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Bilevel Programming for Manufacturers Operating in an Omnichannel Retailing Environment

Gupta, V.K.; Dakare, S.; Fernandes, K.J.; Thakur, L.S.; Tiwari, M.K.

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V.K. Gupta

S. Dakare

L.S. Thakur

M.K. Tiwari


This paper presents a joint production, pricing and inventory control problem that can help manufacturers manage revenue in an omnichannel environment. The paper puts forward a multi-period Stackelberg game between a manufacturer and a retailer, assuming the former to be the leader. The leader– follower game is formulated as a mixed-integer non-linear bilevel optimization problem wherein both players seek to maximize their respective profits. The manuscript envisions an omnichannel retailing environment where online, offline, direct and drop-shipping channels coexist. It then investigates how enabling showrooming and webrooming on the drop-shipping channel account can affect supply chain profitabilities. Analyses suggest that when customers are aided with showrooming and webrooming services and are allowed to place drop-shipping orders from retailers’ stores, additional profit can be generated in the supply chain. To solve the proposed bilevel optimization problem, we investigated a) single-level reduction using Karush–Kuhn–Tucker (KKT) conditions and b) hierarchical optimization technique based on Simulated Annealing and Randomized Decomposition Solver. To assess the efficacy of the solution techniques, a comparative analysis was carried out. Thereafter, with the aid of numerical experiments and sensitivity analyses, the paper draws key managerial insights for manufacturers.


Gupta, V., Dakare, S., Fernandes, K., Thakur, L., & Tiwari, M. (2023). Bilevel Programming for Manufacturers Operating in an Omnichannel Retailing Environment. IEEE Transactions on Engineering Management, 70(11), 3958 - 3975.

Journal Article Type Article
Acceptance Date Jun 13, 2021
Online Publication Date Jul 20, 2021
Publication Date 2023-11
Deposit Date Jun 16, 2021
Publicly Available Date Jun 17, 2021
Journal IEEE Transactions on Engineering Management
Print ISSN 0018-9391
Electronic ISSN 1558-0040
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 70
Issue 11
Pages 3958 - 3975
Public URL


Accepted Journal Article (771 Kb)

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