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Multiple order-up-to policy for mitigating bullwhip effect in supply chain network

Keshari, Anupam; Mishra, Nishikant; Shukla, Nagesh; McGuire, Steve; Khorana, Sangeeta


Anupam Keshari

Nagesh Shukla

Steve McGuire

Sangeeta Khorana


This paper proposes a multiple order-up-to policy based inventory replenishment scheme to mitigate the bullwhip effect in a multi-stage supply chain scenario, where various transportation modes are available between the supply chain (SC) participants. The proposed policy is similar to the fixed order-up-to policy approach where replenishment decision “how much to order” is made periodically on the basis of the pre-decided order-up-to inventory level. In the proposed policy, optimal multiple order-up-to levels are assigned to each SC participants, which provides decision making reference point for deciding the transportation related order quantity. Subsequently, a mathematical model is established to define optimal multiple order-up-to levels for each SC participants that aims to maximize overall profit from the SC network. In parallel, the model ensures the control over supply chain pipeline inventory, high satisfaction of customer demand and enables timely utilization of available transportation modes. Findings from the various numerical datasets including stochastic customer demand and lead times validate that—the proposed optimal multiple order-up-to policy based inventory replenishment scheme can be a viable alternative for mitigating the bullwhip effect and well-coordinated SC. Moreover, determining the multiple order-up-to levels is a NP hard combinatorial optimization problem. It is found that the implementation of new emerging optimization algorithm named bacterial foraging algorithm (BFA) has presented superior optimization performances. The robustness and applicability of the BFA algorithm are further validated statistically by employing the percentage heuristic gap and two-way ANOVA analysis.


Keshari, A., Mishra, N., Shukla, N., McGuire, S., & Khorana, S. (2018). Multiple order-up-to policy for mitigating bullwhip effect in supply chain network. Annals of Operations Research, 269(1-2), 361-386.

Journal Article Type Article
Acceptance Date May 4, 2017
Online Publication Date May 28, 2017
Publication Date 2018-10
Deposit Date Jun 6, 2017
Publicly Available Date May 29, 2018
Journal Annals of operations research
Print ISSN 0254-5330
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 269
Issue 1-2
Pages 361-386
Keywords Bullwhip effect; Optimal order-up-to inventory level; Bacterial foraging algorithm; Supply chain
Public URL
Publisher URL
Additional Information This is a description of an article published in Annals of operations research, 2017.
Contract Date Jun 6, 2017


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