Analytical models for analysis of automated warehouse material handling systems

Automated storage and retrieval systems (AS/RSs) and autonomous vehicle storage and retrieval systems (AVS/RSs) are two competing technologies for the handling, storage and retrieval of unit-loads in the reserve section of an automated warehouse. In this paper, we model variants of the two systems as an open queuing network (OQN) and use an existing tool for the analysis of OQNs, called the manufacturing system performance analyser (MPA), for analysing the performance of the AS/RS and AVS/RS. Experimental results are provided to show that MPA is a better choice than simulation to quickly evaluate alternate configurations of the two systems. We use MPA to answer a series of design questions for AS/RS and AVS/RS design conceptualisation.     

Analytical model to estimate performances of autonomous vehicle storage and retrieval systems for product totes

In today's competitive scenario of increasingly faster deliveries and smaller order sizes, material-handling providers are progressively developing new solutions. A recent, automated material-handling technology for unit load storage and retrieval consists of an autonomous vehicle storage and retrieval system (AVS/RS). The present paper presents an analytical model to estimate the performances (the transaction cycle time and waiting times) of AVS/RS for product tote movement. The model is based on an open queuing network approach. The model effectiveness in performance estimation is validated through simulation.     

A decision model to determine the number of shuttles in a tier-to-tier SBS/RS

Shuttle-based storage and retrieval systems (SBS/RSs), which are designed to increase throughput capacity and flexibility, are a type of automated storage and retrieval system used for lightweight loads. SBS/RSs can increase throughput capacity by using multiple shuttles and elevators as storage and retrieval machines (SRMs). They can also facilitate improvements in flexibility since they are able to adjust the number of SRMs according to transaction demands. Thus, determining the number of shuttles is an important issue in tier-to-tier SBS/RSs. In this paper, a decision model to determine the number of shuttles is proposed. The model is based on the travel time model, and it considers parameters such as the physical configuration, velocity profile and the probability that the shuttle operates a dual command. Finally, the throughput capacity from the travel time model is compared with that from a simulation-based approach in order to verify the effects of the model. In addition, a critical discussion regarding the characteristics of the tier-to-tier system is provided.     

Optimal partitioning of vertical zones in vehicle-based warehouse systems

New innovations in warehouse automation systems such as autonomous vehicle-based storage and retrieval (AVS/R) system offer greater flexibility and responsiveness in processing unit-load storage and retrieval transactions in high-density storage areas. To optimise system performance, new technologies should be implemented with optimal setting of design parameters. This research is a first attempt to model a ‘zone-captive’ AVS/R system and understand the effect of number and boundary of vertical zones on system performance measures. Further, we also analyse the effect of aisle orientation within a tier on cycle times. A detailed simulation model of a multi-tier zone-captive system is built to capture the dynamics of the system i.e. interaction among the vehicles, lift and incoming transaction requests, and estimate the performance measures of interest. The numerical experiments show that the transaction cycle times can be reduced by 1–12% with optimal partitioning of vertical zones and further reduced by 0.2–15.0% by a better aisle orientation.     

Travel time models for deep-lane unit-load autonomous vehicle storage and retrieval system (AVS/RS)

Autonomous vehicle storage and retrieval systems use vehicles that move horizontally along rails within the storage racks, while vertical movements are provided by lifts. The solution proposed in this paper addresses a particular system configuration that works with multiple deep storage lanes that are widely used in the food and beverage industry, characterised by large volumes of products of limited variety. The generic deep lane is single item, i.e. one stock keeping unit, and single batch, i.e. one production lot, thereby affecting the performance of the system in terms of storage capacity utilisation and throughput. Determining the number and depth of the lanes is crucial to aid the design and control of such a storage system. The aim of this paper was to support the design of AVS/RSs though a set of original analytic models for the determination of the travelled distance and time for single-command and dual-command cycles given alternative layout configurations. The models are validated by simulation and exemplified with a real-warehousing case study. The paper presents useful guidelines for the configuration of the system layout including the determination of the optimal shape ratio and the length of the lanes.     

