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Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Gains In The Life-Cycle Of Adaptable, Self-Organizing Material Handling Systems, Jan R. Nopper, Guido Follert, Michael Ten Hompel Sep 2010

Gains In The Life-Cycle Of Adaptable, Self-Organizing Material Handling Systems, Jan R. Nopper, Guido Follert, Michael Ten Hompel

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Compared to conventional material flow controls, self-organized material handling systems and the Internet of Things in facility logistics promise several advantages during the life-cycle. Most important is the increased adaptability in case of expansions or modifications due to a consistent modular design; this also promotes an increased robustness due to clearly defined interfaces and a decreased complexity of each module. The use of RFID technology increases the availability of real-time data about the system and the transported units. However, the introduction of self-organized material handling systems also causes costs, e.g. for necessary RFID tags and readers. Against this background, it …


Design Of Cross-Chain Internet Order Fulfillment Centres, Kees Jan Roodbergen, Iris F. A. Vis, Jaap Boter Sep 2010

Design Of Cross-Chain Internet Order Fulfillment Centres, Kees Jan Roodbergen, Iris F. A. Vis, Jaap Boter

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Many consumers have embraced the option of ordering via the Internet, which has resulted in an enormous increase in direct orders compared to the times when direct ordering was done by catalogue and phone. The fulfillment process in the supply chain is an important factor for these consumers impacting how long they must wait between ordering and delivery. This fact has significantly increased the importance of the back-end fulfillment process. We present a novel supply chain design to enable cross-chain coordination of order fulfillment operations for internet sales. Shared warehousing facilities are used more and more to achieve competitive advantage. …


A Real-Time Picking And Sorting System In E-Commerce Distribution Centers, Yeming Gong, Erik M. M. Winands, Rene B. M. De Koster Sep 2010

A Real-Time Picking And Sorting System In E-Commerce Distribution Centers, Yeming Gong, Erik M. M. Winands, Rene B. M. De Koster

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Order fulfillment is the most expensive and critical operation for companies engaged in e-commerce. E-commerce distribution centers must rapidly organize the picking and sorting processes during and after the transaction has taken place, with the ongoing need to create greater responsiveness to customers. Sorting brings a relatively large setup time, which cannot be well admitted by existing polling models. We build a new stochastic polling model to describe and analyze such systems, and provide approximate explicit expressions for the complete distribution of order line waiting time for polling-based order picking systems and test their accuracy. These expressions lend themselves for …


Spiral Facility Layout Generation And Improvement Algorithm, Hatice E. Sanli, Fahrettin Eldemir Sep 2010

Spiral Facility Layout Generation And Improvement Algorithm, Hatice E. Sanli, Fahrettin Eldemir

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

This study is concerned with construction and improvement of a facility layout heuristic called Spiral Facility Layout Generation and Improvement Algorithm (SFLA). The algorithm starts with positioning departments from center point and continues like a hologram from center to outside. The aim of any facility layout algorithm is to better allocate the departments within facility. SFLA is compared with the existing space filling curve methods, MCRAFT and MULTIPLE, that are available in the literature. To form an initial spiral curve, a block system is used, like the bands for MCRAFT. The width and length of the blocks are given by …


Merge Problems With High Speed Sorters, Dirk Jodin, Andreas Wolfschluckner Sep 2010

Merge Problems With High Speed Sorters, Dirk Jodin, Andreas Wolfschluckner

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

To meet customer demands on distribution the necessity of sorting systems for unit loads in regard to quantity and capacity is growing up constantly.

Due to that, manufactures offer powerful sorting machines with a capacity up to 15.000 pieces per hour. Those machines are for instance Crossbelt or Tilt-Tray sorters. The output of these sorters is calculated by the equation of throughput.

