I come from Naihati, a suburban area not far from the state capital of West Bengal. Raised in a middle-class family, I completed my schooling at a local school before moving to Jadavpur University for higher studies. During my student life, I was actively involved in student politics. Later, while pursuing my research at Jadavpur University, I served as the General Secretary of the Jadavpur University Research Scholars’ Association for two years. I have been a bibliophile since childhood. While I read widely across genres, I am especially drawn to thrillers, horror, and historical literature. Although I once enjoyed watching sports, my interests have gradually shifted towards debates and history-related podcasts (thanks to YouTube), and thriller or comedy films and web series (thanks to torrents). I would describe myself as jovial, thoughtful, disciplined, and adaptable, yet uncompromising when it comes to issues like corruption.
EDUCATION
B.Sc. (H) in Mathematics, Jadavpur University, 2004-2007, 66.33% (with distinction)
M.Sc. in Mathematics, Specialization in Operations Research, Jadavpur University, 2007-2009, 74.8%, 1st class 5th
CSIR-UGC NET JRF in June 2009 & December 2009
Ph.D. in Supply chain management, Jadavpur University, 2010-2015
RESEARCH, TEACHING, or OTHER INTERESTS
Management Science and Operations Research, Control and Optimization, Algebra and Number Theory, Statistics and Probability
27
Scopus Publications
901
Scholar Citations
14
Scholar h-index
18
Scholar i10-index
Scopus Publications
Vendor managed inventory under price-and-stock-dependent demand, buyer’s space limitations and preservation investment Nabin Sen, Indrani Modak, Bibhas C Giri, Sudarshan Bardhan IMA Journal of Management Mathematics, 2025 Accepted by: M. Zied Babai This study explores a two-level vendor managed inventory model for deteriorating items facing demand dependent on stock and price, while operating under a consignment stock policy. It presents a joint vendor-buyer model that considers varying deterioration rate and preservation technology investment for both parties. The model is developed under the constraint of limited warehouse space at the buyer’s end. The study offers an analytical discourse on the model that aims to determine the optimal values for the selling price, preservation technology investment and shipment time. An assessment is conducted to determine the optimal model for a specific business through a comparative analysis of the capacitated and uncapacitated models. The applicability and robustness of the proposed model are established through the inclusion of numerical illustration and sensitivity analysis. The proposed model is deemed suitable for industries that specializes in clothing, food and pharmaceutical products, provided that all underlying assumptions of the model are adequately met.
A multi-period inventory model with price, time and service level dependent demand under preservation technology investment Sudarshan Bardhan, Indrani Modak, Bibhas Chandra Giri European Journal of Industrial Engineering, 2025 Price and time are two important parameters having significant impact on market demand, especially for fashion items, newly launched electronic products, etc. After-sale service facility offered by the retailers is seen to boost demand while investing in preservation technology reduces product spoilage. All these issues are taken into consideration while developing a multi-period inventory model where market demand depends on all three of the above-mentioned factors. The replenishment cycles are all of equal length, but due to the time-dependent nature of demand, the stock-in (and consequently stock-out) periods in the cycles are allowed to vary. The policy of planned shortages followed by replenishment in each cycle is adopted and seen to be fruitful indeed. Learning effect in holding and ordering costs are taken into account. The effects of limited capital and warehousing space are investigated. Numerical examples are employed to demonstrate the developed model and gain managerial insights from it. [Received: 23 December 2022; Accepted: 3 August 2023]
Optimal dynamic pricing and preservation policies under quality-, stock- and price-sensitive demand with partial backlogging and controllable lead time Indrani Modak, Sudarshan Bardhan, Bibhas C. Giri International Journal of Systems Science Operations and Logistics, 2025 In any inventory system, price is one of the key factors to stimulate demand and generate profit. Apart from price, market demand usually depends on product's stock level and its freshness. However, freshness declines with time and customers tend to avoid such items. In such a dynamic environment, price is expected to vary with time as well. Reducing the transport time is crucial for perishable products particularly when products start deteriorating soon after production. This paper addresses the dynamic pricing problem under price, stock, and freshness-dependent demand. Investments in both preservation and lead time reduction are considered. The business period under consideration is divided into two parts: the first one is the stock-out period where investments for preserving freshness and reducing lead time are considered, and the second one is the stock-in period. The optimal dynamic pricing strategy is determined using Pontryagin's maximum principle. Numerical results reveal that, even for products with inventory level-dependent demand (or similar characteristics), the stock-in price can be lower than the stock-out price and the slope of the price function depends on stock sensitivity.
