A lower bound on a class of coordinated inventory/production problems

Atkins, Derek; Iyogun, Paul

doi:10.1016/0167-6377(87)90031-9

Cited by 29 publications

(7 citation statements)

References 9 publications

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“…Continue this procedure until all the transportation cost has been allocated. The details of the allocation can be found in Atkins and Iyogun (1987). Update the setup costs of the retailers with the inclusion of the allocated fraction of the transportation cost.…”

Section: Heuristic H1mentioning

confidence: 99%

“…To account for the transportation cost in each delivery period, we propose to allocate a fraction of this cost to the setup cost of the individual retailers. The method of allocation has been discussed by Atkins and Iyogun (1987). Given the modified setup cost of the individual retailers, the power-of-two policies for the retailers are then chosen with an aim to make the associated inventory cost low.…”

Section: The Heuristicmentioning

confidence: 99%

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A two-echelon inventory system with transportation capacity constraint

Huang

Chew

Goh

2005

European Journal of Operational Research

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Section: Heuristic H1mentioning

confidence: 99%

Section: The Heuristicmentioning

confidence: 99%

A two-echelon inventory system with transportation capacity constraint

Huang

Chew

Goh

2005

European Journal of Operational Research

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“…This leads to a new lower-bound function. (Many lower bounds have been derived by setup-cost allocations, see, e.g., Atkins and Iyogun 1987, Atkins 1990…”

Section: Alternative Lower-bound Functionsmentioning

confidence: 99%

Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems

Chen¹,

Zheng²

1998

Operations Research

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We study echelon-stock (R, nQ) policies in a multistage, serial inventory system with compound Poisson demand. We provide a simple method for determining near-optimal control parameters. This is achieved in two steps. First, we establish lower and upper bounds on the cost function by over-and under-charging a penalty cost to each upstream stage for holding inadequate stock. Second, we minimize the bounds, which are simple, separable functions of the control parameters, to obtain heuristic solutions. We also provide an algorithm that guarantees an optimal solution at the expense of additional computational effort. A numerical study suggests that the heuristic solutions are easy to compute (even for systems with many stages) and are close to optimal. It also suggests that a traditional approach for determining the order quantities can be seriously suboptimal. All the results can be easily extended to the discrete-time case with independent, identically distributed demands.

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“…This decomposition enables us to use the results described in Section 1. A similar technique is used in Atkins and Iyogun (1987).…”

Section: Worst-case Analysismentioning

confidence: 99%

Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging

Chen

1998

Operations Research

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A stationary policy conducts replenishment activities-the placement and fulfillment of orders-in a stationary fashion. That is, each facility receives a constant batch (facility specific) in equal time intervals (facility specific) under a stationary policy. Although the advantages of stationary policies are clear (i.e., smooth operations), they represent a restriction in policy selection. This paper investigates how costly this restriction can be. For two multiechelon systems (serial and distribution) with deterministic demand and backlogging, we show that stationary policies are 70%-effective. This bound is tight in the sense that an example exists where the bound is reached. On the other hand, the average effectiveness of stationary policies is very high. In a set of 1,000 randomly generated numerical examples, we observed that the average effectiveness was 99%, and the standard deviation was 1.5%. The numerical examples also suggest that the performance of stationary policies deteriorates in systems where the setup cost decreases dramatically from an upstream stage to a downstream stage. Finally, a key building block of the above results is the existing lower bounds on the average costs of all feasible policies in the above systems. We provide a simpler derivation of these bounds.

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A lower bound on a class of coordinated inventory/production problems

Cited by 29 publications

References 9 publications

A two-echelon inventory system with transportation capacity constraint

A two-echelon inventory system with transportation capacity constraint

Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems

Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging

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