DAT561: Midterm Project:
Smart Logistic Warehouse System in Walmart

Walmart Inc. is an American multinational retail corporation that operates a chain of hypermarkets,
discount department stores, and grocery stores in the United States, headquartered in Bentonville,
Arkansas. Walmart warehouses are located throughout the country to ship out products and provide
on-time delivery for customers.

Example of one Walmart warehouse (Received from Walmart Corporate)
Recently, Walmart is planning a 21-day countdown promotion for Christmas, and Marlon Brown, a
manager of Walmart Company, must make sure that the stored products in each warehouse are proper
and sufficient. After consideration, Marlon breaks this project into two parts:
1. Selecting products for each warehouse before the promotion starts
2. Simulating cross-warehouse-transshipment solution for possible product shortage problem for
a random warehouse after the promotion starts
Working as a consulting team, you would provide your analysis to Marlon, and all the data you need is
available in the “Products.csv” file.
Here is some information about this dataset:
Each column contains the weight and value of each product, and there are a total of 50 available
product options (Product No. 0 - Product No. 49) that can be selected for one warehouse.
Every two rows contain all product information in one warehouse, and there are 300 warehouses
(Warehouse No. 0 - Warehouse No. 299) in total.
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For each warehouse, there are four variables:
1. n - total number of products chosen to be stored in the warehouse
2. C - total weight capacity of the warehouse
3. Vi - the value of available product i
4. Wi - the weight of available product i
Specifically, for each warehouse, there is a weight capacity (C) of 650, which means that the total
weight of n products that are selected to be stored in a warehouse should be less than or equal to 650.
Each available product i has its own weight (Wi) and value (Vi). Besides, the product information for
each warehouse is different.


Problem 1: The Estimated Value for Each Warehouse
In this part, Marlon wants to select products for each warehouse. He will choose products that have
the top “Value Weight Ratios” as many as possible before reaching the capacity of each warehouse
(650).
_ℎ =

ℎ

Product 2 Product 0
Warehouse3
Warehouse2
Warehouse1
Weight
Value
Product 1

Product 3

Warehouses can store all boxes within Capacity C.
There are n products available for selection.
Each product i: Value Vi and Weight Wi
≥ ෍ ()
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That is, he will first choose the product with the highest “Value Weight Ratio” to store in the warehouse,
and then choose the product with the second-highest “Value Weight Ratio” to store, and so on until
the warehouse reaches its capacity.
Here is a simplified example for one warehouse, assuming its capacity is 265 and 10 products could be
selected. The weights and values of these products are listed below:
Package No 0 1 2 3 4 5 6 7 8 9
Weight 112 67 94 58 47 9 98 31 81 12
Value 195.71 62.59 105.44 57.15 64.21 8.79 71.14 11.19 62.89 1.64

First of all, calculate the Value Weight Ratio for each product.
Package No 0 1 2 3 4 5 6 7 8 9
Value/Weight 0.5723 1.0705 0.8915 1.0149 0.732 1.0239 1.3776 2.7703 1.288 7.3171

Secondly, sort the products based on the Value Weight Ratio in descending order.
Thirdly, start selecting products, and at the same time, look at the accumulated weight of products to
make sure the accumulated weight does not exceed the warehouse weight capacity. With the capacity
of this warehouse (265), after we select products 0, 4, and 2, the accumulated weight approaches 253,
and only 12 are left for the next product. When we choose the fourth product, we select product 5
rather than product 3 because the weight of product 3 (58) is larger than the remaining capacity (12).
Moreover, there is no more space to contain extra products in this warehouse. As a result, we finally
have products 0, 2, 4, and 5 stored in this warehouse.
Lastly, calculate the corresponding estimated value of the warehouse, and in this case, it is 374.15.

Now you would try to help Marlon with his product selection problem for those 300 warehouses
(capacity of each is 650) with the dataset “Products.csv”. Calculating the estimated total value and the
You should perform this
step with python codes!
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accumulated weight of each 300 warehouses will be helpful for the later decision of the cross-
warehouse-transshipment solution.
Notes:
1. Please do not use other packages to read the CSV file.
2. You should perform all the steps above with python codes rather than a spreadsheet
3. Sometimes when the warehouse is nearly full, the next product with the next highest ratio
cannot be put in the warehouse, but there are still chances that one or more remaining
products can be put in the warehouse. Make sure you take every product into consideration;
otherwise, you may have the risk of missing products.
4. You are NOT allowed to use the dynamic programming method in this problem; otherwise, you
may get 0.

Problem 2: Top Alternative Selections
Thank you for your great job helping Marlon with the warehouse storage arrangement! In this part, he
would like to simulate the situation when a random warehouse is out-of-stock during the promotion
period.
It is expected that a warehouse would run out of all the products during promotion, and in order to
keep the promotion activities and make sure on-time delivery in one region, cross-region shipment
from other warehouses (let’s call them “Helpers”) is necessary. More specifically, among the 300
warehouses, 1 is out-of-stock, then the rest 299 would all be Helpers.
Before seeking help from those Helpers, Marlon needs to figure out which Helpers he could choose.
For Helpers selection, Marlon would choose those Helpers with the top 10 highest “Value_per_Weight”
ratios. It’s acceptable to recommend more than 10 Helpers because two or more Helpers may have the
same “Value_per_Weight” ratio.
__ℎ =
_
_ℎ
− × _
1. Total_Value: total value of the stored products in one warehouse
2. Total_Weight: total weight of the stored products in one warehouse
3. Distance: the distance, generated by you, between the out-of-stock warehouse and the Helpers
4. Transportation_Cost: 0.016 per distance

