Technical Note—A Stationary Infinite-Horizon Supply Contract Under Asymmetric Inventory Information

Alain Bensoussan (), Suresh Sethi () and Shouqiang Wang ()
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Alain Bensoussan: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080; and School of Data Science, City University of Hong Kong, Kowloon Tong, Hong Kong
Suresh Sethi: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080
Shouqiang Wang: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080

Operations Research, 2025, vol. 73, issue 1, 270-277

Abstract: We consider a decentralized supply chain in which a supplier sells goods to a retailer facing general random demand over an infinite horizon. The retailer satisfies the demand to the extent of the inventory on hand. The retailer has private information about the retailer’s stock in each period, and the supplier offers the retailer a supply contract menu to account for the information asymmetry. We obtain a necessary condition for optimizing a long-term stationary truth-telling contract under general demand and belief distributions. We apply it to a batch-order contract, which replenishes a prespecified inventory quantity for a fixed payment in each period only when the retailer’s beginning inventory becomes zero. Methodologically, we formulate the supplier’s contract design as a calculus of variations problem and apply the concept of Gâteaux derivative to obtain these results. This methodology can potentially be applied to other dynamic contracting problems.

Keywords: Stochastic Models; inventory; mechanism design; calculus of variations; Gâteaux derivative; batch-order contract (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:73:y:2025:i:1:p:270-277

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