The point of interest is the merge, referring to the overall efficiency of the single sorter. The motion sequence during merging has to be absolutely quick and precise to achieve exact positioning using minimized distances of the single …


Dispatching Vehicles Considering Uncertain Handling Times At Port Container Terminals, Vu Duc Nguyen, Kap Hwan Kim Sep 2010

Dispatching Vehicles Considering Uncertain Handling Times At Port Container Terminals, Vu Duc Nguyen, Kap Hwan Kim

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

This paper considers the problem of vehicle dispatching at port container terminals in a dynamic environment. The problem deals with the assignment of delivery orders of containers to vehicles while taking into consideration the uncertainty in the travel times of the vehicles. Thus, a real-time vehicle dispatching algorithm is proposed for adaptation to the dynamic changes in the states of the container terminals. To evaluate the performance of the proposed algorithm, a simulation study was conducted by considering various values of decision parameters under the uncertainty in travel times. Further, the performance of the proposed algorithm was compared with those …


Investigating Possible Synergies In Intermodal Operations With Truck And Rail, G. Don Taylor, Mia K. Burns, Gary L. Whicker Sep 2010

Investigating Possible Synergies In Intermodal Operations With Truck And Rail, G. Don Taylor, Mia K. Burns, Gary L. Whicker

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

As the trucking industry continues to examine ways to provide better service at lower cost, many companies are more heavily utilizing intermodal (IM) strategies between truck and rail, especially for those loads that are relatively non-critical in terms of delivery time requirements and that have longer lengths of haul. As IM business grows, supporting dray infrastructure naturally develops around IM rail yards. What is unknown is whether it is best to have a dedicated set of drivers performing dray operations or if efficiency and cost savings can result when utilizing a joint driving fleet to concurrently support IM and traditionally …


Optimization Of Costs And Service Level By Choosing The Best Customer Order Decoupling Point, Michael Schmidt, Detlef Spee Sep 2010

Optimization Of Costs And Service Level By Choosing The Best Customer Order Decoupling Point, Michael Schmidt, Detlef Spee

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

The customer order decoupling point (CODP) as the link in the supply chain between processes based on uncertain information, such as sales forecasts, and certain information in the form of customer orders is crucial for production efficiency, storage costs, and the quality of logistics. This paper focuses on developing an approach for identifying a CODP that provides the highest potential for achieving business objectives. Within the context of the above-mentioned topics, this paper focuses on the interrelations and the tradeoffs that have to be made when positioning the COPD. The goal of the paper is to present an effective and …


Analysis Of Picker Blocking In Narrow-Aisle Batch Picking, Soondo Hong, Andrew L. Johnson, Brett A. Peters Sep 2010

Analysis Of Picker Blocking In Narrow-Aisle Batch Picking, Soondo Hong, Andrew L. Johnson, Brett A. Peters

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

This study analyzes impacts by batch picking on picker blocking in narrow-aisle order picking, and determines appropriate batch formations for a better order picking throughput. We present multiple-pick analytical models to offer insights about picker blocking in batch picking. Several simulation studies over a variety of batching situations scrutinize order batching situations which give throughput benefits in narrow-aisle configurations by satisfying the analytical results. Our results highlight three findings for narrow-aisle batch picking processes: 1) variation of pick probability in batch picking is inevitable and is a primary driver of picker blocking; 2) a near-optimal distance-based batching algorithm can experience …


Drive And Motion Design In Material Handling Equipment, Jorg Oser, Christian Landschutzer Sep 2010

Drive And Motion Design In Material Handling Equipment, Jorg Oser, Christian Landschutzer

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Drives account in many cases up to one third of the costs of material handling equipment. This fact justifies a closer look to important drive and motion issues. Typical design criteria for drives are energy and power consumption, wear, heat and noise generation. Engineering design activities start with the generation of the system configuration, that is to make appropriate topological decisions where to locate the drives in the equipment structure. These decisions define to a great extent the functional quality of the mechanical structure and the distribution of forces in the power train. For early design stages an elasto-kinetic model …


