Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics

Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics Sadia Quader, Krystel K. Castillo-Villar n Department of Mechanical Engineering, University of Texas at San Antonio, 78249, United States

ar t ic l e i nf o

a b s t r a c t

Article history: Received 21 April 2015 Received in revised form 17 December 2015 Accepted 29 December 2015

Order-picking is the activity to retrieve items from the shelves to fulfill customers' orders. Order-picking is one of the most costly operations in warehousing accounting for 50–75% of total operating costs. This paper presents a novel model that is motivated by the normative order-picking algorithm known as “bucket brigades” to address multiple aisles in warehouses where workers have finite walk-back velocities and are allowed to pass successors. In order-picking operations, the majority of the previous research works have applied bucket brigades over a single-line (serial) system. The contributions of this research work are as follows. (1) A summary of an updated literature review of bucket brigades using a state-of-the-art-matrix. (2) A novel multi-aisle order picking model motivated by the normative singleaisle bucket brigade, which represents a more comprehensive and realistic scenario in order fulfillment warehouses. (3) A comparison between the single-line and multi-aisle models in order to analyze the difference in performance in terms of average system utilization, order cycle time and throughput. (4) A sensitivity analysis of different parameters and scenarios in order to identify the best routing heuristic, storage assignment and order type that maximizes utilization, minimizes cycle time and maximizes throughput in multi-aisle order picking systems. The results of the simulation studies are reported and analyzed. The proposed model is flexible and easily scalable to include other real-life warehousing considerations. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Warehousing Order-picking Bucket brigades Self-balancing Dynamic behavior Simulation

1. Introduction Order-picking refers to the operations where items are retrieved from shelves to fulfill customer orders. It accounts for 50– 75% of total operating costs of a warehouse [1]. Thus, maximizing the throughput of an order picking system has the effect of relieving some of the operating costs. Bucket brigades is a viable solution as it yields a high throughput and has been implemented in a multitude of functions particularly in order-picking and assembly operations. Bucket brigades have effectively emerged into a functional management model with several applications in industry since the first time the concept was introduced by Bartholdi et al. [2]. The simplicity of this model, its self-balancing nature and independence from managerial supervision serves to its practicality and makes it a desirable option to use in manufacturing, warehousing, and assembly operations. Since the normative bucket brigades model was introduced; it has been predominantly represented as a single line. A few papers modified the normative n

Corresponding author. E-mail address: [email protected] (K.K. Castillo-Villar).

bucket brigades model and presented hybrid forms of bucket brigades suitable for practical industrial applications [3–6]. However, there is a need for scholarly research of order-picking bucket brigade systems in a multi-aisle warehouse, which is a more representative scenario in real life operations. Potential limitations of the normative bucket brigade system are blocking and the assumption of negligible walk-back time. Blocking tends to increase the average cycle time and the infinite walk-back velocity is an assumption that may skew the estimation of cycle time for large warehouses. This paper presents a multiaisle order-picking model inspired by the normative single-aisle bucket brigade. This novel multi-aisle model overcomes these limitations by allowing passing and considering finite walk-back velocity. The proposed model allows modeling real-life scenarios in warehouses. For a fair comparison, the single-line model (used as a benchmark) has the same considerations. Additionally, the multi-aisle model extends the backward rule of the normative model so that workers do not have to maintain their relative positions when looking for more work. This extended rule is expected to result in reduced average cycle time, increased average system utilization and increased average throughput. After testing the performance of the multi-aisle order-picking model against the single-line model in terms of average system

http://dx.doi.org/10.1016/j.rcim.2015.12.009 0736-5845/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

S. Quader, K.K. Castillo-Villar / Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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utilization, cycle time and throughput in phase I; we will study how management's storage assignment and routing heuristics affect the average system utilization, cycle time and throughput of a multi-aisle order picking system in an order fulfillment warehouse in phase II. To the best of our knowledge, the impact of storage and routing policies on the performance of a multiple-aisle order picking system has not been studied. This paper is organized as follows: Section 2 summarizes the related literature and presents a state-of-the-art-matrix which highlights all the literature related to bucket brigades. Section 3 discusses the single-aisle and multi-aisle model rules and assumptions. Section 4 explains the methodology which is divided into two phases: (1) comparison of the single-line versus multiaisle models and (2) sensitivity analysis of the multi-aisle model. Section 5 examines the simulation results and presents an optimization technique based on Pareto efficiency condition to find the non-dominated solutions. Finally, Section 6 presents concluding remarks, managerial implications and future research directions.

2. Literature review The idea of bucket brigades was inspired by the Toyota Sewn Production Management System (also known as TSS) production lines in the 1970s, registered mark of Aisin Seiki Co. Ltd. (www. aisin.com) [7–9] where the workers were sequenced from slowest to fastest, and were independent of where they exactly began [2].

Bartholdi and Eisenstein [7] discussed the idea of bucket brigades in detail, how the deterministic model works, and the dynamics of the workers. It was found that when the workers are arranged from slowest to fastest according to their work velocities, the hand-off points between two consecutive workers converge to a fixed point [7]. This is the self-balancing feature of bucket brigades. There have been several papers that have discussed bucket brigades under various scenarios and applications. Bratcu and Dolgui [10] present a literature review with descriptions on the different mathematical modeling assumptions made in research and discuss several real-life applications. Quader and Castillo-Villar [11] present an updated literature review in the form of a stateof-the-art matrix which shows the different categories that bucket brigades can be split into as shown in Fig. 1. The matrix has been split into four main categories. The basic model category corresponds to introductory papers which discuss the normative model and the dynamics of it. The extensions of bucket brigades category consists of different dynamics and scenarios the normative bucket brigades model can be applied to. The hybrid models of bucket brigade category includes bucket brigades models which have been modified and enhanced using concepts from other types of models. Finally, applications category consists of papers that discuss real-life applications of bucket brigades. One area of interest is the behavior of bucket brigades in a stochastic setup. Bartholdi et al. [12] have discussed the concept of stochastic work content and found using simulation that with an increase in the number of discrete stations, the stochastic model behaves very similar to the deterministic one.

