Duration-of-Stay Storage Assignment under Uncertainty
Authors: Michael Lingzhi Li
Elliott Wolf
Daniel Wintz
Venue:  (2020)
Keywords: Storage Assignment
Deep Learning
Duration-of-Stay
Application
Natural Language Processing
Parallel Network

Abstract: Storage assignment, the act of choosing what goods are placed in what locations in a warehouse, is a central problem of supply chain logistics. Past literature has shown that the optimal method to assign pallets is to arrange them in increasing duration of stay in the warehouse (the Duration-of-Stay, or DoS, method), but the methodology requires perfect prior knowledge of DoS for each pallet, which is unknown and uncertain under realistic conditions. Attempts to predict DoS have largely been unfruitful due to the multi-valuedness nature (every shipment contains multiple identical pallets with different DoS) and data sparsity induced by lack of matching historical conditions. In this paper, we introduce a new framework for storage assignment that provides a solution to the DoS prediction problem through a distributional reformulation and a novel neural network, ParallelNet. Through collaboration with a world-leading cold storage company, we show that the system is able to predict DoS with a MAPE of 29%, a decrease of ~30% compared to a CNN-LSTM model, and suffers less performance decay into the future. The framework is then integrated into a first-of-its-kind Storage Assignment system, which is being deployed in warehouses across United States, with initial results showing up to 21% in labor savings. We also release the first publicly available set of warehousing records to facilitate research into this central problem.

Published as a conference paper at ICLR 2020
DURATION-OF-STAY STORAGE ASSIGNMENT UNDER UNCERTAINTY
Michael Lingzhi Li Operation Research Center Massachusetts Institute of Technology Cambridge, MA 02139 mlli meiimmmt.eee. edu
Elliott Wolf
Lineage Logisties
San Francisco, California ewo fê www.ineelliiisiiss...oomm
Daniel Wintz
Lineage Logistics
San Francisco, California d laatz:@@iingeellsssiiccs...o
ABSTRACT
Storage assignment, the act of choosing what goods are placed in what locations in a warehouse, is a central problem of supply chain logistics. Past literature has shown that the optimal method to assign pallets is to arrange them in increasing duration of stay (DoS) in the warehouse (the DoS method), but the methodology requires perfect prior knowledge of DoS for each pallet, which is unknown and uncertain under realistic conditions. Attempts to predict DoS have largely been unfruitful due to the multi-valuednes nature (every shipment contains identical pallets with different DoS) and data sparsity induced by lack matching historical conditions. In this paper, introduce that provides a solution to the DoS prediction problem through a distributional reformulation and novel neural network, ParallelNet. Through collaboration with world-leading cold storage company, we show that the system is able to predict DoS with a MAPE of 29%, decrease of ~30% compared LSTM model, and suffers less performance decay into the future. The framework is then integrated into first-of-its-king kind Storage Assignment system, which is being deployed in warehouses across United States, with initial results showing up to 21 in labor savings. We also release the first publicly available set of warehousing records to facilitate research into this central problem.
framework for storage assignment
CNN-
INTRODUCTION
The rise of the modern era has been accompanied by ever-shortening product life cycles, straining the entire supply chain and demanding efficiency at every node. One integral part of any supply chain is warehousing (storage); warehouse operations often have major impacts downstream on the capability to deliver product on time.
One of the largest cold storage companies in the world is looking to improve the efficiency of their warehouses by optimizing the scheduling storage systems. According to Hausman et al. (9766). the scheduling of labor in warehouses can be divided into three main components:
Pallet Assignment:
The assignment of multiple items to the same pallet.
Storage Assignment: The assignment of pallets storage location.
Interleaving: The overarching rules for dealing with concurrent inbound and outbound requests.
For this particular paper, focus the problem of storage assignment. Various papers such as Goetschalckx Ratliff (1990) show labor efficiency to be a bottleneck. In a modern warchouse, the process of storage assignment usually involves forklift drivers moving inbound pallets from the

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staging area of the warehouse to the storage location, so a sub-optimal assignment system causes unnecessary long travel times to store the pallet. Unfortunately, the inefficiency is quadrupled when the return of the forklift and the retrieval of the pallet considered.
To increase the efficiency of the warchouse, we would thus like to minimize the total travel time needed to store set of shipments from the staging area. Many different theoretical frameworks exist, and the details of such frameworks are contained in Appendix 99.1 The ones of chief interest are tumover-based, class-based, and Duration-of-Sine (DoS) based strategies.
Turnover-based strategies (e.g. Hausman et al. 1976). Yu & De Koster 2009)) assign locations so that the travel distance is inversely proportional the turnover of the product. Class-based strategies (e.g. Hausman et al. (976). Schwarz et al. (1788) separate products into & classes, with each class assigned a dedicated area of storage. DoS-based strategies (e.g. [Goetschalkkx & Ratliff (1990), Chen et al. 2016)) assign pallets to locations with travel distance proportional to the duration-of of-stay.
Simulation experiments in Goetschalckx & Ratliff (1990) and Kulturel et al. (1999) demonstrated that under complex stochastic environments, boseb strategies outperform other methodologies significantly. However, among all three categories, the most commonly used strategy class-based, as pointed out by Yu et al. (2015) and Yu & De Koster (2013). The authors and industry evidence suggest that this is due the fact that class-based systems are relatively easy to implement, but also because DoS is not known in advance. To utilize DoS system realistically would therefore require an accurate prediction model using the features available at shipment entry to the warehouse.
