Software for dynamic reconfigurable order picking systems

Computers ind. Engng Vol. 27, Nos 1--4,pp. 245-248, 1994

Pergamon

Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-8352/94 $7.00 + 0.00

0360-8352(94)00057-3

SOFTWARE FOR DYNAMIC RECONFIGURABLE ORDER PICKING SYSTEMS Thomas L. Landers* Melinda K. Beavers'l" Malik Sadiq:~ Don E. Stuart** *University of Arkansas, Fayetteville, Arkansas, USA fAT&T, Bentonville, Arkansas, USA :[:Humco, Inc., Texarkana, Texas, USA **AT&T, Little Rock, Arkansas, USA

ABSTRACT This paper describes an approach, conceptual framework, and software architecture for dynamic reconfiguration of the order picking system. The research and development project was sponsored by the Material Handling Research Center (MHRC), a National Science Foundation sponsored Cooperative Industry/University Research Center. The storage configuration is assumed to be an in-the-aisle order picking system in which stockkeeping units (SKUs) can occupy variable capacity storage locations and stock-splitting is allowed among zones (clusters). The product mix may include multiple product families with different life cycles, correlated demand within families and commonality of demand across families. Key words: algorithm

order picking, stock location assignment, clustering

1 Introduction

Fig. 1 Dynamic order picking system forecasts of correlated demand. To break ties, for a particular location assignment the algorithm also considers the history of usage of the SKUs. Location assignments within a cluster consider ergonomic objectives. The D-SLAA utilizes a new hybrid clustering (HYCLUS) approach that allows variable overlapping of clusters and automatically determines the number of final clusters. The software to implement D-SLAA was designed to operate on a personal computer platform and to interface with business information systems. A prototype version has been integrated with a radio frequency (RF), barcode-driven inventory tracking and control system at an MHRC member company.

In a dynamic distribution environment, the forward order picking area requires an intelligent approach to on-going rewarehousing (reassignment of stock items to storage locations). Figure 1 illustrates the dynamic order picking system. The products go through life cycles and the product mix changes. Some items are common across multiple families in the product mix. Several of the items also tend to be picked in conjunction with other items, so their locations in the picking face should be made considering correlated assignment. This problem arises in the distribution centers of hightechnology industry, where product life cycles are short, and in retail, where there are seasonalities and promotional programs. The proposed approach to deal with this challenging problem is 2 Relevant Literature the Dynamic Stock Location Assignment Algorithm (D-SLAA), The following bodies of literature are relevant to this problem: (1) developed by Sadiq, The D-SLAA is an improvement algorithm order picking systems, (2) the forward/reserve problem, (3) the which is run periodically and attempts to revise the assignments of warehouse layout problem, (4) the stock location assignment storage locations as the stock mix changes. The objective of the Dproblem, and (5) clustering analysis. In addition to these topics, SLAA is to minimize total order processing time (OPT) defined as the sum of order picking time and order picking system group technology algorithms, multi-dimensional scaling techniques, rewarehousing time. and fuzzy clustering techniques provide some valuable insights and potential solution methods, but were deemed less appropriate for this Unlike some existing approaches that only assign an SKU to a problem domain. zone (cluster), the D-SLAA assigns an SKU to a specific location. For the case of carton flow rack, the algorithm determines the size The assignment of stock keeping units (SKUs) to storage and number of lanes to assign to an SKU. To assign stock to slots, locations (slots) is the main issue of this research. Choe and Sharp [6] showed that class based storage yields significant savings in travel the D-SLAA considers furore product mix, structure, popularity and 245

