Point and interval estimation of decomposition error in discrete-time open tandem queues

We analyze the approximation quality of the discrete-time decomposition approach, compared to simulation, and with respect to the expected value and the 95th-percentile of waiting time. For both performance measures, we use OLS regression models to compute point estimates, and quantile regression models to compute interval estimates of decomposition error. The ANOVA reveal major influencing factors on decomposition error while the regression models are demonstrated to provide accurate forecasts and precise confidence intervals for decomposition error

Automated Warehouse Systems: A Guideline for Future Research

This study aims to provide a comprehensive tool for the selection, design, and operation of automated warehouse systems considering multiple automated storage and retrieval system (AS/RS) options as well as different constraints and requirements from various business scenarios. We first model the retrieval task scheduling problem in crane-based 3D AS/RS with shuttle-based depth movement mechanisms. We prove the problem is NP-hard and find an optimality condition to facilitate the development of an efficient heuristic. The heuristic demonstrates an advantage in terms of solving time and solution quality over the genetic algorithms and the other two algorithms taken from literature. Numerical experiments illustrate that when a company tends to have multiple short planning horizons with small task batches (i.e., aims to increase the responsiveness level), adding more shuttles is helpful. However, if a company has a long planning horizon with a large task batch size, having faster cranes is more efficient to reduce the makespan. We then focus on the impacts of the number of shuttles, operational mode, storage policies, and shuttle dispatching rules on the expected cycle time of a tier-to-tier shuttle-based storage and retrieval system. The system is modeled as a discrete-time Markov Chain to derive the shuttle distribution under each scenario create the expected travel time models. Numerical experiments indicate that class-based storage is always better than the random storage policy. The best shuttle dispatching rule under each combination of the number of shuttles, operational mode, and storage policy can be quickly identified through the expected cycle time models which are simple and computation friendly. At last, we study the warehouse design problem considering the choice, design, and operation of 2D AS/RS and 3D AS/RS in a systematic way. The warehouse design problem under consideration aims to reduce the investment while satisfying different business needs measured by the desired throughput capacity. We propose a branch-and-bound algorithm to conquer the computational challenges. With the developed algorithm, an optimal warehouse design can be obtained under different application environments, characterized by the desired throughput capacity, inventory level, and demand rate of each SKU

Optimal Design and Planning for Compact Automated Parking Systems

Compact automated parking (CAP) systems are fully automated parking systems, which store cars densely. Such systems are mainly used in congested cities all over the world, providing rapid parking access and safe vehicle storage. We study a prominent new technology, with relatively low cost and rapid response. The system has a rotating ring equipped with shuttles in each tier for horizontal transport, and uses two lifts in the middle of the CAP system for vertical transport. We present a dedicated lift operating policy under which it uses one lift for storage and another for retrieval, and a general operating policy under which it uses both lifts for storage and retrieval. We propose queuing networks for single-tier and multi-tier systems based on two different policies for operating the lifts (a dedicated and general operating policy). We validate the analytical models using simulation based on a real application. We also conduct a sensitivity analysis in which we vary speeds of lifts and car rotation. Then we use the analytical models to optimize the system layout by minimizing the retrieval time. Furthermore, combining time efficiency and system cost, we find an appropriate system layout for designers. Third, we compare two lifts under dedicated and general operating policies. Forth, we find the optimal number of the lifts through a general compact automated parking system. Finally, we calculate the investment cost of a CAP system under different system configurations and compare it with an alternative design: a cubic parking system

Optimal Design and Planning for Compact Automated Parking Systems

International audienceCompact automated parking (CAP) systems are fully automated parking systems, which store cars densely. Such systems are mainly used in congested cities all over the world, providing rapid parking access and safe vehicle storage. We study a prominent new technology, with relatively low cost and rapid response. The system has a rotating ring equipped with shuttles in each tier for horizontal transport, and uses two lifts in the middle of the CAP system for vertical transport. We present a dedicated lift operating policy under which it uses one lift for storage and another for retrieval, and a general operating policy under which it uses both lifts for storage and retrieval. We propose queuing networks for single-tier and multi-tier systems based on two different policies for operating the lifts (a dedicated and general operating policy). We validate the analytical models using simulation based on a real application. We also conduct a sensitivity analysis in which we vary speeds of lifts and car rotation. Then we use the analytical models to optimize the system layout by minimizing the retrieval time. Furthermore, combining time efficiency and system cost, we find an appropriate system layout for designers. Third, we compare two lifts under dedicated and general operating policies. Forth, we find the optimal number of the lifts through a general compact automated parking system. Finally, we calculate the investment cost of a CAP system under different system configurations and compare it with an alternative design: a cubic parking system.<br/