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.     

A bi-directional flow-rack automated storage and retrieval system for unit-load warehouses

Flow-rack is a multi-deep rack containing multi-row and multi-column slope bins. Traditionally, bins slope in the same direction in a flow-rack to make unit-loads slide from the storage face to the retrieval face driven by gravity, which cause unit-loads are stored to the storage face and retrieved from the retrieval face. In this paper, a bi-directional flow-rack (BFR) is designed, in which bins in adjacent columns slope to opposite directions. In each side of a BFR, unit-loads are stored in half of the bins and retrieved from the other half. Therefore, dual-command (DC) operations could be simultaneously performed on both faces and blocking unit-loads are re-stored to available bins on the same face directly. We develop a travel time model for BFR systems, which provides the throughput baseline for different configurations of BFR. A DC operation generation method is introduced for BFR systems. Simulation experiments are conducted to evaluate the effectiveness of the BFR travel time model, to compare the throughput performance between BFR and SFR systems and to evaluate the performance of the proposed DC operation generation method.     

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.     

Propagation of unit location uncertainty in dense storage environments

Dense storage systems provide high-space utilisation; however, because not all units are immediately accessible, selectively offloading units can require shifting of other stored units in order to access the requested unit. Given an initial certainty in unit location, a discrete time Markov Chain is developed to quantify the growth of unit location uncertainty as a function of retrieval requests. As the first to mathematically model uncertainty propagation in dense storage operations, metrics are developed to analyse the model. A theoretical understanding of the relationship among storage density, retrieval times and unit location uncertainty is provided. Finally, a case study using inventory and load plan data from a military application illustrates how the developed models can be used by managers to evaluate selective offloading policies and layouts.     

Analytical models for pick distances in fishbone warehouse based on exact distance contour

The pick distance models for a unit load warehouse employing fishbone layout conventionally use semicircular approximation for distance contour which can result in significant error. This paper develops discrete and continuous pick distance models for fishbone layout under random, full turnover, and class-based storage policies based on exact polygonal distance contour. Class-based storage policy with three classes was found to give pick distance comparable to full turnover policy over a range of demand skews and warehouse shapes studied. The discrete and continuous models are compared considering finite storage space, aisle width and discontinues in the ABC curve for a real life data. The sensitivity of warehouse performance over a range of warehouse parameters is studied. We also outline a methodology for class-based storage design where class partitions can be derived for a warehouse of any dimension from the results of a unit area warehouse.     

Optimal order picker routing in a conventional warehouse with two blocks and arbitrary starting and ending points of a tour

This paper investigates manual order picking, where workers travel through the warehouse to retrieve requested items from shelves. To minimise the completion time of orders, researchers have developed various routing procedures that guide order pickers through the warehouse. The paper at hand contributes to this stream of research and proposes an optimal order picker routing policy for a conventional warehouse with two blocks and arbitrary starting and ending points of a tour. The procedure proposed in this paper extends an earlier work of Löffler et al. (2018. Picker routing in AGV-assisted order picking systems, Working Paper, DPO-01/2018, Deutsche Post Chair-Optimization of Distribution Networks, RWTH Aachen University, 2018) by applying the concepts of Ratliff and Rosenthal (1983. “Order-picking in a Rectangular Warehouse: a Solvable Case of the Traveling Salesman Problem.” Operations Research 31 (3): 507–521) and Roodbergen and de Koster (2001a. “Routing Order Pickers in a Warehouse with a Middle Aisle.” European Journal of Operational Research 133 (1): 32–43) that used graph theory and dynamic programming for finding an optimal picker route. We also propose a routing heuristic, denoted S*-shape, for conventional two-block warehouses with arbitrary starting and ending points of a tour. In computational experiments, we compare the average order picking tour length in a conventional warehouse with a single block to the case of a conventional warehouse with two blocks to assess the impact of the middle cross aisle on the performance of the warehouse. Furthermore, we evaluate the performance of the S*-shape heuristic by comparing it to the exact algorithm proposed in this study.     

Modelling and performance evaluation of explosive storage policies in internet fulfilment warehouses

Internet Fulfilment Warehouses (IFWs) are designed to exclusively process online retail orders. An observational study reveals that IFW operating and design attributes are significantly different from traditional warehouses in their storage and fulfilment policies. Specifically, we identify six IFW differentiators: explosive storage, very large number of beehive storage locations, bins with commingled SKUs, immediate fulfilment, short picking routes with single unit picks and high transactions with total digital control. Explosive storage of incoming bulk allows for faster fulfilment of customer orders often within a few hours. A new IFW control model is developed. This describes the associated receiving and fulfilment flows. Two decision algorithms for generating (i) a stocking list and (ii) an order picking list are presented. A simulation model was built to evaluate the fulfilment performance of the explosive policy. Experimental runs on a problem with 400 SKUs, 3240 bins and 22,000 customer orders over nine days are reported. Results show that increasing levels of explosion reduce the linear fulfilment time by as much as 16%, confirming the IFW storage policy is advantageous. The results also show that fulfilment time behaviour is convex as a function of the maximum number of stops allowed by the picking algorithm parameter.     

