We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance … Read more
Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear Bellman equation, we propose a Primal-Dual π Learning method in light of the linear duality between the value and policy. The … Read more
Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty, which applications include financial and investment planning, inventory control, energy production and trading, electricity generation planning, supply chain management and similar fields. Theoretical solution of multi-stage stochastic programs can be found explicitly only in very exceptional cases due to the complexity of the … Read more
We consider dynamic selection problems, where a decision maker repeatedly selects a set of items from a larger collection of available items. A classic example is the dynamic assortment problem with demand learning, where a retailer chooses items to offer for sale subject to a display space constraint. The retailer may adjust the assortment over … Read more
Online bipartite matching (OBM) is a fundamental model underpinning many important applications, including search engine advertisement, website banner and pop-up ads, and ride-hailing. We study the i.i.d. OBM problem, where one side of the bipartition is fixed and known in advance, while nodes from the other side appear sequentially as i.i.d. realizations of an underlying … Read more
We study the problem of a retailer that maximizes profit through joint replenishment, pricing and removal decisions. This problem is motivated by the observation that retailers usually retain rights to remove inventory from their network either by returning it to the suppliers or through liquidation in the face of random demand and capacity constraints. We … Read more
We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by parametric linear programs. This type of problems finds applications in the area of optimal planning under uncertainty, and can be thought of as … Read more
We consider the coordination of planning decisions of a single product in a supply chain composed of one supplier and one retailer by using contracts. We assume that the retailer has the market power to impose his optimal replenishment plan to the supplier. Our concern is on the minimization of the supplier’s cost. In order … Read more
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be solved along the iterations of the method are solved with a bounded error. We show that any accumulation … Read more
Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs) arising in applications. VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost, which can be used to assess the suboptimality of heuristic policies. However, … Read more