Fig. 1. State-of-the-art matrix [11].

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

S. Quader, K.K. Castillo-Villar / Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

One important area of bucket brigades is allowing workers to pass. The idea of passing was introduced as a solution to blocking where workers are allowed to pass the successor if they are faster. Hirotani et al. [13] presented the idea of passing and the concept that certain initial positions of workers with passing can lead to a shorter processing cycle time. Armbruster and Gel [14] also studied the idea of passing and blocking in a two-worker model in detail, studying the dynamics and throughput. In addition, they examined stochastic situations where workers were faster on one part of the line but slower in other parts and presented a new rule which allows the workers to converge to a fixed point. Another recent area of bucket brigades is considering the walkback velocity of the workers to be finite. Bratcu and Dolgui [15] studied this area and conducted experiments on continuous time simulations, which suggested that there is a difference in the patterns between a model with finite walk-back velocity and the original model where walk-back velocity is infinite. Bratcu and Dolgui's [15] results indicated the importance of considering finite walk-back velocity. There have been several simulation studies in previous works. Simulation was used to study the in-depth dynamics of 2–3 worker models [16]. Bartholdi et al. [12] also used simulation to compare stochastic work content to deterministic work content. In addition, Bratcu and Dolgui [15] have used Simulinks to analyze bucket brigades under finite walk-back velocity scenarios. Parthasarathi [17] conducted bucket brigades simulations in ARENAs and assessed work content variability and worker assignment patterns. Munoz and Villalobos [18] have conducted simulation studies in ProModels to analyze worker learning behavior and turnover rates in assembly lines. They modeled a three-station serial assembly line and a six-station serial assembly line. Bucket brigades’ performance was better than traditional assembly lines for both assembly lines.

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been discussed in detail in Section 4.2. The following are the definitions used for all models:


Orders: Orders are the entities in the system. An order consists





of a list of particular items which need to be picked from specific locations. Workers/order pickers: Workers are the resources in the models. In phase II, models consist of only one depot. Phase I consists of 2 depots to provide a fair comparison between the single-line and multi-aisle models. Order arrival depot: Order arrival depot is the location where the orders arrive into the system. Ship depot: Ship depot is the location where the order is placed upon completion. For phase I, the order arrival depot and ship depot are separate for the purpose of observing the differences of how the dynamics of workers vary in a single-line from a multi-aisle model and performing a fair comparison of both models.


Aisle: Aisles are the spaces which enable workers to move in a




bi-directional path and provide the workers access to the stations in shelves as can be seen on Fig. 2. The single-line model consists of a single aisle (Fig. 3). Pick-location: Represents the stations where items for an order need to be picked.


Work content: It is the amount of work done or items picked along the line. For the single-line and multi-aisle model, the work content is a discrete value, that is, it is defined by the number of items picked and is not uniform along the line as shown in Fig. 4.


Pick time: It is the time taken for the workers to pick a single item from a station.

3. Description of the models 3.2. Assumptions of the models This section focuses on the definitions, the assumptions and rules of the proposed multi-aisle simulation model for both phase I and II, as well as of the single-line model used as a benchmark in phase I. 3.1. Definitions Figs. 2 and 3 illustrates the multi-aisle model and single-line simulation models used in phase I, respectively. The basic definitions of phase II models, which focus solely on the multi-aisle models, are similar to the multi-aisle model definitions discussed in this section. Alterations to the model in Fig. 2 for phase II have

The single-line and the multi-aisle order-picking models have the following assumptions in phases 1 and 2: 1) There are 3 workers in every model sequenced from slowest to fastest. 2) The work content is not continuous along the line; the line will be split into forty discrete stations. Furthermore, each item picked will have a work content of 1. 3) The walk-back velocity of the workers is finite. 4) The workers will be sequenced from slowest to fastest but if required, the slower worker will be able to pass a faster worker

Fig. 2. Multi-aisle model.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Fig. 3. Single-line model.

and not be blocked. 3.3. Model rules 3.3.1. Single-line model The single-line order-picking model (only used for comparison purposes in phase I) follows the same rules as the normative bucket brigade model with one exception. According to the normative model, the forward rule specifies that worker i will work forward with the order in hand until his/her idle successor (worker iþ1) walks back to him/her and takes over his/her work and moves forward. At this point, worker i goes back to his/her predecessor to get more work. This is the backward rule. If (s)he is the last worker, then (s)he places the compiled order on the shipping dock and goes back to his/her predecessor to take over his/her work. The backward rule for the single-line model remains the same but the forward rule has exceptions. The modified forward rule is that if a successor is busy with an order at hand, workers are allowed to pass and move forward. Once the passing worker is done with his/her work, the sequence resets to the original. Priority of taking over work is always worker3 4 worker24 worker 1. This means if worker 2 passes worker 3 and completes an order, worker 2 will go back and take over worker 1's order. Even if worker 3 may be closer to the idle worker 2, worker 3 is more efficient and will complete an order in less time and with higher overall throughput. Similarly, if worker 1 passes worker 2 or worker 3 or both, worker 1 will start a new order instead of taking over worker 2 and worker 3's orders. 3.3.2. Multi-aisle order-picking system The multi-aisle model for phases 1 and 2 follows the modified forward rule as in the single-line model but extensions in the backward rule were needed because the aisles, unlike the serial line, present shortcuts. The modified backward rule will account for the three possible scenarios after the items are shipped: 1) If worker 3 finishes an order, (s)he would take over either worker 2 or worker 1's order depending on whoever came first. This rule is significantly different from the normative model and