However, even with the availability of modern high-powen predictive methods including Gradient Boosted Trees and Neural Networks, there has been no documented progress in employing DoS-based methods. This reflects the following significant challenges in dynamic, real warehouse:
Multi-valuedness It is common for 10+ identical pallets of the same product to arrive in single shipment, and then leave the warehouse different times depending on the consumption of the end consumer. This causes the ground truth for the DoS of a product entering at a given time to be ill-defined.
Data Sparsity: A large warehouse would have significant available historical DoS data, but such data is scattered across thousands of products/SKUS, and different operating conditions (e.g. time of the year, day of the week, shipment size). Given strong variation of DoS in warchouse, it is very unlikely that all dnvironment-produce combinations would exist in data for the historical average to be valid for future DoS. Furthermore, new SKUs are created relatively frequently, and the predictive algorithm needs to be robust against that as well.
To solve such difficulties, we reformulate the DoS as a distribution and develop a new framework based nonparametric estimation. Then we combine it with parallel architecture of Residual Deep Convolutional Networks (He et al. (2015)) and Gated Recurrent Unit (GRU) networks (Cho al. (2014) provide strong estimation results. As far as the authors know, this is the first documented attempt to predict DoS in warehousing systems. We further release the first public dataset of warchousing records enable future research into this problem.
This neural network is then integrated into the larger framework, which is being implemented in live warehouses. We illustrate how initial results from the ground show appreciable labor savings.
Specifically, our contributions in this paper include:
We develop an novel end-to-end framework for optimizing warehouse storage assignment using the distribution of DoS.
We release a curated version of a large historical dataset of warehousing records that can be used to build and test models that predicts DoS.
We introduce type of neural network architecture, ParallelNet, that achieves state-of-the-an performance in estimating the DoS distribution.
Most importantly, we present real-life results of implementing the framework with Parallel- Net in live warehouses, and show labor savings by up to 21%.
The structure of the paper is as followed. In Section 2. we introduce the storage assignment problem formally, and how this leads to estimating DoS in distributional way. In Section 3, we develop the
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storage assignment framework. We would introduce the dataset in Section 4 and Section 5 contains the implementation with ParallelNet, and its results compared to strong baselines. Section 6 shows the computational results, while real-life evidence is provided in Section 7.
SOLVING THE STORAGE ASSIGNMENT PROBLEM
The general storage assignment problem asks for an assignment function that outputs storage location given a pallet and warehouse state so the total travel time for storage is minimized. We formalize such statement below and show how it naturally leads to the problem of estimating DoS.
Let warehouse W have locations labeled {1, .N where the expected travel time from the loading
dock location i is We assume pallets arrive in discrete time periods (1, 21. _T} where T is the lifetime of the warehouse and each of the pallets has an integer DoS in (1...., P). The warehouse
uses an assignment function A that assigns each arriving pallet to available location in { N..
Define nz (t) as the number of pallets (0 or 1) stored in location i in time period under assignment function A. Then our optimization problem can be stated as:
T N
min ΣΣ (t)
The constant 4 is to allow for the 4 distances traveled during storage/retrieval. Given that future pallet arrivals could be arbitrary, we need additional assumptions to make the theoretical analysis tractable. In particular, we assume the warehouse is in steady state or perfect balance:
Definition 1. Let np(t) be the number of pallets arriving at time period t that has a DoS of p. A warehouse is in perfect balance iff for all p and 1. > we have np(t pet-pp p) = (t))))
This means that each time period & > p. the ny p) outgoing pallets with DoS of p are replaced exactly by incoming pallets with DoS of p. so the number of pallets with DoS of p in the warehouse remains constant at 2p = ΣPT 1 (1) for every period & > p. For a real-life large warehouse, this steady state assumption is usually a good approximation except when shock events happen. Under such assumption, ideally we only need 2, positions to store all the pallets with DoS of p. or in total E Zp locations. Goetschalekx & Ratliff (1990) showed that the DoS strategy below is optimal:
Theorem (Goetschalekk & Ratliff (1990). Assume the warehouse is in perfect balance, and P is large enough so that 2p S 1 for every p. Define ((t)
Eyc-r Sp. as the cumulative distribution YTT -y-1 2y
of pallet DoS. ret== Ei=rty be the average occupancy rate of the warehouse. Then the optimal N
solution to 7 A", would assign pallet with DoS of p to the NrW (p)th location.
In other words, the locations are arranged in increasing order of DoS. We can always make P large enough so that 2p < 1 by separating time periods to finer intervals. With Theorem we can implement A in real warehouse using three approximations:
1. We approximate W(t) with the historical pallet cumulative DoS distribution (t)..
2. We approximate with the historical average occupancy rate of the warchouse A.
3. We approximate the DoS p with prediction p.
Both (l) and f are easily retrieved from the historical data, and N is known. We stress however that (t) needs to be size-debiased. This because pallets of DoS p would appear with frequency pap in period of time, and thus the historical data needs to be corrected to match the definition above, which is x zp- This is done through standard theory of biae-d distributions (Gove (2003)).
Therefore, in the next subsection, we would focus on the task of generating a prediction ý of the DoS.
