5 research outputs found
The Value of the Right Distribution for the Newsvendor Problem and a bike-sharing problem
No full textIn this thesis, we introduce the new concept of Value of the Right Distribution, which measures the importance in Stochastic Programming of knowing the right probability distribution of the stochastic demand. We also introduce the new concepts of Recourse Penalty Bound and Maximum Recourse Penalty bound, which measure respectively the error bound and the worst-case performance bound given a certain mismatch between two probability distributions. In order to show how they apply, we study a cost-based variant of the Newsvendor problem. Moreover, we obtain closed-form and approximate expressions for the optimal quantity to order depending on the probability distribution assumed for the stochastic demand. Then, we use this new concepts to investigate bike-sharing problems. Two-stage and multi-stage stochastic optimization models are proposed. Finally, numerical results are provided
The value of the right distribution in stochastic programming with application to a Newsvendor problem
No full textStochastic optimization models for a bike-sharing problem with transshipment
No full textWe study the problem faced by a bike-sharing service provider who needs to manage a fleet of bikes over a set of bike-stations, each with given capacity and time-varying stochastic demand. In particular, we focus on One-way bike sharing systems with transshipment in which: (1) The user can pick up a bike at a station and drop it off at a different station; (2) Transshipment of bikes among stations is performed at the end of the day, to have the optimal number of bikes at each station at the beginning of the service on the next day. For this problem, we propose two-stage and multistage stochastic optimization models, to determine the optimal number of bikes to assign to each station at the beginning of the service. Numerical results are provided for the bike-sharing service “LaBiGi” in Bergamo (Italy), from which managerial insights are drawn
The value of the right distribution in stochastic programming with application to a Newsvendor problem
No full textIn this paper we introduce the concepts of the Value of the Right Distribution (VRD), the Performance Bound (PB) and the Worst-Case Performance Bound (WPB), which allow us to quantify how much we lose if we guess the wrong distribution of the uncertain parameters affecting a stochastic optimization problem. In order to show how they apply, we introduce a cost-based variant of the classical Newsvendor problem and model it as a two-stage stochastic programming model. For this problem, we first provide optimal solutions in closed form for different probability distributions and then compute, both analytically and computationally, the VRD measure and the corresponding performance bounds PB and WPB. Finally, systematic numerical results are provided
Stochastic Optimization Models for a Bike-Sharing Problem with transshipment
No full textWe study the problem faced by a bike-sharing service provider who needs to manage a fleet of bikes over a set of bike-stations, each with given capacity and time-varying stochastic demand. In particular, we focus on One-way bike sharing systems with transshipment in which: (1) The user can pick up a bike at a station and drop it off at a different station; (2) Transshipment of bikes among stations is performed at the end of the day, to have the optimal number of bikes at each station at the beginning of the service on the next day. For this problem, we propose two-stage and multistage stochastic optimization models, to determine the optimal number of bikes to assign to each station at the beginning of the service. Numerical results are provided for the bike-sharing service “LaBiGi” in Bergamo (Italy), from which managerial insights are drawn