aims to help in reducing average cycle time, increasing system utilization and throughput as indicated in Section 5.1. 2) If worker 2 finishes an order, (s)he would inspect every aisle to look for worker 1. It is inefficient for worker 2 to take over worker 3's order since that would increase the time the order spent in the system. 3) If worker 1 finishes an order, (s)he would start a new order. For the modified backward rules 1 and 2, when workers 2 or 3 are looking for work they are able to find their predecessor's location. The simulation is built to search for a particular busy predecessor when one resource becomes idle. In doing so, the simulation is set to find the shortest route to that busy resource. For instance, if worker 2 becomes available then worker 2 goes back to the busy worker 1 and the rules allow it to use the shortest (and less time consuming) route back.

4. Methodology The main objective of this research work is two-fold: (1) compare single-line and multi-aisle order-picking systems in terms of average system utilization, cycle time and throughput, and (2) find combination(s) of design parameters that improves the performance of a multi-aisle bucket brigades system according to different performance metrics. The analytical approaches are limited since the natural dynamics of real-life scenarios cannot be included and the models tend to have unrealistic assumptions. A simulation approach overcomes this limitation and it was the preferred approach. Thus, a discrete-event simulation model for the single-line and multi-aisle systems is developed. The experimental design is divided into two phases: the first phase aims to analyze whether there is a significant difference between a singleline model and a multi-aisle model; and the second phase consists of a sensitivity analysis to analyze the performance of the multiaisle model under storage assignments, order types and routing strategies. The performance metrics considered in this study are: average system utilization, cycle time and throughput. Average system utilization refers to how much time the workers as a team spent

Fig. 4. Illustration of work content.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

S. Quader, K.K. Castillo-Villar / Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 1 Designed factorial experiment. Factors Factor type

Levels Level description

A

2

B

C

Type of bucket brigades Order type

Different walk speed

3

3

Single-line model Multi-aisle model Order A pick: 3,6,9,12,15,18,21,24,27, 30,33,36 Order B pick: 1,2,3,4,5,7,8,9,10,20,30,40 Order C pick:1,11,21,31,32,33,34,35,37,38, 39, 40 110 fpm 150 fpm 190 fpm

on picking items for their orders and walking with the orders at hand (i.e., whenever the workers had an order at hand it was considered as value added time). This metric is important from a management point of view to ensure workers are being productive as a team. The second metric is average cycle time for an order at each run. The average cycle time for each scenario is represented from the time a worker starts an order until the time a worker drops it off at the ship location. Cycle time is important from a customer point of view because a shorter average cycle time will enable goods to reach customers on time. Besides being output performance metric, the cycle time is also an important measure of chaotic behavior. As Bartholdi et al. [19,20] have presented, it is desirable to have a system with a steady cycle time because an unsteady cycle time would indicate variability in the system which could lead to erratic behavior. The third metric is the average throughput of the system which represents how many orders will be completed at the end of the eight hour work day. This performance metric can help management determine the efficiency of the model. 4.1. Phase I: Comparison of the single-line versus multi-aisle orderpicking system The statistical factorial design of experiment (DOE) is shown in Table 1. The factor levels are deterministic in order to assess the differences between a single-line and multi-aisle model without any randomness and this design served as the factor-screening phase of the study. The DOE has eighteen runs and each run considers eight hours representing a work day. A warm-up period of 100 minutes was allowed for the system to reach stability.

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Several parameters in the simulation were fixed. There were three workers in every run, the layout for the single-line and the multi-aisle models followed the same dimensions where a station was 4 feet apart. For multi-aisle runs, the aisles were 10 feet wide. Fig. 5 shows the dimensions taken in the multi-aisle model. In the simulation model, the networks were built with consideration of the width and length of the stations. Therefore, during a simulation run, any additional time that is taken as a result of additional distance traveled is reflected in the models. Also, in the multi-aisle model, there were 8 shelves and each shelf had 5 stations as shown in Fig. 2. Based on a case study of a manufacturing facility [21], order sizes range 5 lines per order to 25 lines per order. For each run in this DOE, an order size of 12 lines was assumed which would represent 12 different stations for the order pickers to pick. In the multi-aisle model, the workers will follow a traversal or S-shape route, as shown in Fig. 6, which is the traditional approach in warehouses [21]. However, while walking back, the workers choose the shortest route back. In the single-line model, the workers walking forward and backward follow a straight line. Factor A represents the type of bucket brigades model, that is, the single-line and proposed multi-aisle model. Factor B is the order type which was influenced by the type of storage assignment. The first level of the order type (Order A) is evenly spaced out in the warehouse. The second level of order type (Order B) represents items picked nearer to the order arrival location since a common practice is to place popular items near order arrival location [21,22]. This storage assignment is called front-loaded. Order C has the same idea as order B except it represents items picked from closer to the ship location. It is assumed that the popular items are shelved closer to the ship location than order arrival; the assignment is called end-loaded. Both of these storage assignments are also called within-aisle storage as the most popular items are placed on the aisles near the order arrival or ship location [23]. Pick numbers for the multi-aisle model are shown in Fig. 7 which represent the sequence that workers will follow in picking items as they walk forward and is similar to the sequence of a single-line model. Factor B in Table 1 describes the pick numbers for each level where items are to be picked. For orders B and C, the pick locations were determined by the Pareto principle. According to Petersen et al. [24], twenty percent of the items in the warehouse account for eighty percent of picking. Therefore, nine items are placed among ten stations located at the beginning or at the end (Order B/Order C) and three items were evenly distributed amongst the remaining thirty stations.