Data mining-based algorithm for storage location assignment in a randomised warehouse

Data mining has long been applied in information extraction for a wide range of applications such as customer relationship management in marketing. In the retailing industry, this technique is used to extract the consumers buying behaviour when customers frequently purchase similar products together; in warehousing, it is also beneficial to store these correlated products nearby so as to reduce the order picking operating time and cost. In this paper, we present a data mining-based algorithm for storage location assignment of piece picking items in a randomised picker-to-parts warehouse by extracting and analysing the association relationships between different products in customer orders. The algorithm aims at minimising the total travel distances for both put-away and order picking operations. Extensive computational experiments based on synthetic data that simulates the operations of a computer and networking products spare parts warehouse in Hong Kong have been conducted to test the effectiveness and applicability of the proposed algorithm. Results show that our proposed algorithm is more efficient than the closest open location and purely dedicated storage allocation systems in minimising the total travel distances. The proposed storage allocation algorithm is further evaluated with experiments simulating larger scale warehouse operations. Similar results on the performance comparison among the three storage approaches are observed. It supports the proposed storage allocation algorithm and is applicable to improve the warehousing operation efficiency if items have strong association among each other.     

Models for automated storage and retrieval systems: a literature review

Automated Storage and Retrieval Systems (AS/RS) are warehousing systems that use mechanised devices to accomplish the repetitive tasks of storing and retrieving parts in racks. Since these systems represent a significant investment and considerable operating costs, their use must be as efficient as possible. AS/RS performance is the result of the interaction of many complex and stochastic subsystems. This reality creates a need for robust and efficient evaluation models. This article complements previous surveys on AS/RS by focusing on the particular research question addressed by each work and the associated assumptions used for the various models designed for evaluating AS/RS. Dynamic models based on simulation dominate the most recent literature; however, static approaches based on travel-time modelling have strongly contributed to the study of AS/RS. This review includes dynamic – simulation-based – models, but considers also steady-state (travel-time-based) models. We believe that this review may be of great help to researchers and industrial users in their search for the best modelling approach for a specific problem.     

On a selection and scheduling problem in automatic storage and retrieval warehouses

Warehousing is one of the main components of the supply chain and its optimisation is crucial to achieve global efficiency. Warehouse operations involve receiving, shipping, storing and order picking, among other things, and the coordinated optimisation of all these different operations is highly complex. This paper examines a real selection and scheduling problem that arises in an automatic storage/retrieval warehouse system involving the scheduling of forklift pickup operations. The objective is to minimise the total loading time of the vehicles performing transportation, while respecting their departure due dates. This complex problem is approached via a two-phase decomposition method, combining both exact and heuristic procedures. The performance of the proposed solution method is evaluated using extensive computational results from several scenarios from a real case study using data from a real mattress warehouse.     

Enhancing performance in order picking processes by dynamic storage systems

Increasing productivity and reducing labour cost in order picking processes are two major concerns for most warehouse managers. Particularly picker-to-parts order picking methods lead to low productivity as order pickers spend much of their time travelling along the aisles. To enhance order picking process performance, an increasing number of warehouses adopt the concept of dynamic storage where only those products needed for the current order batch are dynamically stored in the pick area, thereby reducing travel time. Other products are stored in a reserve area. We analyse the stability condition for a dynamic storage system with online order arrivals and develop a mathematical model to derive the maximum throughput a DSS can achieve and the minimum number of worker hours needed to obtain this throughput, for order picking systems with a single pick station. We discuss two applications of dynamic storage in order picking systems with multiple pick stations in series. In combination with simulation modelling, we are able to demonstrate that dynamic storage can increase throughput and reduce labour cost significantly.     

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.     

Order picking in a parallel-aisle warehouse with turn penalties

In many real-life routing problems, incorporating the negative effects of turns is an important, but often overlooked aspect. This is especially true for order picking in warehouses, where making the turns not only decreases the picking efficiency by reducing the speed of the vehicle, but it also results in other unquantifiable effects such as vehicle tipovers, increased congestion and increased risk of collision with pedestrians or other vehicles. In this paper, we consider the order picking problem in a parallel-aisle warehouse by taking into account the number and effect of the turns. In particular, we show that the problem of minimising the number of turns, minimising travel time under turn penalties, the biobjective problem that involves turn and travel time minimisation as separate objectives, and the triobjective problem with U-turn minimisation as a third objective can all be solved in polynomial time. Our computational results show that the algorithms we develop can generate the corresponding Pareto front very quickly, and significantly outperform heuristic approaches used in practice.     

