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.     

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.     

Travel time model for double-deep shuttle-based storage and retrieval systems

Technological developments in the global supply chain have changed processes in warehousing. This reflects in short response time in handling the orders, which has a consequence on high automation degree in warehousing. An important part of automated warehouses is presented by shuttle-based storage and retrieval systems (SBS/RS), which are used in practice when demand for the throughput capacity is high. In this paper, analytical travel time model for the computation of cycle times for double-deep SBS/RS is presented. The advantage of the double-deep SBS/RS is that fewer aisles are needed, which results in a more efficient use of floor space. The proposed model considers the real operating characteristics of the elevators lifting table and the shuttle carrier with the condition of rearranging blocking totes to the nearest free storage location during the retrieval process of the shuttle carrier. Assuming uniform distributed storage locations and the probability theory, the expressions for the single and dual-command cycle of the elevators lifting table and the shuttle carrier have been determined. The proposed model enables the calculation of the expected cycle time for single- and dual-command cycles, from which the performance of the double-deep SBS/RS can be evaluated. The analysis show that regarding examined type of the double-deep SBS/RS, the results of the proposed analytical travel time model demonstrate good performances for evaluating double-deep SBS/RS.     

An optimal dwell point policy for automated storage/retrieval systems with uniformly distributed,rectangular racks

This study is to develop an optimal dwell point policy for automated storage/retrieval systems with uniformly distributed racks. For non-square-in-time racks, we present the closed form solution for the optimal dwell point in terms of the probability of the next transaction demand type: storage or retrieval. We also introduce various return paths to the dwell point for the efficient operation of the storage/retrieval machine.     

Relative pre-positioning of storage/retrieval machines in automated storage/retrieval system to minimize expected system response time

This paper is focused on the control problem of determining the dwell point of an idle storage/retrieval (S/R) machine in an automated S/R system to improve the overall system service level as measured by the turnaround time of requests to the system. The emphasis of the paper is on the minimization of the expected response time over all retrieval and storage requests executed by the system. The model presented is developed under the operating condition that each machine serves several dedicated aisles of the system. The aisles are assumed to exist in the same region of the automated storage/retrieval system (AS/RS) and thus form a valid order S/R zone. A solution algorithm for determining the optimal dwell point location is developed. The paper assumes a dynamic environment where orders arrive over time and are to be serviced by the S/R machine. A dwell point or strategic point to pre-position the machine is to be determined whenever the machine becomes idle in anticipation of an incoming service request. A numerical example is provided to demonstrate how the technique can be used in an actual production setting to improve the overall order turnaround time.     

Performance of carousel systems with ‘organ-pipe’ storage

It is well known that, for carousel systems, a dedicated storage, referred to as the ‘organ-pipe’ storage in the literature, is optimal with respect to the expected travel distance for processing successive requests. What remains unanswered is how to determine its performance, which is the motivation of this study. We consider bi-directional carousels under a ‘floating’ dwell point strategy. Two important performance measures considered are system capacity (maximum throughput) and job sojourn time. We also investigate the effect of activity skew on system performance.     

Relative pre-positioning of storage/retrieval machines in automated storage/retrieval systems to minimize maximum system response time

In this paper, the problem of pre-positioning a storage/retrieval (S/R) machine in an automated storage/retrieval system (AS/RS) when the machine is idle is addressed. The objective of the pre-positioning strategy is to minimize the maximum response time to service incoming requests into the AS/RS. A model is developed under the operating condition that each machine can serve one or multiple dedicated aisle(s) of the system. The aisles are assumed to exist in the same region of the AS/RS and thus form a valid order storage/retrieval zone. A solution algorithm for determining the optimal dwell point or location is developed. The paper assumes a dynamic environment where orders arrive over time and are to be serviced by the S/R machine. A dwell point or strategic point to pre-position the machine is to be determined whenever the S/R machine becomes idle in anticipation of an incoming service request. A numerical example is provided to demonstrate how the technique can be used in an actual production setting to improve the overall order turnaround time.     

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.     