Fig. 5. Dimensions of the multi-aisle model.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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S. Quader, K.K. Castillo-Villar / Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 6. Traversal routing for multi-aisle model.

The reason for introducing this factor was to analyze whether storage assignments has an effect on worker utilization and order cycle time. Factor C pertained to the pick-time to walk-time ratio. The picktime is the time taken by an order picker to pick an item off a single station. The walk-time is the time to walk across a station and is calculated by the distance of the station (4 feet in this case) over the walk-speed of the individual worker [25,26]. Once the walk time is calculated, the pick time can be calculated by using the ratio. For example, a ratio of 3:1 represents that it takes the worker three times longer to pick an item than walk across a station. For Factor C, each level is represented by a different walk speed. However, the ratio for the three workers remains constant for all three levels. According to Gue et al. [25], based on real life cases, the ratio never exceeded 20:1. Table 2 represents the calculated pick time based on the pick to walk ratios and the walk speeds. 4.2. Phase II: Sensitivity analysis for the multi-aisle model The execution of phase II depends on the findings from phase I. If the first DOE shows that the multi-aisle order-picking system was statistically different from the single-line system, a comprehensive analysis of the multi-aisle model will be conducted. The designed experiment for phase II is presented in Table 3. In this experimental design, the run parameters are eight hours representing a work day with 100 minutes for warm-up as in phase I. The number of workers is fixed to three who have pick times as shown in Table 2 when the walk speed is 150 fpm (0.53, 0.32 and 0.13). The layout for the experiment is much larger than the one presented in phase I as this experiment aims to study the multiaisle model in detail. The multi-aisle system has 10 shelves where each shelf has 20 stations (i.e., 200 stations) as it is depicted in

Table 2 Pick-times for different walk-speed levels. Pick to walk ratio

20:1 12:1 5:1

Workers

Worker 1 Worker 2 Worker 3

Walk speed levels 110 (min)

150 (min)

190 (min)

0.73 0.44 0.18

0.53 0.32 0.13

0.42 0.25 0.11

Table 3 Design of experiment for multi-aisle model. Factors

Factor type

Levels

Level description

A

Storage assignment

2

B

Type of order

2

C

Routing strategy

4

Within-aisle storage Across-aisle storage Fixed order Random orders Traversal or S-shaped Return Mid-point Largest gap

Fig. 8. In the design for phase I, the order arrival depot and the ship depot were located at the beginning and end of the warehouse; this was done to fairly compare the multi-aisle model to the single-line model. In phase II, there is only one depot, that is, the order arrival and ship depots are located at the same place as illustrated in Fig. 8. Class-based storage assignment is when items are ranked in classes of A, B and C based on popularity where A are the most popular items [23]. In warehouses, there are unlimited possibilities of placing the different classes A, B, C to generate a productive assignment.

Fig. 7. Pick numbers sequence.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Fig. 8. Multi-aisle system with a within-aisle storage.

Factor A (storage assignment) aims to further investigate classbased storage assignment since Factor B from phase I was found to be significant in terms of average system utilization, cycle time and throughput (refer to 5.1). In phase I, for Factor B, two classbased storage assignments were explored: front-loaded and endloaded, both of which correspond to within-aisle storage type. Fig. 9 shows within-aisle storage assignment (Level 1 in factor A). Jarvis and McDowell [27] proposed that each aisle represent one class and the more popular classed aisle should be closer to the depot. Fig. 8 shows an example of how an order is arranged in a within-aisle setup. Another class-based storage is an across-aisle assignment (Level 2 in factor A) where every aisle has all three classes but class A is closer to the depot than the rest as depicted in Fig. 10 [23]. It is expected to see a difference in the two classbased storages and it is of interest to determine from the computational experiments which storage assignment works best for multi-aisle bucket brigades. The pick-numbers for the different storage assignments are shown in Table 4.

Factor B aims to determine if operating with a fixed order is different from operating with random orders arriving into the system in terms of average system utilization, cycle time and throughput. For the random orders, there are five different orders (see Table 4) for each level of Factor A (storage assignment) which arrive randomly following a uniform distribution. When the orders arrive randomly, it is expected to observe random dynamics between the workers where sometimes workers may pass their predecessors and successors (using the extended rules for multi-aisle bucket brigades) due to the difference in the type of order. For the fixed order level, only one order is created as shown in Table 4. Factor C aims to analyze different routing heuristics and determine which routing strategy works best for multi-aisle bucket brigades. In warehouses, one of the objectives of routing strategy is to find the shortest and efficient route for order pickers. In literature, there have been several heuristics proposed [24,23]. Fig. 11 shows examples of the four common routing heuristics which each serves as a level for Factor C.

Fig. 9. Within-aisle storage assignment.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Fig. 10. Across-aisle storage assignment.

The first routing strategy is traversal routing (Fig. 11a), which represents when the workers walk forward in an S-shaped routing. The second level of routing heuristic is return strategy in which workers enter and leave the aisle from the same end as shown in the Fig. 11b. Fig. 11c shows mid-point strategy in which the warehouse is divided into half, where the workers first travel to back aisle and pick items and then to the front aisle. The fourth level represents the largest gap strategy which is an extension to the mid-point strategy (Fig. 11d). Like the mid-point, the back aisle is accessed in the beginning and the worker picks items but the worker can pick an item from the other half if the gap between the two items is lesser than when accessing from the front aisle. It is important to note that in phase II (Figs. 9–11) there is only one depot, unlike in phase I (Figs. 2 and 3) where the objective was to fairly compare the single-line and multi-aisle order-picking. Phase II aims to observe the designs multi-aisle models can be applied to. As considered in earlier works, only one depot exists in this phase [24,23,27].

