analyses on synthetic data sets for validation.

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A characterization of optimal base-stock levels for a multistage serial supply chain

Cited by 9 publications

References 29 publications

Dynamic Speed Optimization in Supply Chains with Stochastic Demand

Dynamic Speed Optimization in Supply Chains with Stochastic Demand

Inventory control in production–inventory systems with random yield and rework: The unit‐tracking approach

An Approximate Method for Integrated Stochastic Replenishment Planning with Supplier Selection

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