DYNAMIC PRICING AND PRESERVATION INVESTMENT STRATEGY FOR PERISHABLE PRODUCTS UNDER QUALITY, PRICE AND GREENNESS DEPENDENT DEMAND Indrani Modak, Sudarshan Bardhan, Bibhas C. Giri Journal of Industrial and Management Optimization, 2024 The most significant factor to consider for proper operation of a firm is demand, emphasizing the importance of selecting efficient strategies to regulate it. Price has always been the main factor influencing demand, but as people's awareness about environmental issues grows, customers are now keeping an eye on product's level of greenness too in addition to other qualities. The current paper takes into account all these factors for modelling inventory of perishable products which makes preservation technology investment an intrinsic factor as well. The article's major contribution is to propose optimal pricing strategy that can be used in various situations where demand follows the presumed specific pattern. In addition to pricing, other policies like preservation and greening investments are also taken into consideration, and several important managerial insights are derived analytically and with the help of numerical examples. The model's applicability in numerous contexts is also demonstrated.
Dynamic pricing and replenishment policy under price, time, and service level-dependent demand and preservation investment Indrani Modak, Sudarshan Bardhan, Bibhas Chandra Giri Journal of Management Analytics, 2024 Time, price, and servicing are three important factors which affect the demand for any product. In a multi-period inventory model, different pricing in different periods may have a positive impact on demand. Offering discounts to customers during a shortage period is an efficient way to reduce lost sales. To address all these issues, a multi-period inventory model is developed and analyzed in this paper to obtain optimal pricing and replenishment periods where the market demand depends on price, time and service level provided by the retailer. The time horizon is fixed; the replenishment cycles are of equal length, but the shortage period may vary in different cycles. The retailer is allowed to charge different prices in different periods and provide discounts if someone places demand during a shortage period. Learning effects in holding and ordering costs are considered. Under a dynamic pricing framework, this study examines service improvement through learning and price discounts during shortages as an incentive for customers. It demonstrates that discounting indeed helps to produce more revenue when the back-order rate is low, and the service level is critical in generating demand when the stock-out period is lengthy, revealing a critical relationship between shortage periods and service level. A numerical experiment is performed to investigate the optimal policy in different situations and obtain some managerial insights.
A deteriorating consigned vendor-buyer model with stock-, freshness- and dynamic price-dependent demand under space limitation Nabin Sen, Sudarshan Bardhan, Bibhas Chandra Giri Journal of Management Analytics, 2024 Availability of inventory is a crucial issue while adopting a consignment strategy. The issue becomes paramount when demand depends on stock. To address the issue, a one-vendor one-buyer model under consignment stock (CS) policy is addressed in this paper. Both the channel members are assumed to have space limitations in their respective warehouses. The display area for the buyer is also limited. The buyer receives the product from the vendor under consignment stock policy, and transfers it in small batches to the display area. The market demand is affected by the price, freshness and on-hand stock level. Price is assumed to be dynamic in order to accurately depict real-world scenarios and to exhibit its important role in driving demand and influencing other decision-making factors. This study derives the optimal decisions to maximize the total profit of the supply chain system. Numerical experiments illustrate the optimal strategies such as production rate, shipment sizes, warehouse space limit, and number of shipments. Managerial insights are provided to establish the applicability of the model.