5. Results and discussion 5.1. Results from phase I 5.1.1. Analysis for average system utilization The Analysis of Variance (ANOVA) in Table 5 shows that factor C

which is walk speed is not significant at a confidence level of 5% for the average system utilization. ANOVA indicates that whether workers have an overall lower pick times or whether they have a higher pick times, the average system utilization is unaffected. The main effects plot for A as shown in Fig. 12, suggests that the multi-aisle order-picking system, on average, has significantly higher average system utilization than the single-line model. According to the results in Table 5, factor B, which is the type of order is also significant on average system utilization. Based on Fig. 12, there is a difference in average system utilization when the items are placed differently on the layout. The front-loaded setup keeps workers busier than the end-loaded setup where workers have the least system utilization on average. On closer observation, Fig. 13 shows the system utilization for the single-line and multi-aisle models in the 9 different runs from the DOE in phase I. On average, the utilization of the multi-aisle system outperformed the single-line system in 8%. The combination that increases the system utilization is the multi-aisles layout with front-loaded type of order. The reasoning for the difference is because in single-line models, the walk-back distance is considerably greater than in multi-aisle systems, where shortcuts when walking back are possible. This greater walk-back distance contributed to a higher percentage of time spent walking back and, consequently, a lower overall system utilization. The individual worker utilization was also inspected at each run (Fig. 14) to visualize variability among workers. The individual

Table 4 Pick numbers for combinations of Factor A and B. Type of order (Factor B)

Storage assignment (Factor A)

No. of items

Pick numbers

Fixed order Fixed order Random order

Within-aisle Across-aisle Within-aisle

Random order

Across-aisle

15 15 15 18 12 6 18 15 18 12 6 18

1 3 4 7 9 11 14 17 18 33 42 49 64 173 200 1 5 58 59 61 64 73 87 137 139 142 143 158 173 200 Order A 1 3 4 7 9 11 14 17 18 42 64 69 130 173 197 Order B 1 3 5 6 7 11 12 14 15 17 22 36 45 113 122 146 161 185 Order C 1 2 7 10 12 16 40 50 55 116 121 174 Order D 3 8 12 19 44 118 Order E 2 3 4 5 9 10 13 15 16 18 19 20 33 44 81 100 112 191 Order A 1 39 55 57 58 60 64 87 105 137 138 141 142 155 162 Order B 1 2 16 40 56 57 58 61 63 64 70 82 138 142 143 146 161 185 Order C 1 4 18 59 62 90 93 136 140 143 144 196 Order D 57 133 139 143 175 200 Order E 2 45 57 59 60 63 100 112 133 137 140 141 142 144 147 191 199 200

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

S. Quader, K.K. Castillo-Villar / Robotics and Computer-Integrated Manufacturing ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Fig. 11. Routing heuristics.

Table 5 Analysis of Variance (ANOVA) for average system utilization for phase I. Factors

DF

Seq SS

Adj SS

Adj MS

F

P

A: type of model B: type of order C: walk speed A*B A*C B*C Error Total

1 2 2 2 2 4 4 17

291.21 13.24 0.49 1.10 0.32 1.15 1.35 308.86

291.21 13.24 0.49 1.10 0.32 1.15 1.35

291.21 6.62 0.25 0.55 0.16 0.29 0.34

863.55 19.63 0.73 1.63 0.48 0.85

0.00 0.01 0.54 0.30 0.65 0.56

worker utilization is an important indicator for managers who would like to know which worker is spending more time in walking-back. The first nine runs correspond to single-line models and the last nine correspond to the multi-aisle layout. The first three runs represent an evenly spaced layout, runs 4–6 represent front-loaded layout and the runs 7–9 represent end-loaded layout. As it can be observed in Fig. 14, there is a big variation in worker 1 and worker 3's utilization in the front-loaded layout. For the runs 4–6, worker 3 spends more time walking back than worker 1 who is closer to the order arrival and constantly has an order at hand. In runs 7–9, there is not much difference between the utilizations of the three workers since over the span of the simulation, on average, the three workers walked forward over equal distances and walked back over equal distances causing their individual utilizations to be close. Workers in the multi-aisle system (runs 10–18)

have, on average, lower differences in individual utilization when compared to the single-line system. This behavior can be caused by the shortcuts present in the multi-aisle system and passing rules which reduce the difference between individual utilization. 5.1.2. Analysis for average cycle time The factorial designed experiment of phase I was also analyzed using average cycle time as a response. Table 6 shows that factors A, B and C are all significant. From the main effects plot (Fig. 15), it can be seen that single-line models orders have a higher average cycle time (5.8 min) than a multi-aisle system (5.3 min). In multiaisle systems, workers can walk-back through shortcuts and this takes less time whereas in single-line system, it takes longer since workers have to walk-back the entire path. From Fig. 15, it can be seen that factor B, an end-loaded setup, yields a smaller average cycle time. This indicates that worker 3 picks more items than worker 1 and hence the average cycle time is lower. It is noteworthy that even though a front-loaded setup (level 2) has high average system utilization as suggested by Fig. 12, orders at this level have a high average cycle time. For factor C, workers walking at 190 fpm had the least cycle time. This is expected as workers walked at a quicker speed and had the lowest pick times. A concern for not reaching convergence is an unstable cycle time [7]. In Bartholdi et al. [7] showed how when workers were not arranged from slowest to fastest, blocking occurred causing the cycle time to become greater while when arranged from

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Fig. 12. Main effect plot for average system utilization.