2.1 PREDICTING DURATION OF STAY
To utilize Theorem I above, we need to predict the DoS of a pallet at its arrival. However, in most real-life warehouses, a product P; enters the warehouse with multiple 2; > 1 identical pallets,
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which leave different times t. tiz. Thus, assuming the product came in at time 0, the DoS of incoming pallets of P: could be any of the numbers ..,,,. which makes the quantity ill-defined. The uncertainty can further be very large- DoS within a shipment of 10 days when the median DoS was just over 12 days.
collaborating company had average variance of
Therefore, account for such uncertainty, we would assume that for every shipment S which contains multiple pallets, the DoS of a random pallet follows a cumulative distribution (t). Furthermore, we assume that such distribution can be identified using the characteristics Xs of the shipment known at arrival. As in, there exists a function 9 such that:
Es(() - (())((()
for all possible shipments S. This assumption is not as strong as it may seem the most important variables that affect DoS usually the time and the good that is being transported, both of which are known at arrival. As a simple example, if the product is ice cream and it is the summer, then we expect the DoS distribution be right skewed, as ice cream in high demand during the summer. Moreover, the experimental results in Section 6 are indicative that g exists and is highly estimable.
If the above assumption holds true, then we can estimate g using machine learning. Assume we have an optimal estimate ğ of relative to a loss function I(Fs, ()xs)) denoting the loss between the actual and predicted distribution. Since by our assumption F' is identified by Xs, we cannot obtain any further information about DoS relative to this loss function. Thus, for each shipment with
features Xs we take to be random sample from the distribution Fs (()s). ). In the next section, we would outline our storage assignment framework based on using such prediction p.
OVERVIEW OF STORAGE ASSIGNMENT FRAMEWORK
With (L), A, and و defined, we can now utilize the DoS strategy A" For pallet with predicted DoS p. our storage assignment function : + W is:
A(p) arg min d(NFFW()) w) c(w) wEW
Where d(e, w) is the distance between location v and in the warehouse, and c(w) are other costs associated with storing at this position, including anti-FIFO orders, item mixing, height mismatch, and others. W is the set of positions that are available when the pallet enters the warehouse.
The approximate optimal position of DoS optimal location is N-W (p). However, it is probable that such location not ideal, either because it is not available or other realistic concerns. For the collaborating company, one important factor is item mixing due to potential coss-contaminationn of food allergens close pallets. These terms are highly dependent on the specific storage company, so we include them as a general cost c(w) to add to the cost d(N NFW((p) w) of not storing the pallet at the DoS optimal position. The resulting location is chosen based the combination of the two costs.
In summary, our framework consists of three steps:
1. Utilize machine learning to provide an estimate ğ of g with respect to some loss function l.
2. For a shipment S, calculate F3g ((x) and generate random sample from Ps.
3. Apply the assignment function A defined above to determine a storage location A(p).
4
WAREHOUSING DATASET OVERVIEW AND CONSTRUCTION
In this section, we introduce the historical dataset from the cold storage company to test out the framework and model introduced in Section 3
4.1 OVERVIEW OF THE DATA
The data consists of all warehouse storage records from 2016.1 to 2018.1, with a total of 8,443,930 930 records from 37 different facilities. Each record represents single pallet and one shipment of goods usually contain multiple identical pallets (which have different DoS). On average there are 10.6 pallets per shipment in the dataset. The following covariates are present:
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Non-sequential Information: Date of Arrival, Warehouse Location, Customer Type, Prod- uct Group, Pallet Weight, Inbound Location, Outbound Location
Sequential Information: Textual description of product in pallets.
Inbound and Outbound location refers to where the shipment was coming from and will go to. The records are mainly food products, with the most common categories being (in decreasing order): chicken, beef, pork, potato, and dairy. However, non-food items such cigarettes are also present.
The item descriptions describe the contents of the pallet, but most of them are not written a human readable form, such as "NY TX TST CLUB PACK" Acronyms are used liberally due the length restriction of item descriptions in the computer system. Furthermore, the acronyms do not necessarily represent the same words: "CKN WG" means "chicken wing" while "WG CKN" means "WG brand chicken". Therefore, even though the descriptions are short, the order of the words is important.
To enable efficient use of the descriptions, decoded common acronyms by hand (e.g. However, the resulting dataset is not perfectly clean (intentionally so to mimic realistic conditions) and contains many broken phrases, misspelled words, unidentified acronyms. and other symbols.
toast).
4.2 PUBLIC RELEASE VERSION
We release the above dataset, which as far the authors know, is the first publicly available dataset of warehousing records.
The collahorating company transports appreciable amount (> 30%) of the entire US refrigerated food supply, so US law prohibits the release of the full detail of transported shipments. Furthermore, NDA agreements ban any mentioning of the brand names. Thus, for the public version, we removed all brands and detailed identifying information in the item descriptions. The testing in the section below is done on the private version reflect the full reality in the warehouse, but the results on the public version are similar (in Appendix 9.4) and the conclusions carry over to the public version.
5 IMPLEMENTING THE FRAMEWORK
The Framework described in Section 3 requires the knowledge of four parameters: Xg and Fs for pallets in the training data, the loss function ((F's, Fs), and the machine learning model estimate ğ.
Xs is immediately available in the form of the non-sequential and sequential information. For the textual description, we encode the words using Glo Ve embeddings. (Pennington al. (2014) We limit the description to the first five words with zero padding.
For Fs, we exploit that each shipment arriving usually contains p > 1 units of the good. We treat these units copies of a one-unit shipment, denoted S1, ... Sp. Then by using the DoS for each of these p units .Ti....T)) for the DoS of the shipment. This is treated the ground truth for the training data.
can create an empirical distribution function (ss(1) = Ei= Ir.s
To obtain a loss function for the distribution, we selected the 5%, ... 95% percentile points of the CDF, which forms a 19-dimensional output. This definition provides more expressive range of CDFs than estimating the coefficients for a parametric distribution, as many products' CDF do not follow any obvious parametric distribution. Then we chose the mean squared logarithmic error (MSLE) as our loss function to compare each percentile point with those predicted. This error function is chosen as the error in estimating DoS affects the positioning of the unit roughly logarithmically in the warehouse under the DoS policy. For example, estimating a shipment to stay 10 days rather than the true value of day makes about the same difference in storage position compared to estimating a shipment to stay 100 days rather than truth of 10. This is due to a pseudo-lognormal distribution of the DoS in the entire warehouse as seen in the historical data.