Optimal dynamic pricing and preservation policies under quality-, stock-and price-sensitive demand with partial backlogging and controllable lead time I Modak, S Bardhan, BC Giri International Journal of Systems Science: Operations & Logistics 12 (1), 2462098 , 2025 2025 Citations: 4
Vendor managed inventory under price-and-stock-dependent demand, buyer’s space limitations and preservation investment N Sen, I Modak, BC Giri, S Bardhan IMA Journal of Management Mathematics 36 (4), 963-989 , 2025 2025 Citations: 4
Dynamic pricing and preservation strategy for a two-echelon perishable supply chain model with price and time sensitive demand: I. Modak et al. I Modak, S Bardhan, BC Giri Operational Research 25 (3), 79 , 2025 2025 Citations: 4
Random pricing, product collection, and green investment strategies in a closed-loop supply chain with price dependent demand and remanufacturing I Modak, S Bardhan, BC Giri Journal of Cleaner Production 486, 144523 , 2025 2025 Citations: 13
A multi-period inventory model with price, time and service level dependent demand under preservation technology investment S Bardhan, I Modak, BC Giri European Journal of Industrial Engineering 19 (1), 18-44 , 2025 2025 Citations: 13
A deteriorating consigned vendor-buyer model with stock-, freshness-and dynamic price-dependent demand under space limitation N Sen, S Bardhan, B Chandra Giri Journal of Management Analytics 11 (4), 675-704 , 2024 2024 Citations: 2
Dynamic pricing and preservation investment strategy for perishable products under quality, price and greenness dependent demand I Modak, S Bardhan, BC Giri Journal of Industrial and Management Optimization 20 (7), 2260-2281 , 2024 2024 Citations: 10
Dynamic pricing and replenishment policy under price, time, and service level-dependent demand and preservation investment I Modak, S Bardhan, BC Giri Journal of Management Analytics 11 (2), 276-301 , 2024 2024 Citations: 14
Consignment based integrated inventory model for deteriorating goods with price-and green-sensitive demand N Sen, S Bardhan, BC Giri Sādhanā 49 (1), 13 , 2023 2023 Citations: 9
Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield BC Giri, JK Majhi, S Bardhan, KS Chaudhuri Annals of Operations Research 307 (1), 175-206 , 2021 2021 Citations: 25
Effectiveness of consignment stock policy under space limitations and deterioration N Sen, S Bardhan, BC Giri International Journal of Production Research 59 (6), 1834-1851 , 2021 2021 Citations: 24
Optimal production time and preservation technology investment for seasonal deteriorating products with a generalised ramp-type demand H Pal, S Bardhan, BC Giri International Journal of Mathematics in Operational Research 20 (1), 123-148 , 2021 2021 Citations: 7
Consignment stock policy in an integrated vendor-buyer model for deteriorating item with stock dependent demand under buyer’s space limitation N Sen, S Bardhan, BC Giri RAIRO-Operations Research 55, S1425-S1446 , 2021 2021 Citations: 6
Optimal replenishment policy and preservation technology investment for a non-instantaneous deteriorating item with stock-dependent demand S Bardhan, H Pal, BC Giri Operational Research 19 (2), 347-368 , 2019 2019 Citations: 119
Optimal replenishment policy for non-instantaneously perishable items with preservation technology and random deterioration start time H Pal, S Bardhan, BC Giri International Journal of Management Science and Engineering Management 13 (3 … , 2018 2018 Citations: 63
Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production BC Giri, S Bardhan International Journal of Production Economics 191, 66-73 , 2017 2017 Citations: 63
Coordinating a two-echelon supply chain with environmentally aware consumers BC Giri, S Bardhan International Journal of Management Science and Engineering Management 11 (3 … , 2016 2016 Citations: 19
Coordinating a three-layer supply chain with uncertain demand and random yield BC Giri, S Bardhan, T Maiti International Journal of Production Research 54 (8), 2499-2518 , 2016 2016 Citations: 78
Coordinating a two-echelon supply chain with price and inventory level dependent demand, time dependent holding cost, and partial backlogging BC Giri, S Bardhan International Journal of Mathematics in Operational Research 8 (4), 406-423 , 2016 2016 Citations: 18
Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption BC Giri, S Bardhan International Journal of Production Research 53 (16), 5070-5084 , 2015 2015 Citations: 87
