A Match in Time Saves Nine: Deterministic Online Matching With Delays

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays. We present the first deterministic online algorithm for this problem. Its competitive ratio is $O(m^{\log_2 5.5})$ $= O(m^{2.46})$, where $2 m$ is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance

Evaluating Automated Storage and Retrieval System Policies with Simulation and Optimization

In this paper we present a methodology to evaluate policies for automated storage and retrieval system (AS/RS) in warehouses. It is composed by four steps: (1) formal definition of the physical AS/RS and descriptive modeling on a simulation framework; (2) model validation and finding of potential bottlenecks by the statistical analysis of data logs; (3) definition of operational optimization policies to mitigate such bottlenecks; (4) evaluation of the policies using the simulation tool through key performance indicators (KPI). In particular, we take into consideration a unit-load AS/RS, we present a new simulation model combining discrete events and agent based paradigms. We consider an industrial test case, focusing on scheduling policies that exploit mathematical optimization, and we evaluate the effects of our approach on real world data. Experiments prove the effectiveness of our methodology