'Academic users can currently obtain the dataset by inquiring dwintz @ linengelogisties.com. It would be hosted online in the future.
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Sequential Information
Resiuual Convolution Layers
Uidrectional GRU Layers
Non- Cen-Sequential Info
Connected
Fully
Output Layer
Figure 1: ParalleINet Simplified Architecture. Green boxes inputs and the red box is the output. We separate inputs into sequential data and non-sequential data to exploit different types of data.
Thus, our empirical loss function is defined as:
19 Σ
L(Fs.
-0g(FF'(00050) (og(f5''(0005)) + +1) - -log(Fs (0.05i) + 1))
19 ==1
Now, we would introduce the machine learning algorithm ğ to approximate Fs.
5.1 INTRODUCTION OF PARALLELNET
For the dataset introduced in Section 4 the textual description carries important information relating to the DoS distribution. The product identity usually determines its seasonality and largely its average DoS, and therefore would be desirable extract as much information as possible through text.
We would utilize both convolutional neural networks (CNN) and recurrent neural networks (RNN) to model the textual description. As illustrated in Section 3 word order important this context, and RNNs are well equipped to capture such ordering. As the textual information is critical to the DoS prediction, we would supplement the RNN prediction with CNN architecture in parallel manner, as presented in Figure We then utilized residual output layer to produce 19 percentile points (0.05) - (0.1), (...))...... F5 (0.95)) that respect the increasing order of these points.
This architecture is similar to ensembling, which is well known for reducing bias predictions (see Opitz & Maclin (1999)). However, it has the additional advantage of a final co-training output layer that allows a complex combination of the output of two models, compared the averaging done for ensembling. This is particularly useful for our purpose of predicting 19 quantile points of distribution, as likely the CNN and RNN would be better at predicting different points, and thus a simple average would not fully exploit the information contained in both of the networks. We would see Section 6 that this allows the model to further improve its ability to predict the DoS distribution. We also further note that this is similar to the LSTM-CNN framework proposed by Donahue et al. (2014), except that the LSTM-CNN architecture stakes the CNN and RNN in a sequential manner. We would compare with such framework in our evaluation in Section 6
In interest of brevity, we omit the detailed architecture choice in RNN and CNN along with the output layer structure and include in Appendix 9.2 Hyperparameters are contained in Appendix 9.3
COMPUTATION RESULTS
In this section, we test the capability of ParalleINet to estimate the DoS distributions F's on the dataset introduced in Section 4 We separate the dataset introduced in Section into the following:
Training Set: All shipments that exited the warehouse before 2017/06/30, consisting about 60% of the entire dataset.
Testing Set: All shipments that arrived at the warehouse after 2017/06/30 and left the warehouse before 2017/07/30, consisting about 7% of the entire dataset.
Extended Testing Set: All shipments that arrived at the warehouse after 201 2017/09/30 and left the warehouse before 2017/1 2/31, consisting about 14% of the entire dataset.

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We then trained five separate neural networks and two baselines evaluate the effectiveness of ParalleINet. Specifically, for neural networks, we evaluated the parallel combination of CNN and RNNs against a vertical combination (introduced in Donahue et al. (2014)) pure ensembling model, and the individual network components. We also compare against two classical baselines, gradient-boosted trees (GBM) (Friedman (200T)) and linear regression (LRR), below:
CNN-LSTM This implements the model in Donahue et al. 2014). To ensure the best comparability, we use a ResNet CNN and 2-layer GRU, same as ParalleINet.
CNN+LSTM This implements ensembling model of the two architectures used in ParalleINet, where the two network's final output is averaged.
ResNet (CNN) We implement the ResNet arm of ParallelNet.
GRU We implement the GRU arm of ParalleINet.
Fully-connected Network (FNN) We implement 3-layer fully-connected network.
Gradient Boosted Trees with Text Features (GBM) We utilize Gradient Boosted Trees (Friedman 2001) benchmark outside of neural networks. As gradient boosted trees cannot self-generate features from the text data, we utilize 1-gram and 2-gram features.
Linear Regression with Text Features (LR) We implement multiple linear regression. Similar to GBM, we generate 1-gram and 2-gram features. The y variable is transsonddd as we assume the underlying duration distribution is approximately nog-nommal.
All neural networks are trained on Tensorflow 1.9.0 with Adam optimizer (Kingma & Ba 2014). The learning rate, decay, and number of training epochs are 10-fold cross-validated. The GBM is trained on 3.4.4 with the lightgbm package, and number of trees 10-fold cross-validated over the training set. The Linear Regression is trained with the Im function on R 3.4.4. We used a 6-core i7-5820K, GTX1080 GPU, and 16GB RAM. The results on the Testing Set are as followed:
Testing Set
Extended MSLE
Testing Sct
Architecture
MSLE
MAPE
MAPE
ParalleINet
0,4419
20%
0.7945
31%
Architecture
Testing Set
ENN-L_STM
0.4812
41%
0.9021
80%
MSLE
MAPE
CNN+LSTM
0.3024
47%
0.9581
91%
ParalleiNet
0.4419
29%
CNN
0.6123
70%
L.0233
124%
Without Product Group
0.6149
65%
GRU
0,5305
47%
1.1104
122%
Without Date of Anival
0.5723
61%
FNN
0.8331
120%
1.0766
130%
Without Customer Type
0.5687
58%
GBM
1,2490
Without All Nontextual Features
0.8322
110%.
