Technical Note—Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures

Xin Chen · Peng Hu · Simai He

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Supply Chain and Inventory Management Complexity and Algorithms in Graphs Optimization and Variational Analysis

Abstract

This paper establishes a new preservation property of supermodularity in a class of two-dimensional parametric optimization problems, where the constraint sets may not be lattices. This property and its extensions unify several results in the literature and provide powerful tools to analyze a variety of operations models including a two-product coordinated pricing and inventory control problem with cross-price effects that we use as an illustrative example.

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References

2011Supermodularity and Complementarity 2014Coordinating Inventory Control and Pricing Strategies for Perishable Products 1999The Logic of Logistics: Theory, Algorithms, and Applications for Logistics and Supply Chain Management 2008On the Structure of Lost-Sales Inventory Models 2012Pricing and Inventory Management 2008Dynamic inventory management with cash flow constraints 2021Demand Management and Inventory Control for Substitutable Products 2013Technical Note—Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing

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2015Joint Initial Stocking and Transshipment—Asymptotics and Bounds 2017Joint Inventory and Fulfillment Decisions for Omnichannel Retail Networks 2016Revenue Management for Intermodal Transportation: The Role of Dynamic Forecasting 2017L♮-convexity and its applications in operations 2015Optimal Policies for a Two‐Product Inventory System under a Flexible Substitution Scheme

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