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.     

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.     

Assembly block location and sequencing for flat transporters in a planar storage yard of shipyards

Assembly block location and sequencing are two important and related problems for scheduling a flat transporter to perform block storage and transport within a planar storage yard in shipyards. They affect not only the transport efficiency of storage yards but also the productivity and coordination of related workshops. This paper addresses the block location and sequencing at the same time with the purpose of reducing unproductive moves. A heuristic approach is proposed based on a sequencing strategy, a location selecting procedure for the incoming blocks and a policy for relocating blocks. A tabu search algorithm is proposed to improve the solution. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed approach.     

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.     

Lagrangean relaxation for the capacitated hub location problem with single assignment

This article considers the capacitated hub location problem with single assignment. We propose a Lagrangean relaxation to obtain tight upper and lower bounds. The Lagrangean function that we formulate exploits the structure of the problem and can be decomposed into smaller subproblems that can be solved efficiently. In addition, we present some simple reduction tests, based on the Lagrangean relaxation bounds that allows us to reduce considerably the size of the formulation and thus, to reduce the computational effort. Computational experiments have been performed with both benchmark instances from literature and with some new larger instances. The obtained results are impressive. For all tested instances (ranging from 10 to 200 nodes), we obtain or improve the best known solution and the obtained duality gaps, between our upper and lower bounds, never exceed 3.4%.     

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics’ performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.     

A simple and robust Monte Carlo hybrid local search algorithm for the facility location problem

In this article, a new Monte Carlo hybrid local search algorithm (Hyb-LS) is proposed for solving the uncapacitated facility location problem. Hyb-LS is based on repeated sampling using two local search strategies based on best improvement and randomized neighbourhood search. A major advantage of Hyb-LS for its practical use is that the number of restarts is its only parameter to tune. The algorithm is also simple to reimplement, scalable and robust to changes in coefficients within a problem instance. The stopping criterion for local search is learned automatically. Experimental results are presented for four representative and contrasting cost and distance models. The results obtained by Hyb-LS are compared to the optimal or near-optimal solutions found by a mixed integer linear programming (MILP) solver with a generous time limit. For three out of the four models, Hyb-LS obtains better solutions than the upper bound found by the MILP solver for at least one instance.     

Enhancing the order picking process through a new storage assignment strategy in forward-reserve area

This paper reexamines the order picking process in a warehouse facing the challenges that e-commerce brings about and which are characterised by a very large number of small sized orders and returns. Implementing effective storage assignment strategies combined with efficient batching, in this context, is very fundamental to keep the warehouse’s responsiveness and order completion times up to the standards. This paper investigates a new storage assignment strategy, initially implemented by a large shoes and footwear wholesaler, to enhance the performance of the order picking process in its warehouses. The impact of this new storage assignment strategy on the performance of the order picking process is analysed via simulation. The performance of the system, measured in terms of total picking time as well as order lead time while taking congestion into account, is compared to the cases where conventional storage assignment strategies are implemented. A full factorial design is set up and the simulation output is statistically analysed. The results of this analysis are reported and thoroughly discussed. Attending to the results, the proposed strategy presents a remarkable potential to shorten total picking travel distances and order completion time and consequently customer satisfaction.     

On sequencing policies for unit-load automated storage and retrieval systems

Automated Storage and Retrieval System (AS/RS) performance highly depends on the characteristics of the mechanical equipment. However, once the system has been physically implemented, achieving its maximum efficiency depends on the way the system is operated. This paper shows that request sequencing (i.e. planning the order in which storage and retrieval requests are performed) is of paramount importance in AS/RS performance. This paper reviews and adapts the most popular storage and sequencing policies to dynamic contexts, and then it proposes a ‘sequencing mathematical model’ (SMM) to simultaneously solve the sequencing and storage location problems. Extensive computational results based on a thorough simulation experiment plan confirm that performing the requests in the right sequence can have a positive impact on AS/RS performance. Our results show that the proposed SMM regularly outperforms other methods. When used in a dynamic context, the proposed SMM may yield up to a 25% reduction in average travel-time compared to the situation where a no-sequencing method is applied.     

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.     

On a branch-and-bound approach for a Huff-like Stackelberg location problem

Modelling the location decision of two competing firms that intend to build a new facility in a planar market can be done by a Huff-like Stackelberg location problem. In a Huff-like model, the market share captured by a firm is given by a gravity model determined by distance calculations to facilities. In a Stackelberg model, the leader is the firm that locates first and takes into account the actions of the competing chain (follower) locating a new facility after the leader. The follower problem is known to be a hard global optimisation problem. The leader problem is even harder, since the leader has to decide on location given the optimal action of the follower. So far, in literature only heuristic approaches have been tested to solve the leader problem. Our research question is to solve the leader problem rigorously in the sense of having a guarantee on the reached accuracy. To answer this question, we develop a branch-and-bound approach. Essentially, the bounding is based on the zero sum concept: what is gain for one chain is loss for the other. We also discuss several ways of creating bounds for the underlying (follower) sub-problems, and show their performance for numerical cases. This work has been supported by the Ministry of Education and Science of Spain through grant SEJ2005/06273/ECON. M. Elena Sáz was supported by a junior research grant of Mansholt Graduate School (Wageningen Universiteit).     