Application of storage consolidation intervals to approximate random storage transaction times with closest open location load dispatching

A new modelling approach is proposed for estimating storage/retrieval transaction times in warehouse systems using random storage and closest open location load dispatching. The method is based on estimating intervals between consolidations of the active storage envelope defined by the most remote occupied storage position in a warehouse. This enables the calculation of the expected number of interspersed storage vacancies within the storage envelope which can then be applied in transaction time calculations. Computational results for test problems suggest that the method performs well relative to alternative procedures reported in the literature.     

Simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system

In this paper, a simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system (AVS/RS) is presented. The aim of this study is to develop mathematical functions for the rack configuration of an AVS/RS that reflects the relationship between the outputs (responses) and the input variables (factors) of the system under various scenarios. In the regression model, we consider five outputs: the average cycle time of storage and retrieval transactions, the average waiting time for vehicle transactions, the average waiting time of vehicles (transactions) for the lift, the average utilisation of vehicles and the average utilisation of the lifts. The input variables are the number of tiers, aisles and bays that determine the size of the warehouse. Thirty regression models are developed for six warehouse scenarios. The simulation model of the system is developed using ARENA 12.0 commercial software and the statistical analyses are completed using MINITAB statistical software. Two different approaches are used to fit the regression functions–stepwise regression and the best subsets. After obtaining the regression functions, we optimise them using the LINGO software. We apply the approach to a company that uses AVS/RS in France.     

Travel-time models and fill-grade factor analysis for double-deep multi-aisle AS/RSs

Double-deep multi-aisle automated storage/retrieval systems are increasingly applied for storing and retrieving unit loads, with advantages of increased space utilisation, reduced number of aisles and improved efficiency of storage rack (S/R) machines. In such systems, the retrieval process may consist of the rearrangement of blocking loads, based on the assumptions of uniformly distributed storage locations and random storage policy. We formulate analytical travel-time models of both single- and dual-command cycles under three rearrangement rules. We validate the analytical travel-time models by simulation and conduct numerical experiments to analyse the effect of the number of aisles an S/R machine serves, the fill-grade factor and the command cycles on the expected travel time of the S/R machine. The results show that the expected travel time of the S/R machine is increasing with the increase in the number of aisles an S/R machine serves and the increase in the fill-grade factor, and dual command cycle outperforms single-command cycle in terms of cycle time. To deal with the trade-off between the storage space cost and the operational cost of the S/R machine, we develop a decision model for finding an optimal fill-grade factor to minimise the total cost. We find the condition when an optimal fill-grade factor exists and show how to calculate it. Based on the decision model, we compare the performance of double-deep multi-aisle automated storage/retrieval system (AS/RSs) and single-deep single-aisle AS/RSs. The results show that double-deep multi-aisle AS/RSs outperform single-deep single-aisle AS/RSs in terms of total cost, although double-deep multi-aisle AS/RSs need more storage locations.     

Interleaving models for the analysis of twin shuttle automated storage and retrieval systems

A system of state equations is formulated for describing the dynamic behaviour of the queue of storage and retrieval transactions in a storage aisle served by twin shuttle storage and retrieval (S/R) machines. Using estimates of order picking cycle times in conjunction with storage and retrieval transaction demand levels, an estimate of the probability distribution of storage queue states is derived for a given storage aisle. System performance measures under an opportunistic interleaving discipline including S/R machine utilization, transaction queue lengths, average cycle times and expected transaction waiting times are approximated using the state probability distribution. The modelling tools are demonstrated using sample problems where the performance of twin versus single shuttle systems is contrasted for alternative combinations of storage and retrieval machine travel speeds, storage rack configurations, and transactions demand scenarios.     

Development of a framework for the design of autonomous vehicle storage and retrieval systems

In today’s competitive environment with increasingly faster deliveries and smaller order sizes, material handling providers are progressively developing new solutions. A more recent development in automated material-handling technology for unit load storage and retrieval is the autonomous vehicle storage and retrieval system (AVS/RS). The paper investigates the main design trade-offs for this new solution using simulation, and proposes a comprehensive design framework. Using data from a recently implemented AVS/RS, the application of the proposed framework is presented and the key design differences between the two types of AVS/RS configuration (i.e. tier-captive versus tier-to-tier) are identified.     