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Selected papers from the 16th Annual Conference on Computers and Industrial Engineering

time for both single and dual command operations. The forward/reserve problem deals with determining SKUs to be allocated space in the forward picking area and determining the order picking system storage quantity that minimizes the picking and replenishment costs. Hackman and Platzman [9] developed, for a static stock mix, a near-optimal procedure to determine the set of SKUs that should be located in the forward picking area and the allocation of stock between the forward and reserve storage areas. The warehouse layout problem involves the assignment of locations to SKUs within the warehouse to minimize the travel time during order picking. Heskett Jill developed the cube-per-order index (CPOI) as a location assignment factor. The CPOI for a SKU is the ratio of the space requirement (cubic volume) divided by the demand. The SKUs are ranked in ascending order of the CPOI and assigned in that order to the locations nearest to the input/output point. Several studies have proven the optimality of the CPOI approach for a variety of cases [3, 10, 12, 13, 14 ]. The warehouse layout problem can be formulated as a quadratic assignment problem (QAP). Frazelle [7] addressed the correlated assignment of SKUs in the warehouse layout problem. For the case of a static product mix, Frazelle developed a heuristic "cluster-first, zone-second" (CFZS) algorithm to solve what he called the Stock Location Assignment Problem (SLAP). He stated the SLAP as a quadratic assignment problem, formulated a mathematical programming model, and showed that the SLAP was in the class of NP-hard problems. It is standard research procedure to attack practical-sized cases of the QAP by heuristic means. A classic example in facilities design is the CRAFT algorithm [5]. Frazelle begins by developing a statistical representation of the order profiles, from which he creates a graphical representation of the order data and a ranking of SKUs with respect to their popularities. Based on the graphical representation and the ranking, SKUs which are likely to be ordered together form a cluster. The clusters are then ranked in descending order on the basis of their adjusted popularity and assigned to locations in increasing distance form the input/output point. The adjusted popularity of a cluster is simply the sum of the popularities of the SKUs in that cluster divided by the sum of space occupied by each SKU in the same cluster, and is therefor similar to the CPO1. Fraz~lle's algorithm uses a construction approach (sequentially building up a feasible solution from the null solution). The CFZS algorithm picks the most popular SKU as the seed to start a cluster. Each time a SKU joins a cluster, the popularity of the joining SKU is added to the cluster popularity. New SKUs only join a cluster if their joining does not violate the capacity and congestion constraints. The procedure continues until all SKUs are assigned to clusters. An SKU can be assigned to only one cluster (i.e., stock-splitting is not permitted). Once a SKU joins a cluster, it stays in that cluster. To avoid excessive computational complexity, Frazelle's algorithm only considered pairwise associations (correlated demands) between SKUs. Clustering algorithms provide the best available solution approach for the stock location assignment problem. However, to ensure a globally optimal solution, all possible enumerations of cluster combinations must be considered for every possible number of clusters. The number of ways of sorting n objects into k clusters is a Stirling number of the second kind [ 1 ]. For a small problem of partitioning 25 objects into 5 clusters, the number of possibilities in the solution set is over 2XI0 '5 . Since the clustering problem is in the class of NP-complete problems [81, heuristic solution methods are used. The two general classes of techniques are hierarchical and non-hierarchical. In hierarchical clustering [41, once an item joins a cluster, it does not change to another cluster. The advantage is. that the number of possibilities that need to be subsequently examined is greatly reduced. However, an item can join a cluster early and as the clustering continues another cluster could develop containing,members for which the item has even greater association. Non-hierarchical 12] clustering allows the items to change clusters in

order to improve partitioning, but requires an initialization (set of duster seeds), such as is provided by a hierarchical clustering routine. 3 Problem Description The Dynamic Stock Location Assignment Algorithm applies to an order picking system of known size and configuration which has stock already assigned to locations. The initial stock location assignment may be random or may have been based upon an intelligent constructive assignment algorithm such as Frazelle's CFZS. The existing prototype version of D-SLAA deals with carton flow rack systems as shown in Fig. 2. Flexibility in rewarehousing is provided through division of shelves as follows: cOne slot, full shelf width eTwo slots, each 1/2 shelf width eTwo slots, one of 1/4 and another of 3/4 shelf width eFour slots, each 1/4 shelf width. BAY t