Heuristic algorithms for a storage location assignment problem in a chaotic warehouse

The extensive application of emerging technologies is revolutionizing warehouse management. These technologies facilitate working with complex and powerful warehouse management models in which products do not have assigned fixed locations (random storage). Random storage allows the utilization of the available space to be optimized. In this context, and motivated by a real problem, this article presents a model that looks for the optimal allocation of goods in order to maximize the storage space availability within the restrictions of the warehouse. For the proposed model a construction method, a local search algorithm and different metaheuristics have been developed. The introduced algorithms can also be used for other purposes such as to assess when and how it is convenient to perform relocation of stored items to improve the current level of storage space availability. Computational tests performed on a set of randomly generated and real warehouse instances show the effectiveness of the proposed methods.     

A piecewise nonlinear model for a production system under maintenance,trade credit and limited warehouse space

Small and medium size manufacturers exist commonly in developing countries. Limited warehouse space is a characteristic in small and medium size manufacturers. In today’s business environment, many upstream companies offer a credit period to downstream companies. In production system, a manufacturer usually adopts the system maintenance when the system is in the out-of-control state. Therefore, this paper considers a production-inventory model for a manufacturer under system maintenance, trade credit and limited warehouse space. The objective is to determine the optimal production run time to minimise the total cost. We develop an algorithm based on several theorems for solving the problem described. We provide several examples to illustrate the solution procedure and discuss how system parameters affect the manufacturer’s decision behaviour. Computational analysis demonstrates that the results of the proposed model are consistent with economic insights.     

Modelling load retrievals in puzzle-based storage systems

Puzzle-based storage systems are a new type of automated storage systems that allow storage of unit loads (e.g. cars, pallets, boxes) in a rack on a very small footprint with individual accessibility of all loads. They resemble the famous 15-sliding tile puzzle. Current models for such systems study retrieving loads one at a time. However, much time can be saved by considering multiple retrieval loads simultaneously. We develop an optimal method to do this for two loads and heuristics for three or more loads. Optimal retrieval paths are constructed for multiple load retrieval, which consists of moving multiple loads first to an intermediary ‘joining location’. We find that, compared to individual retrieval, optimal dual load retrieval saves on average 17% move time, and savings from the heuristic is almost the same. For three loads, savings are 23% on average. A limitation of our method is that it is valid only for systems with a very high space utilisation, i.e. only one empty location is available. Future research should investigate retrieving multiple loads for systems with multiple empty slots.     

Robotics in order picking: evaluating warehouse layouts for pick,place, and transport vehicle routing systems

Motivated by recent technological advances in mobile robotics, this paper explores a novel approach for warehouse order picking. In particular, this work considers two types of commercially available mobile robots – one that can grasp items from a shelf (a picker) and another (a transporter) that can quickly deliver all items from the pick list to the packing station. A new vehicle routing problem is defined which seeks to minimise the time to deliver all items from a pick list to the packing station, a problem termed the pick, place, and transport vehicle routing problem. A mixed integer linear programming formulation is developed to answer three related research questions. First, what combination of picker and transport robots is required to obtain performance exceeding traditional human-based picking operations? Second, how should the composition of the robot fleet be altered to affect the greatest performance improvements? Finally, what are the impacts of warehouse layout designs when coordinated mobile robots are deployed? An extensive numerical analysis reveals that, (1) increasing the number of cross aisles decreases system performance; (2) centrally located packing stations improve system performance; and (3) the average distance from each pick location to the packing station and the average distance between pick locations are effective metrics for identifying specific fleet modifications that are likely to yield system improvements.     

An optimal and a heuristic algorithm for the single-item retrieval problem in puzzle-based storage systems with multiple escorts

Puzzle-based storage systems consist of densely stored unit loads on a square grid. The problem addressed in this paper is to retrieve a stored unit load from a puzzle-based storage using the minimum number of item moves. While previous research contributed optimal algorithms for only up to two empty locations (escorts), our approach solves configurations where multiple empty locations are arbitrarily positioned in the grid. The problem is formulated as a state space problem and solved to optimality using an exact search algorithm. To reduce the search space, we derive bounds on the number of eligible empty locations and develop several search-guiding estimate functions. Furthermore, we present a heuristic variant of the search algorithm to solve larger problem instances. We evaluate both solution algorithms on a large set of problem instances. Our computational results show that the algorithms clearly outperform existing approaches where they are applicate and solve more general configurations, which could not be solved to optimality before. The heuristic variant efficiently yields high-quality solutions for significantly larger instances of practically relevant size.     

A correlated storage location assignment problem in a single-block-multi-aisles warehouse considering BOM information

This paper deals with a correlated storage location assignment problem by considering the production bill of material (BOM) information. Due to the large number of parts in a BOM, the picking capacity constraint is considered. A mathematical model is formulated and a multi-stage heuristic is proposed. The heuristic relaxes the close interrelationships within the original problem through an improvement algorithm and an iterated approach to incorporate the effect of BOM splitting. In order to evaluate the performance of the heuristic, numerical experimentation is conducted in a single-block-multi-aisles warehouse, by using a randomly generated data set.     

小型氨库改造中的常见故障分析

对小型氨库改造中常见问题进行分析，给出冷库管道及排空气系统的改造措施，阐述解决冷库高能耗、低效率等问题的方法。