LR
0.9520
132%
L,1357
140%
Without Textual Features
0.9213
125%
Table 1: Table of Prediction Results for Different Machine Learning Architectures
Table 2: Ablation Studies
We can see that ParallelNet comfortably outperforms other architectures. Its loss is lower than the vertical stacking CNN-LSTM, by 8%. The result of 0.4419 shows that on average, our prediction in the 19 percentiles is 44% away from the true value. We also note that its loss is about 15% less than the pure ensembling architecture, indicating that there is a large gain from the final co-training layer.
We also note that the baselines (GBM, LR) significantly underperformed neural network architectures, indicating that advanced modeling of text is important. We also conducted ablation studies to find that product group, date of arrival, and customer type are important for the task, which is intuitive. Furthermore, both nontextual and textual features are required for good performance.
We then look different statistic: the Median Absolute Percentage Error (MAPE). For every percentile in every sample, the Absolute Percentage Error (APE) of the predicted number of days f and the actual number of days T is defined as:
I -1]
APE(f,
T
Then MAPE is defined as the median value of the APE across all 19 percentiles and all samples in the testing set. This statistic is more robust outliers in the data.
As seen in Table 2 ParallelNet has a MAPE of 29%. This is highly respectable given the massive innate fluctuations of dynamic warehouse, this means the model could predict 50% of all
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Before
Befone
1400
Plotomere poncerkle
percerble
1900
100
Resement
Placoment parcarts
Figure 2: Placement percentile of putaway pallets before and after using DoS system for months in two selected facilities. Red line denotes the mean and blue line denotes the median.
percentiles with an error less than 29%. The result also compares well with the other methods, as ParalleINet reduces the MAPE by 29.3% when compared to the best baseline of CNN-LSTM.
If we look further out into the future the Extended Testing Set, the performance all algorithms suffer. This is expected as our information in the training set is outdated. Under this scenario, we see that ParallelNet still outperforms the other comparison algorithms by a significant amount. In fact, the difference between the pairs (CNN-LSTM, ParallelNet) and (CNN+LSTM, ParallelNet) both increase under the MSLE and MAPE metrics. This provides evidence that a parallel co-training framework like that of ParalleINet is able generalize better. We hypothesize that this is due the reduction in bias due to ensembling like qualities leading to more robust answers.
7 REAL-LIFE IMPLEMENTATION RESULTS
With the favorable computational results, the collaborating company implementing the framework with ParalleINet across their warchouses, and in this section we would analyze the initial results.
The graphs in Figure 2 records the empirical distribution of the placement percentiles before and after the DoS framework was online. The placement percentile is the percentile of the distance from the staging area to the placement location. Thus, 40% means pallet is put at the 40th percentile of the distance from staging. The distance distribution of locations is relatively flat, so this is close proxy of driving distance between staging and storage locations, and thus time spent storing the pallets.
Additionally, plotted two curves obtained by simulating placement percentiles under perfect DoS' strategy (blue) and a greedy strategy that allocates the closest available position to any pallet ignoring DoS (black). These simulations assumed all locations in the warchouse are open to storage and ignored all other constraints in the placement; thus they do not reflect the full complex workings of warehouse. However, this simple simulation show clearly the advantages of the DoS strategy as it is able to store more pallets in the front of the warehouse. We observe that in both facilities. the real placement percentiles behaved relatively closely the blue curve. This strong evidence that the implemented DoS framework is effective in real-life and provides efficiency gains. We note that there a drop the lower percentiles compared to the DoS curve this is due to some locations close to the staging area being reserved for packing purposes and thus not actually available for storage.
Specifically, Facility had an average placement percentile of 51% before, and 41% after, while Facility B had an average placement percentile of 50% before, and 39% after. On average, record a 10.5% drop in absolute terms or 21% in relative terms. This means that the labor time spent on storing pallets has roughly declined by 21%. An unpaired t-test the average putaway percentile shows the change is statistically significant on the 1% level for both facilities. This provides real-life evidence that the system is able to generate real labor savings in the warehouses.
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8 CONCLUSION AND REMARKS
In conclusion, we have introduced a comprehensive framework for storage assignment under an uncertain DoS. We produced an implementation of this framework using a parallel formulation of two effective neural network architectures. We showed how the parallel formulation has favorable generalization behavior and out-of-sample testing results compared with sequential stacking and ensembling. This has allowed this framework to be now implemented in live warehouses all around the country, and results show appreciable labor savings on the ground. We also release the first dataset of warehousing records to stimulate research in this central problem for storage assignment.
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httpp:://oll wwt.orggggoo. wwwp://......1//mmemee www.:/1s7m//..... 36. 9. 9.1120
Jeffery H. Gove. Estimation and applications of size-biased distributions in forestry. Modeling Forest Systems, 2003.