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T h e D-SLAA considers product structures and forecast information available from existing engineering, marketing, and inventory control systems. It determines if and how the existing configuration can be improved by rewarehousing (moving items to different locations within the picking system, removing items from the picking system, and adding items to the picking system). The decision to rewarohouse is ultimately determined based on cost tradooffs and should occur when the cost of picking from an undesirable location is predicted to exceed the cost of rewarehousing. Intelligent stock assignment within the picking area should explicitly consider relationships among SKUs. Some items may belong to several different product families, and thus have common demand. Items which are always ordered together comprise a product family and their demands are considered correlated. The number of times that an item is ordered with another item determines the strength of the relationship between the two items. In cluster analysis, this strength of relationship is used to determine logical clusters of items that are frequently ordered together and so should be located physically close together. The cluster relationship are based upon dynamic demand and should be determined from forecast inibrmation and bills of materials or parts lists for product families. For manufacturing, the bill of materials defines dependencies of demand. In the retail industry dependencies are determined from catalogs, promotional plans, market surveys and the like. Based on correlated demand for SKUs, the number, size and location of logical clusters can be determined. Once items are assigned to clusters, physical assignment of clusters to stock locations should be based upon popularity with the objective of minimizing the total picking time, subject to physical, ergonomic, and congestion constraints.. An SKU should be moved into a cluster when the order picking costs associated with picking the SKU outside the cluster outweigh the rewarehousing cost to assign the item inside the cluster. The

Selected papers from the 16th Annual Conference on Computers and Industrial Engineering rewarehousing costs are determined by the number and type of moves, relocations, and slot size changes required to form a cluster. There is a packing constraint since the package size of an SKU may prohibit the item from fitting into the picking system. Slot size is variable to accommodate different size items and to maximize space utilization. However, some items will still be larger than the maximum slot size available and/or have excessive demand requiring too frequent replenishment. In either case the SKU might be allotted to pallet flow storage also located in a fast pick area or to a bulk storage location. Stock splitting is also considered. An SKU may be assigned to more than one location within the cluster and could also be assigned to more than one cluster. Ergonomic factors such as weight and number of pick activities per SKU are considered when locating an SKU within a cluster. Heavy weight and high demand items are located within the most accessible locations in the cluster. 4 Overview of Algorithm Figure 3 provides an overview of the D-SLAA. The algorithm interfaces with the external information and control systems of the warehouse and considers future order profiles, product structure and correlated demands in assigning SKUs to locations on the order picking system (OPS). A hybrid clustering (HYCLUS) approach blends the strengths of both hierarchical and non-hierarchical clustering. Figure 4 provides a detailed view of the SLAA assignment and cost phases, including the Global assignment phase, the Local assignment phase with ergonomics, and an optional CPO1 assignment.

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The main purpose of the Global assignment phase is to perform capacity analysis. If the OPS is operating at 100% capacity, decisions need to made about which SKUs should be on the system. In the Global phase no physical moves are performed; assignments are made considering future requirements, slot size constraints, and usage history. The Global phase considers correlated demands in determining the popularity of an SKU but does not cluster SKUs into families. After the capacity analysis is performed in the Global phase, a relationship matrix (symmetric matrix containing metrics of pairwise relationship between SKUs) is developed using those SKUs that are on the OPS and required in the current period. The hierarchical clustering algorithm (HCA) develops a set of clusters for use as the starting solution for the non-hierarchical clustering algorithm (NHCA). Candidate locations on the OPS for the proposed clusters from NHCA are selected using the CPOI rule. Next, in a procedure similar to CRAFT, pairwise interchanges for same-sized clusters and adjacent clusters are performed to trade off set-up time for the OPS and order picking time. For the most efficient arrangement, the actual assignments are performed and the number of required slot changes is determined. Finally, the ergonomic analysis is performed. The final result is a detailed slot-level assignment of all SKUs needed on the OPS during the next operating period. 5 Software and Information Requirements The following input data are required for full utilization of the prototype D-SLAA: eTwelve week forecast for each orderable product eList of SKUs which comprise each orderable product ePhysical size information for each SKU eHistory of usage for each SKU oCurrent configuration and stocking requirements for the OPS The prototype development platform for the project was an AT&T 6386E/33 Model S, 80386-based, 33 Mhz CPU with math co-processor, 8Mb RAM, 300Mb SCSI hard disk unit, 3.5 inch 1.44Mb floppy disk unit, and 120Mb cartridge tape unit. The Model S runs Unix System V, Release 3.2. The application software was developed for an lnformixTM relational database and all input and output information storage for the software modules are in the form of InformixTM tables. All software was written in the C language with Informix Embedded Structured Query Language (ESQLTM) to interface with the database and existing SQL-based inventory systems of a case study user site. Relational Database Structured Query Language (RDSQL TM) is the interactive query language used by Informix SQLTM. RDSQLTM is a software product of Relational Database Systems, Inc., and is an extension of the ANSI Standard SQL. The statements of RDSQLTM create and manipulate relational databases. The software was designed to be run on a schedule coincident with the replenishment cycle for the OPS and assumes that the problem of determining the replenishment cycle and sizing of the OPS is solved separately. It was designed for use in the warehouse by warehouse personnel and to run as a background process without user interaction unless desired. The software was structured in modular fashion to facilitate management, understanding, modification and further research. Memory is allocated and freed dynamically. Linked list structures and structure pointers were used to implement the clustering algorithms efficiently. A linked list approach for storing and processing a sparse matrix (consisting mostly of zeros) was used for efficient memory management. The so,ware depends extensively upon functions of the Informix-SQLTMDatabase Management System for data storage, retrieval, queries, and manipulation. Figure 5 shows the software architecture. The input phase is concerned with filling the dynamic databases. The input can come from external systems, users, or the database creating module