An integrated storage assignment method for manual order picking warehouses considering cost,workload and posture

This paper presents an integrated storage assignment method for low-level picker-to-parts order picking warehouses taking into account economic and ergonomic objectives. Three different pallet rack layouts are studied in this paper, namely (a) picking from full pallets on the floor, (b) picking from half-pallets on the floor, and (c) picking from half-pallets on the upper rank of the shelf. First, cost functions are developed to assess the total order picking performance impact of these different pallet rack layouts. Second, with regard to workload, the metabolic cost and energy expenditure rates for picking from the different rack layouts under study are derived. Third, for assessing the working posture during order picking, the Ovako Working Posture Analysing System index is used where the required data is collected using a motion capturing system. The developed models are combined to propose a heuristic storage assignment procedure that supports the decision of which item to store on which pallet. The developed storage assignment method is then applied to an industrial case study. The results of the paper support warehouse managers in assessing the order picking storage assignment from an ergonomics viewpoint and in estimating its impact on financial order picking performance.     

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.     

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.     

New solution algorithms for asymmetric traffic assignment model

Abstract

The asymmetric traffic assignment model can improve the traditional traffic assignment model by adopting detailed network representation and more realistic asymmetric cost functions. The diagonalization, streamlined diagonalization, and projection methods are three widely mentioned solution algorithms for solving asymmetric traffic assignment models. The diagonalization and streamlined diagonalization methods have the advantage of requiring less computer memory but typically require greater computational time. The projection method has the advantage of converging more rapidly but requires a large computer memory. In order to balance computer memory and computational time, we propose two new algorithms; i.e., hybrid and streamlined hybrid methods. According to our case study, the proposed algorithms show their superiority over the diagonalization and streamlined diagonalization methods in terms of computational time, and over the projection method in terms of computer memory. Both new algorithms can handle small or medium networks sized asymmetric traffic assignment problems on personal computers.     

A 0-1 integer programming model and solving strategies for the slab storage problem

We consider the slab storage problem (SSP) in slab yard operations. A set of slabs enter a slab yard in a specific order. A proper stack needs to be selected for each inbound slab, so that the number of relocations in the subsequent retrieval stage is minimised. We present a 0-1 integer programming model of the SSP that minimises the lower bound of the number of relocations. Four solving strategies are derived from several interesting properties of the mathematical model to speed up the solving process of the model. Making use of randomly generated instances and practical instances, we testify the effectiveness of the solving strategies and study the influence of problem parameters on the computational time of the model. Computational results show that the solving strategies can effectively reduce the computational time of the model and is applicable in medium-sized practical instances.     

Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems.This is an expanded version of a survey lecture presented at the DGOR/NSOR Symposium, Amsterdam, 1993     

An optimal storage assignment for automated rotating carousels

Automated rotating carousels (ARCs) are increasingly used as building blocks for material storage and control systems in factories to provide easy and quick access to materials. This technical note introduces a simple and robust storage assignment policy that minimizes the expected turnaround time for accessing an item in an automated rotating carousel. The policy is shown to be optimal for a class of dwell point strategies.     

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.     

Differentiated service policy in smart warehouse automation

Smart warehouse automation has emerged as an effective, competitive solution for suppliers and distributors. With the increasing demand for physical storage and distribution services, suppliers and service providers are challenged to respond not only effectively, but with minimal latency. Differentiated service levels for different classes of customer orders have not yet, however, been developed for physical storage and retrieval. In this paper, in the context of smart warehouse automation services, a novel policy, called Differentiated Probabilistic Queuing (DPQ) is developed for servicing customers’ orders by Automated Guided Vehicles (AGV). Applying the DPQ policy, the average overall latency of each customer order, the mean overall processing time of this customer’s orders in the smart warehouse automation system, is characterised under Poisson customer order arrival patterns. The weighted average latency of all customer orders is optimised over the choice of (1) storage assignment and (2) DPQ policy. Due to the existence of two types of variables, Alternating Minimisation method is applied to solve this joint optimisation problem. Compared with a combination of the classical turn-over rate storage assignment method and FCFS policy, the new approach yields 19.64% lower (better) objective function value with statistical significance. Numerical analysis results also indicate, as expected, that when the smart warehouse system resources become more limited, and the price difference among different classes of customer orders increases, the improvement becomes even more significant.