The Effect Of Interaction Between The Production System (Ps) And A Looped Conveyor-Based Material Handling System (Lcmhs) In A Manufacturing Facility, Vernet Lasrado, Dima Nazzal Sep 2010

The Effect Of Interaction Between The Production System (Ps) And A Looped Conveyor-Based Material Handling System (Lcmhs) In A Manufacturing Facility, Vernet Lasrado, Dima Nazzal

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

In this paper, we provide empirical evidence that shows the effect of the interaction between the production system (PS) and a looped conveyor-based material handling system (LCMHS) in a manufacturing facility. A rudimentary simulation model captures the interaction between the two systems. Varying several key factors, we test for a statistically significant difference in the work in process (WIP) of the production system with and without the LCMHS to find if the squared coefficient of variation (SCV) of the interarrival time distribution to the PS is affected. The results suggest the need to model the interaction between the two systems …


Multiple-Grooved Magnetic Traction Sheaves, Thorsten Schmidt, Thomas Leonhardt, Martin Anders Sep 2010

Multiple-Grooved Magnetic Traction Sheaves, Thorsten Schmidt, Thomas Leonhardt, Martin Anders

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

This paper discusses a new and innovative form of traction sheaves, which can be used in many hoisting applications that are driven with wire ropes in material handling systems. By use of high performance permanent magnets, integrated in the periphery of traction sheaves, a significant increase of driving capacity is achieved. In this special case it concerns high energy magnets consisting of rare earth materials known as NdFeB magnets. These magnets provide a 20 times higher force than conventional magnets. The results of the research show that the driving capacity of traction sheaves with a round groove design can be …


Determining Warehouse Storage Location Assignments Using Clustering Analysis, Carl Egas, Dale Masel Sep 2010

Determining Warehouse Storage Location Assignments Using Clustering Analysis, Carl Egas, Dale Masel

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

The methodology used to assign products to a storage location in a warehouse can have a significant impact on the amount of time required to retrieve all of the items needed to fill an order. This paper describes a methodology that uses a clustering approach to determine storage assignments, where the metric of the strength of the relationship between two stock-keeping units (SKUs) is the number of times that the SKUs appear in the same order. Clustering is performed to maximize the frequency with which SKUs in the same cluster are ordered together. In testing, the clustering assignments were compared …


Webasrs – A Web-Based Tool For Modeling And Design Of Abstract Unit-Load Picking Systems, Jeffrey S. Smith, Sabahattin Gokhan Ozden Sep 2010

Webasrs – A Web-Based Tool For Modeling And Design Of Abstract Unit-Load Picking Systems, Jeffrey S. Smith, Sabahattin Gokhan Ozden

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

This paper describes a web-based tool that supports the modeling and design of abstract unit-load picking systems. The term “abstract” implies that the model is not specific to any equipment or vendors’ products, but, instead, focuses on the generic system components such as pallets, racks, slots, forklifts, cranes, etc. that comprise typical unitload picking systems. The objectives of the tool are to support the design of an AS/RSbased or a manual forklift-based picking system based on a set of design parameters and to be able to convert from an AS/RS design to a flat warehouse design and vice versa. The …


The Future Of Modeling In Material Handling Systems, Leon F. Mcginnis Sep 2010

The Future Of Modeling In Material Handling Systems, Leon F. Mcginnis

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Today, when we talk about “modeling” in the context of material handling systems, invariably we are referring to a mathematical or computational model for analyzing some aspect of the system, such as its throughput rate, response time, cost of ownership, required storage capacity, etc. Creating these kinds of models requires considerable knowledge in at least two domains the material handling system domain, and the analysis methodology domain—and considerable skill in the “art of modeling” in order to express the former in the terms of the latter. The results can be somewhat ad hoc—e.g., two different modelers are likely to create …


Optimizing Distribution Center Configuration: A Practical View Of A Multi-Objective Problem, Russell D. Meller, Lisa M. Thomas Sep 2010

Optimizing Distribution Center Configuration: A Practical View Of A Multi-Objective Problem, Russell D. Meller, Lisa M. Thomas

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

The shape of a distribution center, as well as whether dock locations are on one side or two sides of the facility, impacts measures like travel distances and the number of dock locations that may be utilized. Thus, for a required number of pallet locations, there are multiple combinations of distribution center shape and dock configurations that should be evaluated against multiple measures. We have developed a practical model for making such evaluations and illustrate the model with data reflective of a partner in the Center for Engineering Logistics and Distribution.