slowest to fastest, the cycle time eventually converged. In phase I, where workers are allowed to pass and finite walk-back velocity is considered, it was seen that cycle time was stable for both models (all the 18 runs). Fig. 16 shows the dynamic cycle time plot of one of the runs. It can be observed from the plots that the cycle time becomes steady over time; thus, it can be inferred that cycle time does not fluctuate and is not erratic for the proposed models (single-line and multi-aisle models). 5.1.3. Analysis for average throughput Phase I's factorial design was also solved for average throughput as shown in Table 7. It was found that factor A, B and C were all significant. From the main effects plot (Fig. 17), it can be noted that multi-aisle models have a higher average throughput than singleline models because of the shortcuts present in multi-aisle models. The end-loaded setup performs well in terms of average throughput which implies that worker 3 picks more items than worker 1. For factor C, a higher throughput was achieved when the walk-speed was greater. The main effects plot for throughput (Fig. 17) is the opposite of the main effects plot for average cycle time (Fig. 15). This indicates an inverse relationship between throughput and average cycle

time may exist, that is, as the number of orders completed increases the cycle time decreases. If the average cycle time is higher, the average throughput is lower.

5.2. Results from phase II 5.2.1. Analysis of average system utilization From Table 8, it can be concluded that Factor A is statistically significant with 5% confidence level (p-value o0.05). In addition, Factor C is significant with 10% confidence level. It was found that whether the order was fixed or random, the impact on the average system utilization is negligible. This indicates that the dynamics of the workers is independent of the type of orders in the system whether fixed or random. The main effect plot displayed in Fig. 18 indicates that when the storage assignment is different (within-aisle or across-aisle), the workers’ utilization varies. Fig. 18 shows how the within-aisle assignment has higher average system utilization than the acrossaisle storage. This is because the walk-back is larger in the acrossaisle storage assignment causing workers to be less occupied than in the within-aisle assignment.

Fig. 13. Comparison of average system utilization of single-line and multi-aisle models.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Fig. 14. Individual worker utilizations for first DOE. Table 6 Analysis of variance for average cycle time for phase I. Factors

DF

Seq SS

Adj SS

Adj MS

F

P

A: type of model B: type of order C: walk speed A*B A*C B*C Error Total

1 2 2 2 2 4 4 17

0.85 1.87 23.02 0.11 0.16 0.14 0.09 26.23

0.85 1.87 23.02 0.11 0.16 0.14 0.09

0.85 0.93 11.51 0.06 0.08 0.04 0.02

39.72 43.70 538.43 2.58 3.64 1.64

0.00 0.00 0.00 0.19 0.13 0.32

For Factor C, it can be concluded that the return-strategy has the highest average system utilization indicating that the workers stay productive and do not walk-back as much as in other routing strategies. Mid-point and largest gap have the lowest average utilization indicating the workers spend more time in walking back than traversal and return strategies. Fig. 19 shows the combinations of parameters. It can be noted that, overall, the within-aisle storage is a better option than across-aisle storage for all the routing strategies since average

system utilization is greater than 90%. It can be concluded that the within-aisle storage with return strategy provides the highest overall average system utilization (with fixed Orders: 93.5%, and with random Orders: 93.1%). The difference in utilization between the worst design and the best design is 11.2%. Fig. 20 shows the individual average worker utilization per run. Odd numbered runs are for across aisle storage and even numbered aisles are for within-aisle layout. The within-aisle layout maximizes the average system utilization and also presents less variability on individual worker utilization, on average. 5.2.2. Analysis of average cycle time Table 9 shows how all three factors and interaction A*B are significant (their p-values are less or equal than 0.05). From the main effect plot (Fig. 21), it can be observed that orders in acrossaisle have a smaller cycle time than within aisle. The plot also shows that random orders have a smaller average cycle time than fixed orders. This can be attributed to the fact that, in random orders, some of the orders have a work content of 6 or 12 items which is less than the work content in the fixed order which has 15 items. For Factor C, the largest gap routing exhibits the lowest average cycle time (8.37 min), on average; followed by the mid-

Fig. 15. Main effects plot for average cycle time.

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Fig. 16. Cycle time for multi-aisle, front loaded layout with walk speed ¼ 190 fpm. Table 7 Analysis of variance for average throughput for phase I.

Table 8 Analysis of variance for system utilization for phase II.

Factors

DF

Seq SS

Adj SS

Adj MS

F

P

Factors

DF

Seq SS

Adj SS

Adj MS

F

P

A: type of model B: type of order C: walk speed A*B A*C B*C Error Total

1 2 2 2 2 4 4 17

78.65 9.28 834.45 0.23 2.07 1.67 1.35 926.72

78.65 9.28 834.45 0.23 2.07 1.67 1.35

78.65 4.64 417.23 0.11 1.03 0.42 0.34

844.69 49.82 4481.11 1.22 11.1 4.49

0.00 0.00 0.00 0.39 0.02 0.08

A:Storage assignment B:Type of order C: Routing strategy A*B A*C B*C Error Total

1 1 3 1 3 3 3 15

49.00 0.36 56.50 0.06 22.51 8.23 7.74 144.40

49.00 0.36 56.50 0.06 22.51 8.23 7.74

49.00 0.36 18.83 0.06 7.50 2.74 2.58

18.99 0.14 7.30 0.02 2.91 1.06

0.02 0.73 0.07 0.89 0.20 0.48

point heuristic route. Contrary, the traversal and return heuristics yield a cycle time above the mean. The interaction plot (Fig. 22) suggests that the interaction between A and B has a significant effect on average cycle time and it can be observed that for the within-aisle storage, the average cycle time is not very different when the order is fixed or random (the slope is smaller). For the across-aisle storage, there is a larger variation in average cycle time for a fixed order compared to random orders. This could imply that adding more variation in order types in the across-aisle storage significantly reduces the average cycle time.

