Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

Gaalman, Gerard

doi:10.1016/j.automatica.2006.04.017

Cited by 49 publications

(30 citation statements)

References 13 publications

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“…A state space representation of a process is not unique and in standard text books several possibilities can be found. Our representation differs from the one commonly used in forecasting economic time series (see also Gaalman, 2006) because we have defined a slightly different state vector, which of course, we are free to do. For this demand process we define a 2-dimensional (demand) state vector t y with components …”

Section: Introductionmentioning

confidence: 99%

“…Here we assume that an infinite amount of past demand information is available. G is the so-called Kalman gain vector that can be calculated from the associated stationary matrix Riccati equation (see also Gaalman, 2006, for the general ARMA(p,q) demand process). The forecast update procedure is similar to (general) exponential smoothing (Brown, 1963) and is an efficient way to calculate the demand forecasts.…”

Section: Introductionmentioning

confidence: 99%

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On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

Gaalman

Disney

2009

International Journal of Production Economics

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. On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times. AbstractA number of papers have recently appeared that investigate the "bullwhip effect" (the variance amplification of ordering decisions in the supply chain) produced by the order-up-to replenishment policy. An adapted policy, with a proportional inventory position feedback controller, has shown improved "bullwhip" behaviour. The dynamic behaviour of this so called "proportional order-up-to" policy has been investigated for arbitrary lead-times and several demand models such as i.i.d. demand and autoregressive moving average AR(1) and ARMA(1,1) models. It has been shown that, for a correct choice of the feedback parameter, the bullwhip effect can always be avoided. However, less attractive properties of this policy have also become clear.Herein, we investigate the behaviour of the proportional order up to policy for ARMA(2,2) demand with arbitrary lead-times. In order to compensate for possible weaknesses of the proportional OUT policy we propose another replenishment rule that accounts for the characteristics of the demand in a superior manner. The characteristics of both policies are compared for several parameter settings of the ARMA(2,2) model. Finally, the consequences of our full-state-feedback order-up-to policy are discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

Gaalman

Disney

2009

International Journal of Production Economics

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“…This method focuses on evaluating and improving supply chain design (Ortega and Lin, 2004;Dejonckheere et al, 2003;Gaalman, 2006). It involves representing the supply chain using mathematical equations based on transfer functions which are then solved to get exact values for performance measures.…”

Section: Control Theorymentioning

confidence: 99%

‘Bullwhip’ and ‘backlash’ in supply pipelines

Shukla

Naim

Yaseen

2009

International Journal of Production Research

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“…Over the last two decades numerous innovative solutions have been presented, and therefore, further in this section we are able to mention only a few, arbitrarily selected examples. In [12] and [16] autoregressive moving average (ARMA) system structure has been applied in order to model uncertain demand. Then in [6,[17][18][19] model predictive control of supply chain has been proposed and in [20] a robust controller for the continuous-time system with uncertain processing time and delay has been designed by minimising H ∞ -norm.…”

Section: Introductionmentioning

confidence: 99%

“…Also estimation techniques have been used in inventory management literature. The recursive least squares method and Kalman filter, were applied in [17] and [21] for lead time identification and in [12] and [16] for demand forecasting respectively. Several other methods, including convex programming [22], genetic algorithms [23], heuristic techniques [24] and simulations [25] have also been applied to improve warehouse operation.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode control of periodic review perishable inventories with multiple suppliers and transportation losses

Bartoszewicz¹,

Maciejewski²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The purpose of this paper is to develop robust and computationally efficient supply chain management strategy ensuring fast reaction to the demand variations for periodic review perishable inventory systems. For that purpose, we apply a sliding mode approach and we propose a new discrete time warehouse management strategy. The strategy employs the sliding hyperplane appropriately designed to ensure a dead-beat performance of the closed loop system. Our strategy not only explicitly takes into account decay of goods stored in the warehouse (perishing inventories) but it also accounts for transportation losses which take place on the way from suppliers to the warehouse. The proposed strategy ensures full customers' demand satisfaction, minimizes the on-hand inventory volume and prevents from exceeding the warehouse capacity. This reflects the need of simultaneous minimization of the lost sales costs and inventory holding costs. Furthermore, the strategy ensures that the ordered quantities of goods are always non-negative and upper bounded. These favourable properties of the proposed strategy are formally stated as a lemma and three theorems and proved in the paper.

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Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

Cited by 49 publications

References 13 publications

On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times

‘Bullwhip’ and ‘backlash’ in supply pipelines

Sliding mode control of periodic review perishable inventories with multiple suppliers and transportation losses

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