A Flowshop Scheduling Problem With Transportation Times And Capacity Constraints, Abraham Mendoza, Jose A. Ventura, Kwei Long Huang Sep 2010

A Flowshop Scheduling Problem With Transportation Times And Capacity Constraints, Abraham Mendoza, Jose A. Ventura, Kwei Long Huang

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Although there are numerous methodologies and research studies on machine scheduling, most of the literature assumes that there is an unlimited number of transporters to deliver jobs from one machine to another for further processing and that transportation times can be neglected. These two assumptions are not applicable if one intends to generate an accurate schedule for the shop floor. In this research, a flowshop scheduling problem with two machines, denoted as M1 and M2, and a single transporter with capacity c is considered. The main focus is on the development of a dynamic programming algorithm to generate a schedule …


Using Data Envelopment Analysis To Evaluate The Performance Of Third Party Distribution Centers, Ching-Jung Ting, Hsueh-Lin Fang Sep 2010

Using Data Envelopment Analysis To Evaluate The Performance Of Third Party Distribution Centers, Ching-Jung Ting, Hsueh-Lin Fang

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

There has been considerable interest worldwide in last few years in the growth of third party logistics (3PL) providers. 3PL distribution center (DC) enables firms to achieve reduced operating costs, increased revenues, and to focus on their core competence. This research aims to find the key performance indicators through a survey of a set of DCs and then evaluate their efficiency over the period 2005-2007 using data envelopment analysis (DEA) models based on selected performance indicators as inputs and outputs. Three inputs and two outputs for all DCs from the surveyed performance indicators were selected in this study. DEA is …


Class-Based Storage With A Finite Number Of Items, Yugang Yu, René B.M. De Koster Sep 2010

Class-Based Storage With A Finite Number Of Items, Yugang Yu, René B.M. De Koster

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

ABC class-based storage is widely studied in literature and applied practice. It divides all stored items into a limited number of classes according to their demand rates (turnover per unit time). Classes of items with higher turnovers are stored in a region closer to the warehouse depot. In literature, it is commonly shown that the use of more storage classes leads to shorter travel time for storing and retrieving items. A basic assumption in this literature commonly is that the required storage space of items equals their average inventory levels, which is right if an infinite number of items are …


Determination Of Operational Parameters For An Efficient Container Service In The Port Of Guaymas, Cesar Meneses, J. René Villalobos Sep 2010

Determination Of Operational Parameters For An Efficient Container Service In The Port Of Guaymas, Cesar Meneses, J. René Villalobos

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

The port of Guaymas is located in Sea of Cortez in the Northern Pacific Coast of Mexico. Its hinterland is basically the Northwestern region of Mexico and the Southwestern United States. The Port currently focuses on bulk and liquid cargo and does not provide container services. In this paper, we explore some of the characteristics that a container service should have to be competitive in servicing the needs of the regional industry. Since the study deals with port selection decision from the industry’s point of view, we introduce a port selection model based on a Total Landed Cost (TLC) metric. …


Empirically-Based Warehouse Design: Can Academics Accept Such An Approach?, James M. Apple Jr., Russell D. Meller, John A. White Jr. Sep 2010

Empirically-Based Warehouse Design: Can Academics Accept Such An Approach?, James M. Apple Jr., Russell D. Meller, John A. White Jr.