Travel time models for double-deep automated storage and retrieval systems

In this paper new analytical travel time models for the computation of cycle times for unit-load double-deep automated storage and retrieval systems (in continuation double-deep AS/RS) are presented. The proposed models consider the real operating characteristics of the storage and retrieval machine and the condition of rearranging blocking loads to the nearest free storage location during the retrieval process. With the assumption of the uniform distributed storage rack positions and the probability theory, the expressions of the single and modified dual command cycle have been determined. The proposed models enable the calculation of the mean cycle time for single and dual command cycles, from which the performance of the double-deep AS/RS can be evaluated. A simulation model of the selected double-deep AS/RS has been developed to compare the performances of the proposed analytical travel time models. The numerical analyses show that with regard to the examined type of double-deep AS/RS with a different fill-grade factor, the results of the proposed analytical travel time models correlate with the results of simulation models of double-deep AS/RS.     

Impact of required storage space on storage policy performance in a unit-load warehouse

The performance of a storage policy in a warehouse is usually evaluated on the basis of the average one-way travel distance/time needed to store/retrieve a load. Dividing the storage space into zones based on item turnover frequency can reduce the travel distance. However, for a given number of stored items, a larger number of storage zones also requires more storage space, because of reduced space sharing between the items, which increases travel time. This study considers the required space consumption by storage zoning in comparing the performance of random, full turnover-based and class-based storage policies for a unit-load warehouse operated by a forklift in single-command mode. A generalised travel distance model that considers the required space consumption is developed to compare the performance of these policies. Results show that the one-way travel distance of a random policy decreases with the increase in skewness of the demand curve. By considering the required space consumption, a class-based storage policy performs generally better than a full turnover-based policy. In addition, the optimal warehouse shape factor (ratio of warehouse width to depth) appears to decrease with the skewness of the demand curve. Warehouse managers are advised to adopt a wide-shallow warehouse layout when the item demands are approximately equal, whereas a narrow-deep layout is preferred when the demand curves are steep.     

Comparison of conventional and automated refrigerated storage systems

High rise warehouses with automated storage and retrieval systems (AS/RS) can frequently be justified as a viable alternative to conventional freezer storage. To determine viability, a design year data base must be developed and both conventional and automated system/facility options tested against this operational standard. To determine which alternative best suits design year requirements, a justification analysis must be completed. This analysis must address investment costs and total operational costs. Operational factors such as expandability, flexibility and maintainability must be considered. This Paper outlines a basic approach to the justification analysis required when considering high rise automated and conventional alternatives for refrigerated warehousing applications.     

A heuristic travel time model for random storage systems using closest open location load dispatching

A heuristic method is proposed for estimating travel times in unit load random storage systems where incoming loads are dispatched to the closest available storage positions. A queuing model representation is used where servers correspond to storage positions and the service rate is based on the turnover distribution of stored loads. The resultant state distribution is applied to approximate storage position occupancy probabilities useful for generating storage and retrieval travel time estimates. Computational results suggest that the heuristic procedure yields smaller errors in random storage travel time estimates than alternative models.     

Travel distance estimation and storage zone optimization in a 2-block class-based storage strategy warehouse

Order picking has been considered as the most critical operation in warehousing. Recent trends in logistics demand faster but more reliable order picking systems. The efficiency of an order picking process greatly depends on the storage policy used, i.e. where products are located within the warehouse. In this paper, we deal with the most popular storage policy that is class-based (or ABC) storage strategy. Particularly, we investigate the problem of determining the optimal storage boundaries (zones) of classes in each aisle for manually operated warehouses.

We first propose a probabilistic model that enables us to estimate the average travel distance of a picking tour. We found that the differences between results obtained from simulation and the model were slight. Using the average travel distance as the objective function, we present a mathematical formulation for the storage zone optimization problem. However, the exact approach can handle only small size warehouse instances. To circumvent this obstacle, we propose a heuristic for the problem. Numerical examples we conducted show that the heuristic performs very well in all the cases.     

