Multi-Stage Contracting Without Sandbagging or Hype

SSRN Electronic Journal · 2026-01-01

Multiproduct Inventory Systems with Upgrading: Replenishment, Allocation, and Online Learning

Manufacturing & Service Operations Management · 2025-11-24

Problem definition: We consider the joint optimization of ordering and upgrading decisions in a dynamic multiproduct system over a finite horizon of T periods. In each period, multiple types of demand arrive stochastically and can be satisfied either with supply of the same type or by upgrading to a higher-quality product. The goal is to find an optimal joint replenishment and allocation policy that maximizes total expected profit, both when the firm knows the demand distributions a priori and when the firm must learn them over time. Methodology/results: We first characterize the structure of the clairvoyant optimal joint ordering and allocation policy. Building on this structure, we propose a new online learning algorithm, termed stochastic subgradient descent with perturbed subgradient (SGD-PG for short), and show that it achieves cumulative regret growing on the order of the square root of T, which matches the known lower bound for any online learning method. We further show that SGD-PG can be extended to a nested censored demand setting. In the course of the algorithmic design, we propose a linear programming (LP)-based approach to compute the subgradient and prove that it produces the same output as the perturbed subgradient method. The LP-based method also allows us to extend the results to general upgrading structures. We demonstrate the efficacy of the proposed algorithms in numerical experiments. Managerial implications: This work provides practitioners with the optimal policy for inventory replenishment and allocation in a multiproduct system with upgrading. When the demand distribution is unknown, we propose an easy-to-implement and provably good algorithm for demand learning. In addition, our numerical results quantify the value of optimal upgrading and identify the conditions under which upgrading is most beneficial. Funding: This research was partially supported by an Amazon research award. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2024.0974 .

An FPTAS for a Multi-period Assortment Problem under an MNL Model with Popularity Effect

SSRN Electronic Journal · 2025-01-01 · 1 citations

Advance Selling under Dynamic Uncertainty and Time-Dependent Penalty

SSRN Electronic Journal · 2025-01-01

Human Decision Making in Dynamic Resource Allocation

Management Science · 2025-09-26

We experimentally study dynamic resource allocation decisions using product development as the context. A product manager must accept or reject a series of design improvement opportunities, given a limited budget. Human subjects perform well when the cost-to-implement is fixed throughout the project. However, in a more complex setting where the cost increases for the latter half of the project, subjects’ performance worsens substantially. We use the strategy frequency estimation method to analyze subjects’ decision mechanisms and find that many subjects are (a) mis-weighting future periods (underweighting in the simple case, overweighting in the complex) and (b) focusing on only the highest value opportunities. These heuristics perform poorly in the complex setting, leading to excess savings and are a counterproductive reaction to the cost increase. Top performers in the complex setting do well by decomposing the problem into two subproblems resembling the simpler setting, which they can handle nearly optimally. In a second study, we test managerial interventions based on prompting this decomposition approach to improve performance in the complex setting. Merely prompting subjects to consider problem decomposition is largely ineffective. However, additionally sharing a “best practice” budget plan that gives information about how and why top performers decompose the problem significantly improves performance. Our results highlight when decision makers will perform well or poorly in a dynamic resource allocation problem and show effective ways to reframe the problem and improve their performance. This paper was accepted by Vishal Gaur, operations management. Funding: The work of D. Beil, I. Duenyas, and J. Li was supported by the Ford Motor Company [Grant AWD006449]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01097 .

Self-matching guarantees in a brand omni-channel retailer

European Journal of Operational Research · 2025-09-11

Pooling Goods of Different Quality: Platform Design under Inventory Commingling

SSRN Electronic Journal · 2025-01-01

The Interplay Between Customer Feedback Solicitation and Innovation: A Dynamic Solution

SSRN Electronic Journal · 2025-01-01

Funding the Real Deal: Dynamic Moral Hazard with Adverse Selection

Operations Research · 2025-12-11

We study dynamic contracts that incentivize an agent to exert effort to increase the arrival rate of a Poisson breakthrough, where both the effort cost and the effort level at any time are the agent’s private information. Optimally, the principal offers a menu of contracts, each tailored to an agent type (with a different effort cost), specifying an initial payment, a contract deadline, and a payment-upon-arrival process over time. We first fully characterize the optimal contract menu in a two-type setting, where the agent is either a good (low-cost) or bad (high-cost) type. Specifically, the principal should hire the agent only if the breakthrough revenue exceeds a threshold. Above this threshold, if the bad agent’s cost is higher than another threshold, it is optimal to motivate only the good type to exert effort. The principal offers the good type a simple linear contract in which the payment-upon-arrival declines linearly over time until the deadline, whereas the bad type receives an initial payment and leaves immediately. The linear contract provides just enough incentive for the good agent to work. If the bad agent’s cost falls below the threshold, it becomes optimal to also motivate the bad agent to work using a linear contract, whereas offering the good agent a one-switch contract. The one-switch contract extends the linear form by allowing the payment-upon-arrival to take a single downward jump at a specific time before the deadline. The optimal contract structure extends to multiple-type cases, in which the one-switch contract becomes a multiple-switch contract. To obtain the entire menu of contracts, one only needs to solve a sequence of linear optimization problems together with a bisectional line-search, which is fast to compute and easy to interpret and implement. Funding: F. Tian acknowledges funding support from Hong Kong Research Grants Council General Research Fund [Grants 17502023 and 17503424]. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1156 .

Benefits of Collaboration on Capacity Investment and Allocation

SSRN Electronic Journal · 2024-01-01