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

It is our opinion that existing research is not sufficient to support the design of a warehouse. As a result, facility designers that work in practice are left to face the design process with their own methods. These methods are in stark contrast to the analytical models developed in academia in that they are highly based on empirical observations. Supported by a collection of empirical observations, facility designers who work in practice employ an ad hoc design process. We present a design process based on empirical observations and then formalize it so that it can be taught and used. We …


Design Of Warehouse For Material, Which Is Non-Uniform And Difficult To Handle, Andrea Seidlova, David Sourek Sep 2010

Design Of Warehouse For Material, Which Is Non-Uniform And Difficult To Handle, Andrea Seidlova, David Sourek

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Main goal of this paper is warehouse layout optimization with emphasis on maximum space utilization. It is about rack system design, which leads to capacity maximization of warehouse for non-uniform material with heavy weight. The warehouse system has to enable at least partial automation (the possibility to use AS/RS system), minimization of service time and minimization of man effort. Initial constraining conditions for warehouse design in our case are warehouse area, maximum load of racks or shelves, maximum allowed floor load and existing location of arrival road for material loading and unloading.


Monitoring Inventory Accuracy With Statistical Process Control, Kyle Huschka, John R. English, Todd Easton, Andrew Huschka Sep 2010

Monitoring Inventory Accuracy With Statistical Process Control, Kyle Huschka, John R. English, Todd Easton, Andrew Huschka

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Inventory accuracy is critical in most industrial environments such as distribution, warehousing, and retail. Many companies use a technique called cycle counting and have realized outstanding results in monitoring and improving inventory accuracy. The time and resources to complete cycle counting are sometimes limited or not available. In this work, we promote statistical process control (SPC) to monitor inventory accuracy. Specifically, we model the complex underlying environments with mixture distributions to demonstrate sampling from a mixed but stationary process. For our particular application, we concern ourselves with data that result from inventory adjustments at the stock keeping unit (SKU) level …


Freight Sequencing To Improve Hub Operations In The Less-Than-Truckload Freight Transportation Industry, Xiangshang Tong, Kimberly Ellis, Amy Brown Greer Sep 2010

Freight Sequencing To Improve Hub Operations In The Less-Than-Truckload Freight Transportation Industry, Xiangshang Tong, Kimberly Ellis, Amy Brown Greer

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

In less-than-truckload freight transportation, hub operations affect the service levels that carriers are able to provide their customers. This paper focuses on improving the efficiency of hub operations by reducing freight handling time and cost. Specifically, the freight sequencing problem (FSP) is investigated to determine the freight unloading and loading sequence that minimizes the time for dock workers to transfer shipments from origin trailers to destination trailers. The FSP is modeled as a Rural Postman Problem (RPP) and three algorithms are compared: trailer-at-atime, nearest neighbor, and balance-and-connect. Using five industrial data sets, the results demonstrate the effectiveness, advantages, and disadvantages …


Distribution Planning Considering Warehousing Decisions, Pratik J. Parikh, Xinhui Zhang, Bhanuteja Sainathuni Sep 2010

Distribution Planning Considering Warehousing Decisions, Pratik J. Parikh, Xinhui Zhang, Bhanuteja Sainathuni

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Modern supply chains heavily depend on warehouses for rapidly fulfilling customer demands through retail, web-based, and catalogue channels. The traditional approach that considers warehouses as cost-centers has affected the profitability of numerous supply chains. A lack of synchronization between procurement and allocation decisions causes warehouses to scramble for resources during peak times and be faced with under-utilized resources during drought times. Warehouses, however, have emerged as service-centers and it is imperative that warehousing decisions be an integral part of supply chain decisions. In this paper we propose a mixed-integer programming model to integrate warehousing decisions with those of inventory and …


Blocking Effects On Performance Of Warehouse Systems With Automonous Vehicles, Ananth Krishnamurthy, Sunderesh Heragu, Charles Malmborg Sep 2010