An open queueing network for lead time analysis

In this paper we develop an open queueing network for a multi-product multi-machine job-shop in a make-to-order environment. The job-shop produces a variety of products which are characterized by individual general arrival rates and individual general production rates for the machines on their deterministic routings. By incorporating the machines into a general open queueing network, we obtain the average, variance and probability distribution of the individual product lead times, The open queueing network will be illustrated by application to a real-life example existing at Recticcl Bedding Hulshout. In addition to using a flexible and computational efficient approach, we methodologically reveal that the approximate queueing network is suitable lo rapidly provide an answer to managerial questions.     

An Analysis of Automated Storage and Retrieval Systems in Manufacturing Assembly Lines

An automated storage/retrieval system is a material handling system that can be used to pick and to deliver materials in a direct access fashion. An M/G/1 queueing model is used to study the system performance under a first-come-first-served dispatching rule. More detailed studies for different dispatching rules have been done by simulation. A number of cases with different hardware characteristics and workloads have been investigated. Conclusion is drawn based upon the results obtained from analysis as well as numerical experiments.     

Optimising two dwell point policies for AS/RSs with input and output point at opposite ends of the aisle

Automated storage and retrieval systems (AS/RSs) are widely used for storing and retrieving products in all types of warehouses. Dwell point policy is a vital control policy that can greatly affect the performance of AS/RSs. In this paper, we study dwell point policies in AS/RSs with input and output stations at opposite ends of the aisle. We first propose two dwell point policies. We find that five existing dwell point policies in the literature are special cases of exactly one of our policies. We then develop expected travel time models for the proposed policies, solve these models with the objective of minimising expected travel time, and obtain closed-form solutions for the optimal dwell location(s). We prove that one proposed policy dominates the other in terms of expected travel time. Numerical experiments are performed to quantify the percentage gap of expected travel time between the proposed policies and policies in the literature. We find that, in some situations, the better proposed policy can achieve up to 8%–10% reduction in expected travel time in comparison with the best literature policy. A real-data case study validates that these situations arise with high probability in typical daily warehouse operations.     

Intelligent control schemes for automated storage and retrieval systems

A new information system approach to the operational controls of automated storage and retrieval systems (AS/RS) is developed and examined. This approach is based on artificial intelligence, state-operator framework for problem solving. Gradually increasing the information level, several operational goal functions are identified for an industrial unit-load food produce AS/RS. These functions use real-time statistical interpolations to select the desired storage and retrieval bins. As a result the AS/RS response adapts itself to stochastic perturbations in the system conditions. Experimental evaluations using multiple variance analysis technique and detailed simulations have shown that the proposed dynamic approach is superior to the common industrial control method currently used in those industrial systems characterized by batch arrivals (and retrievals) of the UL's and non-stationary demand patterns, These evaluations further suggest that improved performance is realized with the increase in the information level. The operational control scheme developed in this paper appears to be an excellent control alternative for unit-load AS/RSs. This is due to its limited computational requirements and the augmented productivity as demonstrated here for a real case study.     

Integrated availability model based on performance of computer networks

An efficient computer network can realize bulk data transfer and real time control with high reliability and precision. Its availability is dependent on its topological structure and network services performed simultaneously. To explore the dynamic interactions between software and hardware failures, generalized stochastic petri net (GSPN) is adopted to model the availability of nodes in the network, and then the study is developed through path selection and service performance evaluation. Network performance indices such as throughput and time delay can be obtained by modeling the network service with queueing theory. With Power formula, this paper presents an integrated availability model. This model considers both topological connectivity and operational performance, developing the availability analysis from the viewpoint of a user.     

Deadlock control of autonomous vehicle storage and retrieval systems via coloured timed Petri nets and digraph tools

This paper addresses the deadlock control problem for the autonomous vehicle storage and retrieval system (AVS/RS). For an AVS/RS with several autonomous vehicles running in bi-direction, deadlock control is one of the key issues in the implementation of AVS/RS. The cycle-deadlock is the main type of deadlock in AVS/RS. In the paper, the dynamic model of AVS/RS is investigated by using coloured timed Petri nets (CTPN). Based on the CTPN model, a route digraph is built to detect cycle-deadlock in AVS/RS with digraph tools; the necessary and sufficient conditions of deadlock-free are established. Moreover deadlock-free control policies are proposed, the critical state in deadlock free is also identified and FCFS policy is applied to solve it. Finally, a case study is given to validate the policies.     

