3 présentations

• 
  08h30 - 08h52

  Stochastic Model-predictive Control for Inventory Management Problems with Uncertain Demand and Lead Times

  • Laurens Lueg, prés., Carnegie Mellon University
  • Nitish Umang, Johnson & Johnson
  • Georgia Stinchfield, Carnegie Mellon University
  • Carl Laird, Carnegie Mellon University

  This work addresses the application of stochastic model-predictive control (MPC) to multi-period inventory management problems, considering multiple products and markets, facing uncertainty in demand and lead times. We follow a sample-based approach, whereby the MPC policy computes reorder quantities at each period, based on multiple uncertainty realizations, i.e. scenarios. This requires the solution of a large-scale linear program (LP) at every period, especially as the number of scenarios grows to cover multiple sources of uncertainty. We discuss approaches to improve computational tractability, such as decomposition through the use of progressive hedging, which allows for the parallel solution of the problem. Furthermore, we investigate the sensitivity of the resulting policy with respect to user-specified parameters such as the number of sampled scenarios, the length of the controller horizon or safety stock levels, and we discuss ways to automatically tune these parameters through simulation.

• 
  08h52 - 09h14

  Dynamic matching in ridesharing

  • Myungeun Eom, prés., Georgia Institute of Technology
  • Alejandro Toriello, Georgia Institute of Technology

  We study a dynamic non-bipartite matching problem, where nodes appear following a type-specific independent distribution and wait in the system for a given sojourn time. This problem is motivated by ridesharing applications. We study the asymptotic properties of batching and greedy policies by analyzing a single-pair case and then converting to the general counterpart using fluid relaxation and randomization. Finally, we present a computational study simulating ridesharing marketplace to assess the empirical effectiveness of the policies. We show that the batching and a greedy with reserve price are asymptotically optimal with respect to the sojourn time. More practically relevant, both policies converge exponentially fast to approximate optimality. We also extend our model to an impatient setting in which each unmatched node leaves at the end of each period with a type-dependent probability. We show that the results for the two policies still hold under different assumptions about the nodes' patience.

• 
  09h14 - 09h36

  Learning While Repositioning in On-Demand Vehicle Sharing Networks

  • Hansheng Jiang, prés., University of Toronto
  • Chunlin Sun,
  • Z. Max Shen,
  • Shunan Jiang,

  We consider a network inventory problem motivated by one-way, on-demand vehicle sharing services. Because of uncertainties in both demand and returns, as well as a fixed number of rental units across an n-location network, the service provider must periodically reposition vehicles to match supply with demand while minimize costs. We introduce the best base-stock repositioning policy as a generalization of the classic inventory control policy to n dimensions, and establish its asymptotic optimality in two distinct limiting regimes under general network structures. We also present reformulations to efficiently compute this best base-stock policy in an offline setting with pre-collected data.

  In the online setting, we show that a natural Lipschitz-bandits approach achieves a regret guarantee, which suffers from a curse of dimensionality as n grows. We illustrate the challenges of learning with censored data in networked systems by discussing the regret lower bound and the sub-optimality of other approaches. Motivated by these challenges, we propose an Online Gradient Repositioning algorithm that relies solely on censored demand. Under a mild cost-structure assumption, we prove that it attains an optimal regret matching the regret lower bound. The algorithm is designed by approximating the objective with surrogate costs to disentangle temporal dependencies and leveraging a subproblem dual solution to determine the gradient step. Numerical experiments illustrate the effectiveness of our proposed methods.