Warren H. Hausman, Leroy B. Schwarz, and Stephen C. Graves. Optimal storage assignment in automatic warehousing systems. Management Science, 22(6):629 -68,66388888 1976. doi: 10. 18.mss// 22.6.629. http::tss://oi..rrr
1287/mnsc 22. 6.66.629 629
Kaiming He, Xiangyu Zhang, Shaoging Ren, and Jian Sun. Deep residual learning for image recognition. CoRR, abs/1552.03388, 2015. URL/attp://aaaet wwwp:iiivorrr.ooooooo abs 1512.03385 03385
Diederik P Kingma and Jimmy Ba. Adam: method for stochastic optimization. arXiv preprint 1r12vv14/2.69900 2014.
Sadan Kulturel, Nur E Ozdemirel, Canan Sepil, and Zafer Bozkurt. Experimental investigation of shared storage assignment policies in automated storage/retrieval systems. IIE transactions, 31() 739-749, 1999.
Charles J Malmborg. Interleaving models for the analysis of twin shuttle automated storage and retrieval systems. International Journal of Production Research, 38(18):4599446) 2000.

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David Opitz and Richard Maclin. Popular ensemble methods: An empirical study. Journal of artificial intelligence research, 11:169-198, 1999.
Jeffrey Pennington, Richard Socher, and Christopher D. Manning. Glove: Global vectors for word representation. In Empirical Methods in Natural Language Processing (EMNLP), pp. 1532-1543,
2014. URL http: ac wwwwweeee web. org/ wothoollyy//om 1162
Charles G Petersen, Gerald R Aase, and Daniel R Heiser. Improving order-picking performance through the implementation of class-based storage. International Journal of Physical Distribution & Logistics Management, 34(7):534-544 2004.
Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, and Ilya Sutskever. Language models are unsupervised multitask learners.
Meir J Rosenblatt and Amit Eynan. Notederiving the optimal boundaries for Lass-based automatic storage/retrieval systems. Management Science, (5(11)::511-1522 1989.
Mike Schuster and Kuldip Paliwal. Bidirectional recurrent neural networks. IEEE Transactions on Signal Processing, 45(1 (1:11)2367-2611 1997.
Leroy B. Schwarz, Stephen C. Graves, and Warren H. Hausman. Scheduling policies for automatic warchousing systems: Simulation results. A E Transactions, 10(3):260 270, 1978. doi: 10. httll:tts/////m / 0ttgg//....000000555555558883100
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Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ily Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The Journal of Machine
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Yugang Yu and MBM De Koster. Designing an optimal turnoeer-based storage rack for a 3d compact automated storage and retrieval system. International journal of production research, 47(6): 1551-1571, 2009.
Yugang Yu and René BM De Koster. On the suboptimality of full turnover-based storage. International Journal of Production Research, 5166)1633-16677, 2013.
Yugang Yu. René BM de Koster, and Xiaolong Guo. Class-basee storage with finite number of items: Using more classes is not always better. Production and operations management, 24(8): 1235-1247 2015.
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9 APPENDIX
9.1 LITERATURE REVIEW ON STORAGE ASSIGNMENT
Since Hausman et al. 1976), many different theoretical frameworks have been introduced, which can roughly be separated into two classes: dedicated storage systems and shared storage systems.
9.1.1 DEDICATED STORAGE SYSTEMS
For this class storage systems, each product gets assigned fixed locations the warehouse. When the product comes in, it is always assigned to one of the pre-determined locations. Under this constraint, it is optimal to dedicate positions with travel distance inversely proportional to the turnover of the product, shown in Goetschalekx & Ratliff (1990). Turnover of a product is defined as the inverse of Cube per Order Index (COI), which is the ratio of the size of the location it needs to the frequency of retrieval needed. Heuristically, those products with the smallest surface footprint and the highest frequency should be put closest to the warehouse entry, so that those locations are maximally utilized.
9.1.2 SHARED STORAGE SYSTEMS
This class of storage systems allows multiple pallets occupy the same position in the warehouse (at different times). is widely considered to be superior than dedicated storage systems due to its savings travel time and smaller need for storage space, shown by Yu et al. (2015), Malmborg (2000). Within this category, there are mainly three strategies:
Turnover (Cube-per-Ordee COI) Based: Products coming into the warehouse assigned locations so that the resultant travel distance inversely proportional to the turnover the product. Examples of such work includes Hausman et al. (1976), Yu & De Koster (2009).
and Yu & De Koster (2013).
Class Based: Products are first separated into & classes, with each class assigned a dedicated area of storage. The most popular type of class assignment is called ABC assignment, which divides products into three classes based on their turnover within the warchouse. Then within each class, a separate system is used to sort the pallets (usually random or turnover-baseds basedd. It was introduced by Hausman et al. (1976). and he showed that a simple framework saves on average 20 25% of time compared the dedicated storage policy in simulation. Implementation and further work in this area include Rosenblatt & Eynan 1989). Schwarz et al. (1978) and Petersen et al. (2004).
Duration-of of--nayy (DoS) Based: Individual products are assigned locations with travel distance proportional to the duration of stay. [Goetschalckx & Ratliff (1990) proved that if DoS is known in advance and the warehouse is completely balanced input/output, then the DoS policy theoretically optimal. The main work in this area was pioneered by Goetschalekx & Ratliff (199)). Recently, Chen et al.] (2016) and Chen et al. (2010) reformulated the DoS-based assignment problem as mixed-intege optimization problem in an automated warehouse under different configurations. Both papers assume that the DoS is known exactly ahead of time.
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In modeling text, there three popular classes of architectures: convolutional neural networks (CNN), recurrent neural networks (RNN), and transformers. In particular recently transformers have gained popularity due their performance in machine translation and generation tasks (e.g. [Devlin et al. (2018), Radford et al.). However, we argue that transformers are not the appropriate model for the textual descriptions here. The words often do form a coherent phrase so there is need for Published as a conference paper at ICLR 2020
9.2 ARCHITECTURE CHOICE
attention, and there is lack of long-range dependency due to the short length of the descriptions.