Closed form models for determining the optimal dwell point location in automated storage and retrieval systems

This paper examines the problem of where a storage/retrieval machine should reside, or dwell, when an automated storage and retrieval system (AS/RS) becomes idle to minimize the expected value of the next transaction time. After a review of the relevant literature on AS/RS dwell point strategies, this paper proposes several analytical models of these expected response times of the AS/RS based on the relative locations of the input and output ports of the AS/RS. It uses a continuous rack approximation to provide analytical models of the dwell point location problem. These models provide closed form solutions for the dwell point location in an AS/RS. Extensions are made to consider AS/RS with a variety of configurations including multiple input and output ports. These models not only provide solutions to the dwell point location problem, but they provide considerable insight into the nature of this problem, which is particularly valuable when the requirements facing the AS/RS are uncertain.     

Optimal dwell point policies for automated storage/retrieval systems with dedicated storage

This study is to develop an optimal dwell point policy for automated storage/retrieval systems. For square-in-time racks with dedicated storage, we determine the optimal dwell points in closed form. We also confirm the intuitive remit that the input point is a good alternative dwell point for dedicated storage.     

Response to Al-Hakim's note

Storage location assignment and interleaving policy are two closely related problems in warehousing management. This paper addresses the location assignment and interleaving problem at the same time in an automated storage/retrieval system with duration-of-stay based shared storage policy. Based on the heuristics for single command operation, a two-step procedure is developed to solve the problem. A tabu search algorithm is proposed to improve the solution for medium and large sized problems. The computational results indicate that the tabu search algorithm is effective in finding high quality solutions, and efficient in solving large sized problems.     

Analytical models for a new turnover-based hybrid storage policy in unit-load warehouses

This paper considers a low-level unit-load warehouse employing single-deep storage lanes and a single-command manual storage and retrieval policy. Analytical travel distance models are developed for class-based and full turnover storage policies under across-aisle, within-aisle and a newly proposed hybrid product placement schemes. Our computational studies show that the analytical models developed in this paper are very accurate as compared to simulation results and a comparative study with a real-world warehouse case. Hybrid storage policies proposed in this paper outperform all other traditional storage policies. The paper also presents insights and simple design rules to warehouse practitioners.     

Optimal storage rack design for a multi-deep compact AS/RS considering the acceleration/deceleration of the storage and retrieval machine

This paper explores the optimal storage rack design for a multi-deep compact Automated Storage and Retrieval System (AS/RS) considering the acceleration and deceleration of storage and retrieval (S/R) machine. The expected travel time under the single-command cycle and dual-command cycle for a random storage strategy is derived. Based on the travel time, the general models we propose calculate the optimal ratio between three dimensions that minimises the travel time under different speed profile scenarios. From the result, it is proven that the optimal storage rack design model in the constant speed situation can be treated as a special case of the model considering the acceleration and deceleration of S/R machine. Finally, this study investigates the effect of speed profile of S/R machine and fixing dimensions by various numerical experiments.     

Travel-time models considering the operating characteristics of the storage and retrieval machine

Existing travel-time models of automated storage/retrieval systems (AS/RS) assume the average uniform velocity, ignoring the operating characteristics of storage/retrieval (S/R) machine such as the acceleration/deceleration rate and the maximum velocity. Consequently, the optimal design and schedule based on the existing models is far from optimal from the practical point of view. This paper presents continuous analytical models of travel time which integrate the operating characteristics of S/R machine. Using a randomized assignment policy, travel times are determined for both single and dual command cycles. The models developed are examined through discrete evaluation procedures.     

Closed form models for dwell point locations in automated storage carousel systems

This research focuses on determining the optimal dwell point location in an automated storage carousel system (ASCS) to minimise the expected response time for incoming service requests (storages and retrievals). This can be achieved by modelling the problem as a minisum location problem on a line segment with two-dimensional existing facilities (demands) using a continuous approximation of the individual storage locations of the ASCS. Closed form solutions of the associated dwell point location problem have been provided for the two different cases used to model this problem. These two cases arise from the two possible different configurations of the ASCS parameters; the travel times in circumference and height.