MOST CITED SCHOLAR PUBLICATIONS
Optimal replenishment policy and preservation technology investment for a non-instantaneous deteriorating item with stock-dependent demand S Bardhan, H Pal, BC Giri Operational Research 19 (2), 347-368 , 2019 2019 Citations: 119
Coordinating a supply chain with backup supplier through buyback contract under supply disruption and uncertain demand BC Giri, S Bardhan International Journal of Systems Science: Operations & Logistics 1 (4), 193-204 , 2014 2014 Citations: 106
Supply chain coordination for a deteriorating item with stock and price‐dependent demand under revenue sharing contract BC Giri, S Bardhan International Transactions in Operational Research 19 (5), 753-768 , 2012 2012 Citations: 93
Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption BC Giri, S Bardhan International Journal of Production Research 53 (16), 5070-5084 , 2015 2015 Citations: 87
Coordinating a three-layer supply chain with uncertain demand and random yield BC Giri, S Bardhan, T Maiti International Journal of Production Research 54 (8), 2499-2518 , 2016 2016 Citations: 78
Optimal replenishment policy for non-instantaneously perishable items with preservation technology and random deterioration start time H Pal, S Bardhan, BC Giri International Journal of Management Science and Engineering Management 13 (3 … , 2018 2018 Citations: 63
Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production BC Giri, S Bardhan International Journal of Production Economics 191, 66-73 , 2017 2017 Citations: 63
A vendor–buyer JELS model with stock-dependent demand and consigned inventory under buyer’s space constraint BC Giri, S Bardhan Operational Research 15 (1), 79-93 , 2015 2015 Citations: 55
Coordinating a two-echelon supply chain through different contracts under price and promotional effort-dependent demand BC Giri, S Bardhan, T Maiti Journal of Systems Science and Systems Engineering 22 (3), 295-318 , 2013 2013 Citations: 37
Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield BC Giri, JK Majhi, S Bardhan, KS Chaudhuri Annals of Operations Research 307 (1), 175-206 , 2021 2021 Citations: 25
Effectiveness of consignment stock policy under space limitations and deterioration N Sen, S Bardhan, BC Giri International Journal of Production Research 59 (6), 1834-1851 , 2021 2021 Citations: 24
Coordinating a two-echelon supply chain with price and promotional effort dependent demand BC Giri, S Bardhan, T Maiti International Journal of Operational Research 23 (2), 181-199 , 2015 2015 Citations: 20
Coordinating a two-echelon supply chain with environmentally aware consumers BC Giri, S Bardhan International Journal of Management Science and Engineering Management 11 (3 … , 2016 2016 Citations: 19
Coordinating a two-echelon supply chain with price and inventory level dependent demand, time dependent holding cost, and partial backlogging BC Giri, S Bardhan International Journal of Mathematics in Operational Research 8 (4), 406-423 , 2016 2016 Citations: 18
Dynamic pricing and replenishment policy under price, time, and service level-dependent demand and preservation investment I Modak, S Bardhan, BC Giri Journal of Management Analytics 11 (2), 276-301 , 2024 2024 Citations: 14
Random pricing, product collection, and green investment strategies in a closed-loop supply chain with price dependent demand and remanufacturing I Modak, S Bardhan, BC Giri Journal of Cleaner Production 486, 144523 , 2025 2025 Citations: 13
A multi-period inventory model with price, time and service level dependent demand under preservation technology investment S Bardhan, I Modak, BC Giri European Journal of Industrial Engineering 19 (1), 18-44 , 2025 2025 Citations: 13
Dynamic pricing and preservation investment strategy for perishable products under quality, price and greenness dependent demand I Modak, S Bardhan, BC Giri Journal of Industrial and Management Optimization 20 (7), 2260-2281 , 2024 2024 Citations: 10
Consignment based integrated inventory model for deteriorating goods with price-and green-sensitive demand N Sen, S Bardhan, BC Giri Sādhanā 49 (1), 13 , 2023 2023 Citations: 9
Optimal production time and preservation technology investment for seasonal deteriorating products with a generalised ramp-type demand H Pal, S Bardhan, BC Giri International Journal of Mathematics in Operational Research 20 (1), 123-148 , 2021 2021 Citations: 7