Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times

Rossi, Roberto; Tarim, Ş. Armağan; Hnich, Brahim; Prestwich, Steven

doi:10.1016/j.ijpe.2010.05.011

Cited by 34 publications

(26 citation statements)

References 23 publications

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“…1, adopted from Coleman, 1994). In particular, varying lead-time increases supply chain cost (Chaharsooghi and Heydari, 2010), exacerbates the bullwhip effect (Kim et al, 2006) and significantly affects policy making (Rossi et al, 2010). Misperceived lead-time creates a so-called phenomenon of 'inventory drift' and attenuates the efficacy of meeting safety stock requirements (Disney and Towill, 2005).…”

Section: The Introduction and Motivationmentioning

confidence: 99%

Stability analysis of constrained inventory systems with transportation delay

Wang

Disney

Wang

2012

European Journal of Operational Research

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Stability is a fundamental design property of inventory systems. However, the often exploited linearity assumptions in the current literature create a major gap between theory and practice. In this paper the stability of a constrained production and inventory system with a Forbidden Returns constraint (that is, a non-negative order rate) is studied via a piecewise linear model, an eigenvalue analysis and a simulation investigation. The APVIOBPCS (Automatic Pipeline, Variable Inventory and Order Based Production Control System) and EPVIOBPCS (Estimated Pipeline, Variable Inventory and Order Based Production Control System) replenishment policies are adopted. Surprisingly, all kinds of non-linear dynamical behaviours of systems can be observed in these simple models. Exact expressions of the asymptotic stability boundaries and Lyapunovian stability boundaries are derived when actual and perceived transportation lead-time is 1 and 2 periods long respectively. Asymptotically stable regions in the non-linear Forbidden Return systems are identical to the stable regions in its unconstrained counterpart. However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region. Simulation shows a complex and delicate structure in these regions. The results suggest that accurate lead-time information is essential to eliminate inventory drift and instability and that ordering policies have to be designed properly in accordance with the actual lead-time to avoid these fluctuations and divergence. Keywords: Inventory; logistics; system dynamics; complexity theory The introduction and motivationOne of the main objectives when designing an inventory system is to maintain its stability and robustness in the face of exterior disturbances. Since the introduction of control theory and system dynamics approaches to the field of inventory control (Simon, 1952;Forrester, 1961), many works have studied this problem. However, the significance of results obtained are frequently limited by both the uncertainty and complexity of the system structure. Often omitted factors in inventory system design include saturation (logistics constraints) and mis-specified delays (lead-times).In previous supply chain stability studies (Riddalls and Bennett, 2002;Nagatani and Helbing, 2004;Warburton et al., 2004;Disney, 2008), linear inventory system models are usually adopted. Linearity assumptions include infinite capacity, ignoring inventory limitations and return restrictions. This has greatly limited the applicability of published results, and has failed to explain many business phenomena (Riddalls et al., 2000). For instance, to maintain linearity of the commonly investigated IOBPCS (Inventory and Order Based Production Control System) models, order rates are permitted to take negative values. This means that all participants in a supply chain are allowed to return excess product freely. Specifically, a negative order rate value leads to a ...

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Section: The Introduction and Motivationmentioning

confidence: 99%

Stability analysis of constrained inventory systems with transportation delay

Wang

Disney

Wang

2012

European Journal of Operational Research

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“…Tempelmeier (2007) used Tarim and Kingsman's model as a basis to formulate different types of service-level constraints. Rossi et al (2010), Rossi et al (2011a) incorporated a stochastic delivery lead time and developed both complete and fast heuristic approaches. Tempelmeier (2011) incorporated supplier capacity constraints.…”

Section: Literature Reviewmentioning

confidence: 99%

An MILP approximation for ordering perishable products with non-stationary demand and service level constraints

Pauls-Worm

Hendrix

Haijema

et al. 2014

International Journal of Production Economics

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“…The stochastic supply chain network design model is provided as a multi-stage stochastic program (Çakanyildirim, Bookbinder et al 2000;Huang and Küçükyavuz 2008;Rossi, Tarim et al 2010). This paper considers the optimal strategy of collaborative order and inventory with one assembly manufacturer and multi-suppliers with stochastic demand and variable lead time.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Reorder Point Strategy of Assembly Manufacturer with Random Variables

Li¹,

Zhang²,

Jin³

2013

IJBM

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For assembly system, randomness and variableness make it impossible to control the inventory accurately specially. Because the negative effect of them have ripple effects. So we investigate reorder point optimization strategy of assembly manufacturing system with random demand and random lead time. We seek the manufacturers order strategy for the minimum integration of the supply chain inventory cost. And we use scale benefits parameters of suppliers in this system to reflect actual influence of the lot's scale. Numerical example of two components assembly system is given to illustrate the effectiveness of the reorder point strategy. From the numerical simulation, it is can be seen backorder rate and order scale effect will impact the total supply chain cost dramatically.

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Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times

Cited by 34 publications

References 23 publications

Stability analysis of constrained inventory systems with transportation delay

Stability analysis of constrained inventory systems with transportation delay

An MILP approximation for ordering perishable products with non-stationary demand and service level constraints

Optimization of Reorder Point Strategy of Assembly Manufacturer with Random Variables

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