Routing problem under the shared storage policy for unit-load automated storage and retrieval systems with separate input and output points

In this study the routing problem for unit-load automated storage and retrieval systems (AS/RSs) with separate input and output points is considered under the shared storage policy. The problem is to find an optimal travel route of a S/R (storage and retrieval) machine to process given storage and retrieval requests so that the total travel time is minimised, where the input and output points are possibly separate and the shared storage policy is assumed. We first give two types of formulations as 0–1 integer linear programming problems corresponding to two types of dwell point settings: the dwell point is the input point and the output point. Next, we propose a simple but efficient exact solution algorithm based on the formulations that utilises a general MILP (Mixed Integer Linear Programming) solver. Its efficiency is then demonstrated by numerical experiments. Instances with 400 items (200 for each storage and retrieval) are solved within 100 s.     

A multi-class approximation technique for the analysis of kanban-like control systems

Analytical methods have been proposed in the literature for performance evaluation of kanban control systems. Among them, the method presented by Di Mascolo and colleagues appears to be of special interest since it can handle manufacturing stages consisting of any number of machines and it is fairly accurate. This paper presents a new way of deriving the analytical method presented by Di Mascolo et al. The approach is to see the queueing network of the kanban control system as a multiclass queueing network in which each kanban loop is represented by a class of customers. This allows one to use the general technique proposed in Baynat and Dallery for analysing multiclass queueing network using product-form approximation methods. In terms of equations, the new method is equivalent to that previously presented. However, the computational algorithm is much more efficient since it avoids the two levels of iterations involved in the original algorithm. Another major advantage of the new method over that originally proposed is that it provides a general framework for the analysis of more general kanban systems. Indeed, it is shown in this paper how this approach can easily be extended in order to handle kanban systems with multiple consumers and multiple suppliers, kanban-controlled assembly systems and generalized kanban systems.     

Modelling of material handling systems for facility design in manufacturing environments with job-specific routing

Traditionally, flow times distance is used as a surrogate for cost in facility design. However, this performance measure does not fully capture the impact of facility design decisions on operational performance measures such as cycle time and work-in-progress in the system, which are often more meaningful for managers, especially in a manufacturing environment. To better measure operational performance, modelling of material handling systems using a queueing network must be integrated in the facility design process. A number of approaches are discussed in the facility design literature for modelling material flow using queueing networks. In these approaches, Poisson arrival or Markovian job routing assumptions have been used. However, for many manufacturing environments, these assumptions lead to an inaccurate estimation of the material handling system's performance and thus lead to poor facility designs. Incorporating more general queueing results for non-Markovian systems is difficult, however, because the facility design process must investigate a large number of potential solutions and thus the results from the queueing models for the material handling system must be quickly obtained. In this paper, the need for more general queueing models of material handling systems in facility design is confirmed. Then, an approach based on multi-class queueing models is adapted to capture the change in variability of the system performance caused by both different arrangements of workstations in the facility and different arrival processes to the workstations due to the job routing in a computationally efficient manner. The proposed modelling approach is shown to provide more accurate results than previous methods used in facility design based on numerical comparisons with results from discrete-event simulation.     

A cross-entropy method for optimising robotic automated storage and retrieval systems

In this paper, we consider a robotic automated storage and retrieval system (AS/RS) where a Cartesian robot picks and palletises items onto a mixed pallet for any order. This robotic AS/RS not only retrieves orders in an optimal sequence, but also creates an optimal store ready pallet of any order. Adapting the Travelling Salesman Problem to warehousing, the decision to be made includes finding the optimal sequence of orders, and optimal sequence of items inside each order, that jointly minimise total travel times. In the first phase, as a control problem, we develop an avoidance strategy for the robot (or automatic stacker crane) movement sequence. This approach detects the collision occurrence causing unsafe handling of hazardous items and prevents the occurrence of it by a collision-free robot movement sequence. Due to the complexity of the problem, the second phase is attacked by a Cross-Entropy (CE) method. To evaluate the performance of the CE method, a computational analysis is performed over various test problems. The results obtained from the CE method are compared to those of the optimal solutions obtained using CPLEX. The results indicate high performance of the solution procedure to solve the sequencing problem of robotic AS/RSs.