Fig. 23 shows that there are two combinations of parameters which yield the lowest average cycle time, both of which are across-aisle storage and have random orders (cycle time ¼7.81 min). One follows mid-point routing strategy and the other follows the largest-gap strategy. One observation that can be made is that the within-aisle storage for all routing strategies leads to a higher cycle time. Both largest gap and midpoint strategy benefitted the most from the storage assignment as it is favorable for the workers and reduced their walk time. The traversal routing was affected the most as the workers had to go through every aisle and every station in an

Fig. 17. Main effects plot for average throughput.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Fig. 18. Main effect plot for average system utilization.

Fig. 19. Comparison of average system utilization for fixed and random orders.

Fig. 20. Individual average worker utilization for phase II.

S-shape manner causing the cycle time to be high. The reason the across-aisle is successful is because of its spreading out of the popular items over multiple aisles which favors hand-offs of

orders by presenting shortcuts to the workers. The within-aisle assignment is where popular items are only in the first aisle where successors would have to walk back longer distances to get to their

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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Table 9 Analysis of variance for average cycle time for phase II. Factors

DF

Seq SS

Adj SS

Adj MS

F

P

A: Storage assignment B: Type of order C: Routing strategy A*B A*C B*C Error Total

1 1 3 1 3 3 3 15

0.96 0.73 4.11 0.22 0.08 0.00 0.07 6.17

0.96 0.73 4.11 0.22 0.08 0.00 0.07

0.96 0.73 1.37 0.22 0.03 0.00 0.02

44.11 33.57 62.97 9.93 1.18 0.04

0.01 0.01 0.00 0.05 0.45 0.99

predecessors. For instance, in the across-aisle setup, when a successor wants to take over an order from the predecessor, it is likely the predecessor will be busy picking at the end of any of the aisles (where the popular items are), which is easier to access than the first aisle. Interestingly, the best combination of routing heuristic, order type and storage assignment does not share the same levels for two of the performance metrics. Thus, the average system utilization and average cycle time yield conflicting warehousing designs in this set of experiments. Analyzing the individual runs, a robust design that counterbalances both performance metrics can be obtained. The within-aisle storage, fixed orders, with mid-point strategy combination yields an average utilization of 91.5 and an average cycle time of 8.75 min. If working with random orders, the within-aisle storage and mid-point strategy combination yields an average utilization of 90.9 and an average cycle time of 8.7 min.; closely followed by the within-aisle storage, fixed/random orders, with largest-gap strategy. 5.2.3. Analysis of average throughput When the factorial design was solved in terms of average throughput, it was found that all three factors were significant (Table 10). From the main effects plot (Fig. 23) it can be seen that an across storage assignment yielded greater average throughput than within-aisle. The average throughput for random orders was greater than fixed orders potentially because of orders varying in size in random orders with some orders having smaller average cycle time. This in turn resulted in a higher average throughput. It can also be concluded that the largest gap is best routing strategy in terms of average throughput.

Fig. 22. Interaction plot for average cycle time for phase II.

An important conclusion can also be made is the relationship between average cycle time and throughput. As phase I suggested, average throughput is inversely proportional to average cycle time. The same can be observed in phase II from the main effects plots of average cycle time and throughput (Figs. 21 and 24). When the average cycle time is less, the average throughput for the same factor level is great. This is logical because if the average cycle time of orders is small, the resulting average throughput of the day will be greater as more orders can be completed. It can also be observed that average throughput and average cycle time share no significant relationship with average system utilization. The reason for this could be that the average system utilization is dependent on the dynamics of the workers and how they behave in the model at different factors. 5.2.4. Determining best designs This section is an extension of phase II, which presents a methodology for finding suitable design parameters depending on the weight that the decision maker put on the two performance metrics: average cycle time and system utilization. Average throughput was not considered because it is a metric that can be explained using average cycle time. Principles from bi-criteria optimization were employed by solving different combination of weights assigned to the two objectives, which were used to find Pareto efficient solutions. The two objectives are: (1) minimize

Fig. 21. Main effect plot for average cycle time for phase II.

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Fig. 23. Comparison of average cycle time for fixed and random orders. Table 10 Analysis of variance for average throughput for phase II.

Table 11 Eight scenarios for the Pareto front.

Factors

DF

Seq SS

Adj SS

Adj MS

F

P

Scenarios (x)

Storage (Factor A)

Routing (Factor C)

A: Storage assignment B: Type of order C: Routing strategy A*B A*C B*C Error Total

1 1 3 1 3 3 3 15

3.20 6.83 15.52 1.21 0.25 0.21 0.52 27.74

3.20 6.83 15.52 1.21 0.25 0.21 0.52

3.20 6.83 5.17 1.21 0.84 0.07 0.17

18.61 39.76 30.14 7.05 0.49 0.42

0.02 0.01 0.01 0.08 0.72 0.76

1 2 3 4 5 6 7 8

Within aisle Across aisle Within aisle Across aisle Within aisle Across aisle Within aisle Across aisle

Largest gap Largest gap Return Return Mid-point Mid-point Traversal Traversal

average cycle time and (2) maximize average system utilization. The Pareto efficient solutions will assist in the decision making process by capturing the trade-offs between conflicting objectives and determining the non-dominated solutions. Obtaining the nondominated solutions under the Pareto efficiency condition will help in selecting the design combination that works best for different management practices. For this optimization, factor A (storage assignment) and factor C (routing strategy) from phase II's factorial design were selected. Eight scenarios are obtained as shown in Table 11, which serve as the decision variable x, where x ranges from 1 to 8. It was assumed

that the orders in the model were random and of different sizes. The average cycle time was given the weight coefficient of W1 and the average system utilization was given the weight coefficient of W2. Assigning different weight combinations to the two objectives helped in exploring more solutions. The different weights are determined by the decision maker and they indicate the importance of one objective over the other. A scaling factor of 11.5 was required to fairly compare the two objectives since it allows the two objectives to have similar magnitude. This is because the average cycle times are much smaller than average system utilization and the evaluation without scaling would always favor

Fig. 24. Main effects plot for average throughput for phase II.