248

Selected papers from the 16th Annual Conference on Computers and Industrial Engineering CONTROLS

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(designed for research purposes). The analysis phase will read from the dynamic databases, write to the internal control tables, and operate upon both the control tables and starting configuration information to determine the total demand levels by SKU including all demand types (independent, common, correlated, forecasted and historical). 6 References

Abramawtiz, M., and Stugun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Nat. Bur. of Stand. Appl. Math. Set.,

4

Garey, M. R., and Johnson, D. S., Computers and Intractability, A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, California, 1979.

9

Hackman, S. T., and Platzman, L. K., "Near-optimal Solution of Generalized Resource Allocation Problems with Large Capacities," Operations Research, 38, 5, 902-910, 1990.

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10 Harmatuck, D. J., "A Comparison of Two Approaches to Stock Location," Logistics and Transportation Review, 12, 4, 282-284, 1976.

Anderberg, M. R., Ouster Analysis for Applications, Academic Press, New York, 1973.

11 Heskett, J. L., "Cube-Per-Order Index - A Key to Warehouse Stock Location," Transportationand Distribution Management, 4, 23-30, August, 1964.

Ashayeri, J., and Gelders, L. F., "Warehouse Design Optimization," European Journal of Operations Research, 21,285-294, 1985.

12 Kallina, C., and Lynn, J. "Application of the Cube-PerOrder Index Rule for Stock Location in a Distribution Warehouse," Interfaces, l, 37-46, 1986.

Blashfield, R. K., and Aldenderfer, M. S., "The Literature on Cluster Analysis," Multivariate BehavioralResearch, 13, 271-295, 1978.

13 Malmborg, C. J., and Bhaskaran, K., "On the Optimality of the Cube-Per-Order Index for Conventional Warehouses with Dual Command Cycles," Material Flow, 4, 169-175, 1987.

Buffa, E. S., Armour, G. C., and Vollmann, T. E., "Allocating Facilities with CRAFT," Harvard Business Review, 136-158, March-April, 1964.

14 Malmborg, C. J., and Bhaskaran, K., "A Revised Proof of Optimality for the Cube-Per-Order Index Rule for Store Item Location," Applied Mathematical Modelling, 14 87-95, 1990.

No. 55), 7~ printing, U. S. Govt. Washington, D. C., 1968. 2

8

Choe, K. 1., and Sharp, G. P., "Class-based Storage with Multi-Command Operation," MHRC-TR-88-08, Material Handling Research Center, Atlanta, Georgia, 1988. Frazelle, E. H., "Stock Location Assignment and Order Picking Productivity," MHRC-TD-89-11, Material Handling Research Center, Atlanta, Georgia, 1990.