9.2.1 BIDIRECTIONAL GRU LAYERS
Gated Recurrent Units, introduced by Cho al. (2014), a partieular implementation of RNN intended to capture long-range pattern information. In the proposed system, we further integrate bi-directionality. as detailed in Schusser & Paliwal (1997), improve feature extraction by training the sequence both from the start to end and in reverse.
The use of GRU rather than LSTM intentional. Empirically GRU showed better convergence properties, which has also been observed by Chhng et al. (2014), and better stability when combined with the convolutional neural network.
9.2.2 RESNET CONVOLUTIONAL LAYERS
In a convolutional layer, many independent filters are used to find favorable combinations of features that leads higher predictive power. Further to that, they are passed to random dropout layers introduced in Srivastava et al.) (014)) to reduce over-fitting and improve generalization. Dropout layers randomly change some outputs in Co, C to zero ignore the effect of the network at some nodes, reducing the effect of over-fitting.
Repeated blocks of convolution layers and random dropout layers are used formulate deep convolution network to increase generalization capabilities of the network.
However, a common problem with deep convolutional neural networks the degradation training accuracy with increasing number of layers, even though theoretically a deeper network should perform at least as well as a shallow one. To prevent such issues, we introduce skip connections in the convolution layers, introduced by Residual Networks in (He et al. (2015). The residual network introduces identity connections between far-away layers. This effectively allows the neural network to map residual mapping into the layers in between, which is empirically shown to be easier train.
9.2.3 OUTPUT LAYER
designed the output layer as below in Figure 3 to directly predict the 19 percentile points (0.05), F5 (0.1)....... FF5'00.5))
Fully Connected, 500
Fully Connected, 1, ReLu
f
f
Fully Connected, 1, Relu
1p
Fully Connected, 1, ReLu
Fully Connected, 1, ReLu
1ry
Fully Connected, Rolu
fta
Fully Connected, ReLu
119
Figure Output Layer. Here 4, ... 41 corresponds to the 5%, 95% percentile points.
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Note that the 19 percentile points are always increasing. Thus the output is subjected to 19 separate 1 --neuonn dense layers with ReLu, and the output of the previous dense layer is added to the next one, creating residual output layer in which each (non-negative) output from the 1-neuron dense layer is only predicting the residual increase 4++1 li-
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9.3 DETAILED SETTINGS OF IMPLEMENTED ARCHITECTURE
Sequential Information
GRU, Bidrrectional
Conv,
4, Conv,
y
Conv,
Conv,
4, Conw, 128
4, Conw, 128 y M
4, Cono, 128
4, Conv,
4, Conv, 256
Cono, M
4, Conw, 258
Global Max Pooling
Global Max Pooling
Non-sequential Info
Fully Connected, 2000
Fully Connected, 2000
Fully Connected, 1000
Fully Connected, 1000
Fully Connected, 500
Fully Connected, 500
Fully Connected, 500
Output Layer
Figure 4: ParalleINet Architecture
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9.4 TESTING RESULTS ON PUBLIC DATASET
Testing Set
Extended Testing Set
Architecture
MSLE
МАРE
MSLE
MAPE
ParalleINet
0.4602
34%
0.7980
50%
CNN 0.6203
73%
1.0087
122%
GBM
1.1749
175%
1,2605
190%
Table 3: Results on Public Dataset for Selected Architectures
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Reviews:
[{"review_id": "rkeHtQxstB", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper tackles the problem of assigning pallets to storage positions in a warehouse so as to minimize total travel time. Previous literature has shown that if durations of stay (DoS) is known in advance then the optimal storage position is inversely proportional to this. The paper proposes to predict a DoS distribution for each pallet using a 19 point CDF with a neural network. The authors show that the proposed network is better than a few other neural baselines and that it can predict the DoS reasonably well.\nThe authors report significant positive real life results in two warehouses and releases their dataset.\n\nThe paper is interesting and seems to make significant progress on an important real-life issue. The release of a large realistic dataset is a major contribution to this field.\n\nDespite this I will not recommend this paper for publishing at ICLR, simply because I think it falls outside the scope of the conference.\n\nI would recommend the authors seek to publish in a venue more focused on logistics or operational research (OR), where I think the paper could have a great impact.\n\nI would have appreciated a more in-depth description of the problem. It seems that the general problem would be to minimize the expected cost (distance moved) over the lifetime of the warehouse. Under what simplifying assumptions does that reduce to minimizing the expected cost of each pallet individually as done here? \n\nSimilarly, I would have preferred a more formal definition of the loss, e.g. start from the expected distance moved and derive the (approximate) loss from there. Approximations are fine as long as you tell the reader what you're approximating, why you need to do it, and what the biases are.\n\nI would also move the detailed description and figures of the actual neural network to the appendix since it's not central to the understanding of the paper (aside from the CDF formulation).\n\n\n------------ UPDATE ------------\n\nThe area chair didn't get back to me, but I'll assume the paper is in scope and as such have changed my rating to weak reject. \n\nI'd prefer if the paper spend less space arguing that a specific network architecture is the right choice and prioritize introducing the problem more formally. I would move the simulations of different storage strategies (figure 2, blue and black lines) into the introduction, as part of introducing the reader to the problem and evaluation, and explain how figure 2 is related to what you really want to minimize: \"total pallet distance moved over time x\". I wonder if the pallet percentile distribution (figure 2) is actually interesting, other than as a way to compute the \"total pallet distance moved over time x\".\n\nI fear the authors feel the need to introduce a \"novel\" NN in order to publish at ICLR and thus spend a lot of effort describing something that is really not very interesting (even giving it a name). Combining textual and non-textual features is not a new concept, and combining a RNN layer and a CNN layer is not novel. I'm skeptical that this exact network structure is needed. It's clear you should combine the textual and non-textual features, but is this *exact* network structure needed? I would find that very surprising. How about MLP(concat(CNN(text), RNN(text), non-text))?