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Table 12 Set of non-dominated solutions. Value of average utilization

Value of average cycle time

Value of x (decision variable)

90.058 89.944 88.530 88.502 88.477 88.458 87.322 87.314 87.234 87.203 86.946 86.829 86.808 82.810 82.623 82.276 82.260 82.185 81.932

9.456 9.416 9.231 9.227 9.217 9.198 8.753 8.740 8.517 8.508 8.460 8.456 8.447 7.828 7.818 7.795 7.791 7.789 7.787

3 3 7 7 7 7 5 5 1 1 4 4 4 6 6 2 2 2 2

average system utilization. The scaling factor was obtained by solving each objective function separately and then computing the ratio of the results. For every combination of weight coefficients for the two objectives, eight solutions resulted (one solution for each scenario). The non-dominated solutions were obtained as shown in Table 12. From Table 12, it can be seen that the highest system utilization (90%) was attained when x¼3, which is with the return routing strategy and the within-aisle storage assignment. The least average cycle time was achieved at scenario 2 (x¼ 2) when the largest gap strategy was used in a warehouse with across-aisle storage assignment. As it can be seen, multiple non-dominated solutions were obtained with the same x but with slight variations in values. This is because the simulations were run under stochastic conditions where the objective functions were affected by the variability of the replications. When the points in Table 12 were plotted, the following graph (Fig. 25) was obtained. From this graph, different average system utilization and the corresponding average cycle time for the non-dominated solutions are shown at the different decision variables (x). It can be observed that there is a trade-off between the two objectives. It must be

noted that all the scenarios from x ¼1 to x ¼7 present non-dominated solutions as shown by Fig. 25 except for scenario 8 (x¼ 8). This method of finding non-dominated solutions can be used as a decision making tool. Besides presenting the design that optimizes each performance metric, the graph also presents the best designs that balance both objectives. Moreover, this approach has the potential to solve large-scale design problems where numerous scenarios are considered.

6. Conclusions and future work We presented a multi-aisle order-picking model, inspired by bucket brigades, which provides a more comprehensive and reallife order-picking scenario in warehouses. We developed discrete event simulation models to compare a single-line model and the proposed multi-aisle order-picking model and it was found that there is a significant difference between the models in terms of average system utilization and cycle time. The multi-aisle model achieved a lower cycle time, higher average throughput and a higher utilization than the single-line model, on average. The average throughput in both phases shared an inverse relationship with average cycle time. Another interesting observation was the fact that both order-picking models presented a stable cycle time. In a warehouse, management decisions on warehouse design are a key factor for improving the efficiency and reducing costs. The proposed simulation model can be used in identifying the best routing heuristics and storage assignment that maximizes the utilization or minimizes cycle time and assessing how the system will behave dynamically for a multi-aisle system. The proposed multi-aisle model can be easily adaptable to study different scenarios such as number of shelves, warehouse dimensions, number of workers, order type and pick-times as well as investigate other complex dynamics. The simulation model can be obtained from the authors. In addition, a bi-objective optimization method was conducted to obtain non-dominated solutions from simulation by assigning weights to the performance metrics. These non-dominated solutions aid in finding the best design options. To provide managers with guidelines on implementing the rules of bucket brigades on a multi-aisle system, we conclude by summarizing the main managerial implications of this study below. The sensitivity analysis on the multi-aisle model showed that depending on the performance metric, that is, average system

Fig. 25. Average system utilization and cycle time for non-dominated solutions.

Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i

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utilization or average cycle time, the optimal combination of storage assignment (within-aisle storage and across-aisle storage), order type (fixed or random) and routing strategy (traversal, largest gap, mid-point, and return heuristics) varies. (1) If the priority is the cycle time then the best design is given by across-aisle storage, random orders and either the largest gap or mid-point heuristic. (2) If the objective is to attain the maximum average system utilization, then the best design is given by either within or across storage, fixed orders and return heuristic. (3) A robust design was obtained which balances out both utilization and cycle time and consists of within-aisle storage, fixed orders, with mid-point strategy. If working with random orders, the within-aisle storage and mid-point strategy combination is recommended. (4) Conducting simulation of the performance metrics at different weights revealed the non-dominated solutions based on the Pareto efficiency condition. To achieve the highest system utilization (90%), the within-aisle storage with return strategy works best. However, it does not yield a good average cycle time. The best average cycle time (7.78 min) is obtained with an across-aisle storage and largest gap routing. Multi-aisle bucket brigades can be studied further in the following research lines: (1) explore a simulation-based optimization approach to find the best routing heuristic and storage assignment depending on the decision maker's parameters and warehousing layout. (2) Another future avenue is to investigate the impact on multi-aisle models of various human interactions like worker learning, forgetting and the combination of these two factors.

Acknowledgments This research was supported in-part by the Office of the Vice President for Research of the University of Texas at San Antonio through the GREAT award. We acknowledge the helpful comments and suggestions of the editor and anonymous referees.

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Please cite this article as: S. Quader, K.K. Castillo-Villar, Design of an enhanced multi-aisle order-picking system considering storage assignments and routing heuristics, Robotics and Computer Integrated Manufacturing (2016), http://dx.doi.org/10.1016/j.rcim.2015.12.009i