Cross-warehouse-transshipment begins with the warehouse that is out-of-stock (total number of
stored products is 0), and this warehouse would contact Helper to see if help is available. Once the
Helper agrees to do the Cross-warehouse-transshipment, it will transport all products in its warehouse.
In this case, Marlon assumes that Helpers have not sold any products since the selection process in
Part 1. In other words, the total number of stored products in each Helper remains the same as it was
before the promotion started. Since the distances between this product-shortage warehouse and the
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Helpers are different, the transportation fee will be correspondingly different. By calculating the
“Value_per_Weight,” Marlon could find Helpers with the top 10 highest “Value_per_Weight” after
considering transportation costs (The cost of a one-way trip from the Helper to the product-shortage
warehouse).
Step 1: Let's generate a distance matrix among the 300 warehouses first. Each of the distances can be
generated by using a normal distribution with a mean of 600 and a standard deviation of 400. (Please
make sure that each generated distance is positive). Below is an example of a 10*10 distance matrix.

You must create your own distance matrix with a size of 300*300. Be careful, all the distances
generated should be positive numbers and rounded to an integer using round (). After successfully
generating the distance matrix, please write it to a new CSV file called “Distances.csv”.
Notes:
1. Please do not use any packages to write the CSV file.
2. For better understanding, we included the warehouse index in the screenshot, but the distance
matrix you generated does not need to include the index.

Step 2: Now, you could calculate the “Value_per_Weight” and help Marlon decide the Helpers with
the top 10 highest “Value_per_Weight”.
First of all, Marlon would randomly choose a warehouse (from Warehouse No.0 to Warehouse No.299)
and assume it would face out-of-stock problems in this simulation.
Secondly, based on the warehouse he picks, you need to find the corresponding distance between this
warehouse and each of the other Helpers from the distance matrix you generated in Step 1. Besides,
you also need to find the corresponding total value and the total weight of all products stored in each
Helper (you have calculated these numbers in Problem 1).
Thirdly, calculate the “Value_per_Weight” ratio for each Helper, sort the ratio in descending order, and
choose the top helpers with the 10 highest “Value_per_Weight” ratios. Recall this formula:
__ℎ =
_
_ℎ
− × _
1. Total_Value: total value of the stored products in one warehouse
2. Total_Weight: total weight of the stored products in one warehouse
3. Distance: the distance, generated by you, between the out-of-stock warehouse and the Helpers
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4. Transportation_Cost: 0.016 per distance unit

Here is a simplified example, suppose now there are 10 warehouses in total, and Marlon needs Helpers
with the top 3 “Value_per_Weight” ratios. He assumes warehouse No. 5 is out-of-stock, and as a result,
the total number of products in it becomes 0, while the rest of the warehouses (Helpers) remain with
the same amount of product as you generated in Problem 1. The corresponding distance data is located
in the 6th row of the distance matrix you have generated in Step 1 (the row starts with index 5
highlighted by the red rectangle below).

Finding the corresponding distance
After calculating the “Value_per_Weight” ratio for each helper, you would sort those Helpers and
return the top 3 “Value_per_Weight” and the corresponding index of the Helpers. (It is important you
show the corresponding relationship between the “Value-per-Weight” and the index of the Helpers!)

The logic of how you calculate the “Value_per_Weight”

Sorted result
(You should use the code to show this logic instead of Excel, you do not need to generate a file here.)
You should perform this step
with python codes!
You should perform this step
with python codes!
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Notes:
1. You are NOT allowed to use dynamic programming in this problem. Otherwise, your project
may receive 0 points.
2. In this problem, there is a chance that the “Value_per_Weight” of the two warehouses are the
same. Return the top 10 Value_per_Weight, the distance to the out-of-stock warehouse, and if
multiple warehouses have the same Value_per_Weight, determine those warehouses in the
output.

Submission of the Project
Your final submission will contain two files:
1. The first would be the "Fall22_Mid_Walmart. ipynb" notebook. You need to provide the
Python code as well as your answers. We strongly recommend you provide explanations for key steps
in the code so that we can understand what you were trying to do when something goes wrong.
2. The second is the “Distances.csv” file.
Note: Please submit all files (Distances.csv, and Fall22_Mid_Walmart.ipynb files) as one zip file on
Canvas. Please add the IDs of all teammates to the name of a zip file. For example,
14325_34672_12345.zip.
Grading
Total - 100 points
25 points - towards how good your solution is – we will rank all projects and will give the grade based on the
project preparation. We will check how to write the code and solve the problem. How it is optimized and
efficient…
• Top 10% (among all groups across sessions) – 25 points
• Rest of top 30% - 20 points
• Middle 30% - 15 points
• Bottom 30% - 10 points
75 points:
The Estimated Value for Each Warehouse – 25 points
The 300*300 distance matrix generated – 25 points
Top 10 Warehouses Chosen for Help - 25 points
• Your code needs to pass the auto-grader for us to see whether it works.
● We will look at your logic and whether your code is working.
● We will look at whether you submitted all files correctly.
● We will look at how effectively you solved the problems.