\n\nAnother gripe is the heuristic nature of the loss function. It's clear predicting the DoS distribution better is the right thing to do, but is the sum of L2 distances to the emprical log CDF the *right* measure or a heuristic? What is the right thing to do? What is it approximating if anything? Why?\nI would expect the right thing to do is to maximize the probability of the observed duration of stay under the model, i.e max_\\theta p(DoS|x, \\theta), i.e. min_\\theta \\sum_i -log(p(DoS_i|x_i, \\theta). If this is log-normally distributed, then a log-normal distribution is probably a good distribution. Or perhaps a mixture of log-normals. I think you can even use the 19 point CDF output layer and evaluate the data likelihood under this, but I *don't* think the 19 point L2 distance to the empirical probability distributions is the correct thing to do. Is that even defined if there's less than 19 pallets with the same inputs x?", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "SyecrTwlFS", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper introduces a model to predict the duration of stay of goods in a warehouse, and releases an extensive dataset of warehousing records used in the experiments.\n\nI found the paper very interesting to read, and I believe it could serve as an inspiration to researches more interested in applied ML, since is shows that relatively standard architectures can make a big impact in solving real-world problems.\n\nI have some questions on the experiments:\n- The model used in the experiments is a combination of a CNN and a GRU architecture. One thing that is not clear to me is why the author chose to limit the sequential input to the model to only 5 words (in particular in the GRU branch).\n- Did you make any analysis on which information is more important for the model when making predictions? Is the sequential information describing the type of product dominating the non-sequential information?\n- What are the generalization/transferability properties of the model across different locations? \n- Based on the results on the extended training set it seems clear that due to the temporal shift in the data the model will have to be retrained fairly often. Did you experiment with this in your real-life implementation?\n\nTo me, the released dataset is one of the key contributions of this work. However, I have some doubts on the reproducibility of the experiments.\n- Due to regulations/NDA you were not able to release some details of the data that seem really important to me. My guess is for example that the brand name is a key information to have when predicting DoS. Is the data really meaningful even without it?\n- To verify the above question as well as to create a baseline for people interested in using the public dataset, you should add your results on the public version of dataset (even in appendix).\n\nOverall I liked the paper so I argue for acceptance, provided that I receive a satisfactory answer to the above concerns. \n\nSmall typo:\n- Assumption 1: \".. exists a function f\" -> \".. exists a function g\"\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper."}, "extra_text": {}}, {"review_id": "S1xwzqPz9S", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper introduces the duration-of-stay estimation problem in the warehouse storage application and describes a way to formulate the problem, prepare datasets, design loss functions and train models. The approach seems to significantly reduce the distance traveled in warehouses and therefore reduce labor costs.\n\nThis paper is an application paper where the problem studied seems to be limited to a small audience. I am not sure if it aligns well with ICLR. However, I do think the problem is interesting since it can directly lead to significant real-world improvements by improving the machine learning task. It is also nice to see the authors will publish the datasets to enable future research along this direction.\n\nThe paper is well written. It introduces the context of the problem very clearly, and outlines the important factors, and how machine learning can help solve the problem. I also like the detailed description of the problem formulation, datasets, and the loss function design.\n\nI think the experiment section needs more work. For example, given that the input features are limited, can a GBDT do the job as well? Is neural network really needed here to learn a complicated representation? By comparing some simpler baselines, we can have a clearer idea into this question. Also, it is better if the paper can include some ablation studies to single out the important factors, for instance, which input features are most important, which kind of modeling enables the potential of which input features.\n\nIt is interesting the proposed approach seems to work well in real-world scenario. But it is not clear to me the comparison presented in Figure 3 really leads to increased efficiency of the warehouse. It is true more pallets are placed in nearby locations, but is the prediction of DoS accurate enough to prevent constantly retrieving pallets placed farther away? In other words, Figure 3 only describes the state after adopting the algorithm, but it does not say whether this configuration is better or not since one can come up with a totally random algorithm to place more pallets in nearby locations without leveraging the input features. \n\n\n=============Update==============\nAfter considering the rebuttal and the updated text, I have changed my rating to weak accept.\n\nThe authors have added more experiment comparisons and also some ablation studies to provide more insights of the problem. Also some clarification to Figure 3 is also added.", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: Thanks to the authors for the submission and the active discussion. The paper applies deep learning to the duration-of-stay estimation problem in the warehouse storage application. The authors provide problem formulation and describe the pipeline of their solutions, including datasets preparation and loss functions design. The reviewers agree that this is a good application paper that showcases how deep learning can be useful for a real-world problem. The release of the dataset can also be a nice contribution. A major debate during the discussion is whether this paper is in scope of ICLR given that it is mostly a straightforward application existing techniques. After several rounds of discussion, reviewers think that this should fit under the category "applications in vision, ... , computational biology, and others." Overall, this paper can be a good example of applying deep learning to real-world problems.

Decision: Accept (Spotlight)