Category Inventory Planning With Service Level Requirements and Dynamic Substitutions

We study a single‐period inventory planning problem for a category of substitutable products. This is an important practical problem facing category managers who have to maintain high service levels for constantly expanding product catalogs. We formulate the problem as a stochastic optimization mode...

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Published in:Production and operations management Vol. 29; no. 11; pp. 2553 - 2578
Main Authors: Akçay, Yalçın, Li, Yunke, Natarajan, Harihara Prasad
Format: Journal Article
Language:English
Published: Los Angeles, CA SAGE Publications 01.11.2020
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ISSN:1059-1478, 1937-5956
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Abstract We study a single‐period inventory planning problem for a category of substitutable products. This is an important practical problem facing category managers who have to maintain high service levels for constantly expanding product catalogs. We formulate the problem as a stochastic optimization model that minimizes the total stocking cost subject to service level requirements, which consist of product‐specific and category‐wide targets for inventory availability (ready rates) through the selling season. Our model accounts for stochastic customer arrivals, captures stockout‐based substitutions, and determines initial stocking quantities jointly for all products. Recognizing the challenges that these aspects pose in solving the problem, we propose an optimization‐based method that estimates the ready rates using a deterministic approximation and discretizes the selling season into a finite number of time intervals. This novel modeling approach permits us to recast the stochastic optimization model as a deterministic mixed integer linear program that can accommodate several common stockout‐based substitution schemes. We characterize the worst‐case behavior of this approach to develop performance guarantees. We also implemented and applied this model to randomly generated numerical instances featuring different types of product differentiation and varying in parameter values. We observe that the approach is robust to changes in problem parameter values and yields solutions very quickly, outperforming an enumeration‐based alternative, a practical heuristic, and an approach based on extant literature. Finally, we applied our approach to data from a re‐seller of Information Technology products. Results illustrate that our approach scales well and has the potential to generate savings in inventory costs.
AbstractList We study a single‐period inventory planning problem for a category of substitutable products. This is an important practical problem facing category managers who have to maintain high service levels for constantly expanding product catalogs. We formulate the problem as a stochastic optimization model that minimizes the total stocking cost subject to service level requirements, which consist of product‐specific and category‐wide targets for inventory availability (ready rates) through the selling season. Our model accounts for stochastic customer arrivals, captures stockout‐based substitutions, and determines initial stocking quantities jointly for all products. Recognizing the challenges that these aspects pose in solving the problem, we propose an optimization‐based method that estimates the ready rates using a deterministic approximation and discretizes the selling season into a finite number of time intervals. This novel modeling approach permits us to recast the stochastic optimization model as a deterministic mixed integer linear program that can accommodate several common stockout‐based substitution schemes. We characterize the worst‐case behavior of this approach to develop performance guarantees. We also implemented and applied this model to randomly generated numerical instances featuring different types of product differentiation and varying in parameter values. We observe that the approach is robust to changes in problem parameter values and yields solutions very quickly, outperforming an enumeration‐based alternative, a practical heuristic, and an approach based on extant literature. Finally, we applied our approach to data from a re‐seller of Information Technology products. Results illustrate that our approach scales well and has the potential to generate savings in inventory costs.
Audience Trade
Author Akçay, Yalçın
Li, Yunke
Natarajan, Harihara Prasad
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  organization: Melbourne Business School, University of Melbourne, 200 Leicester Street, Carlton, Victoria, 3053, Australia
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  organization: Department of Management, Miami Herbert Business School, 5250 University Drive, Coral Gables, Florida, 33124, USA
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  givenname: Harihara Prasad
  surname: Natarajan
  fullname: Natarajan, Harihara Prasad
  organization: Department of Management, Miami Herbert Business School, 5250 University Drive, Coral Gables, Florida, 33124, USA
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Issue 11
Keywords inventory planning
substitutable products
dynamic substitution
mathematical programming
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Snippet We study a single‐period inventory planning problem for a category of substitutable products. This is an important practical problem facing category managers...
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SubjectTerms dynamic substitution
inventory planning
mathematical programming
Optimization
Product differentiation
substitutable products
Title Category Inventory Planning With Service Level Requirements and Dynamic Substitutions
URI https://journals.sagepub.com/doi/full/10.1111/poms.13240
https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fpoms.13240
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Volume 29
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