Blocking Effects On Performance Of Warehouse Systems With Automonous Vehicles, Ananth Krishnamurthy, Sunderesh Heragu, Charles Malmborg

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Distribution centers are under increasing pressure to adopt material handling systems that offer greater flexibility to improve cycle time and throughput capacity in the transfer of unit loads in their high density storage areas. Autonomous Vehicles-based Storage and Retrieval Systems (AVS/RS), have been shown to hold significant promise in this context. In these systems, loads are transferred by autonomous vehicles. Vehicles support horizontal load movement along aisles and cross-aisles within a tier, and lifts support vertical movement between tiers. Existing research in AVS/RS, do not explicitly account for the potential blocking of vehicles and lifts while they are processing transactions. …


Designing Automated Warehouses By Minimising Investment Cost Using Genetic Algorithms, Tone Lerher, Iztok Potrc, Matjaz Sraml Sep 2010

Designing Automated Warehouses By Minimising Investment Cost Using Genetic Algorithms, Tone Lerher, Iztok Potrc, Matjaz Sraml

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

The successful performance of the automated storage and retrieval systems is dependent upon the appropriate design and optimization process. In the present work a comprehensive model of designing automated storage and retrieval system for the single- and multi-aisle systems is presented. Because of the required conditions that the automated storage and retrieval systems should be technically highly efficient and that it should be designed on reasonable expenses, the objective function represents minimum total cost. The objective function combines elements of layout, time-dependent part, the initial investment and the operational costs. Due to the nonlinear, multi-variable and discrete shape of the …


Towards A Physical Internet: The Impact On Logistics Facilities And Material Handling Systems Design And Innovation, Benoit Montreuil, Russell D. Meller, Eric Ballot Sep 2010

Towards A Physical Internet: The Impact On Logistics Facilities And Material Handling Systems Design And Innovation, Benoit Montreuil, Russell D. Meller, Eric Ballot

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Aiming for a radical sustainability improvement, the Physical Internet has the potential of revolutionizing the fields of material handling, logistics, transportation and facilities design. It exploits the enabling concept of standardized, modular and smart containers as well as the universal interconnectivity of logistics networks and services. Its underlying paradigm shift creates a tremendous breakthrough innovation opportunity for the material handling and facility logistics community in terms of equipment, systems and facility design and operation. This paper provides a primer overview of a key subset of the physical elements serving as the foundation of the Physical Internet infrastructure, classified in three …


Plug-And-Work Material Handling Systems, Kai Furmans, Frank Schonung, Kevin R. Gue Jan 2010

Plug-And-Work Material Handling Systems, Kai Furmans, Frank Schonung, Kevin R. Gue

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

One disadvantage of automated material handling systems is their relative Inflexibility: once racks are installed and conveyors are laid, making even mi-nor changes to a system can be cumbersome and expensive. However, recent progress in the capabilities and cost of basic system components, such as controllers, drives, and sensors, has made possible a new class of material handling systems having a much higher degree of flexibility. We propose underlying de- sign principles for such systems and describe several prototype plug-and-work" systems, which feature decentralized control and ease of reconfiguration.


Optimizing The Rearrangement Process In A Dedicated Warehouse, Hector J. Carlo, German E. Giraldo Jan 2010

Optimizing The Rearrangement Process In A Dedicated Warehouse, Hector J. Carlo, German E. Giraldo

11th IMHRC Proceedings (Milwaukee, Wisconsin. USA – 2010)

Determining the optimal storage assignment for products in a dedicated warehouse has been addressed extensively in the Facility Logistics literature. However, the process of implementing a particular storage assignment given the current location of products has not received much attention in the existing literature. Typically, warehouses use downtime or overtime to remove products from their current location and move them to the suggested location. This work presents the Rearrange-While-Working (RWW) policy to optimize the process of rearranging a dedicated warehouse. The RWW policy seeks to relocate products in a warehouse from the initial arrangement to the optimal arrangement while serving …