We consider the stochastic dual dynamic programming (SDDP) algorithm, which is a widely employed algorithm applied to multistage stochastic programming, and propose a variant using batch learning, a technique used with success in the reinforcement learning framework. We cast SDDP as a type of Q-learning algorithm and describe its application in both risk neutral and … Read more
The clique problem with multiple-choice constraints (CPMC), i.e. the problem of finding a k-clique in a k-partite graph with known partition, occurs as a substructure in many real-world applications, in particular scheduling and railway timetabling. Although CPMC is NP-complete in general, it is known to be solvable in polynomial time when the so-called dependency graph … Read more
We consider a stochastic version of the 0–1 Knapsack Problem in which, in addition to profit and weight, each item is associated with a probability of exploding and destroying all the contents of the knapsack. The objective is to maximize the expected profit of the selected items. The resulting problem, denoted as 0–1 Time-Bomb Knapsack … Read more
The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future … Read more
We describe a finite-horizon partially observable Markov decision process (POMDP) approach to optimize decisions about whether and when to perform biopsies for patients on active surveillance for prostate cancer. The objective is to minimize a weighted combination of two criteria, the number of biopsies to conduct over a patient’s lifetime and the delay in detecting … Read more
Online meal delivery is undergoing explosive growth, as this service is becoming increasingly fashionable. A meal delivery platform aims to provide efficient services for customers and restaurants. However, in reality, several hundred thousand orders are canceled per day in the Meituan meal delivery platform since they are not accepted by the crowdsoucing drivers, which is … Read more
This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on … Read more
We study single-item discrete multi-module capacitated lot-sizing problems where the amount produced in each time period is equal to the summation of binary multiples of the capacities of n available different modules (or machines). For fixed n≥2, we develop fixed-parameter tractable (polynomial) exact algorithms that generalize the algorithms of van Vyve (2007) for n=1. We … Read more
This paper presents a novel algorithmic study and complexity analysis of distributionally robust multistage convex optimization (DR-MCO). We propose a new class of algorithms for solving DR-MCO, namely a sequential dual dynamic programming (Seq-DDP) algorithm and its nonsequential version (NDDP). The new algorithms generalize and strengthen existing DDP-type algorithms by introducing the technique of regularization … Read more
In this paper we show that when a multistage stochastic problem with stage-wise independent realizations has only RHS uncertainties, solving one tree provides a valid lower bound for all trees with the same number of scenarios per stage without any additional computational effort. The only change to the traditional algorithm is the way cuts are … Read more