• The results in the code file will not match with the Medium story as I have updated the data to avoid any conflict.

This work explains how OR and ML in tandem can help us making cost-efficient decisions. I have used a Supply Chain Network Design use case to explain benefits of ML+OR together.

Comapny A sell the Finished Good (FG) to its customers. The FG is made of Part-1 and Part-2. Part-1 is manufactured at location LOC and Part-2 is sourced from a supplier. Then Part-1 & Part-2 is assembled, this assembly of the products involve certain cost.

Once the product is assembled, it is shipped to the customers using parcel delivery. Now the company A is looking to establish the Distribution centers (DCs) to benefit from economies of scale shippment to DC and different assembly costs at different DC. The main objective is to idetify the number and location of DCs to located across the country at a minimum total cost. The total cost includes the operating cost of DC, assembly cost, and shipment costs.

This file explains the mathematical modelling using python script. Please note that the data has been anonymized for confidential reasons. However I have defined the guidelines and description how to prepare the data for execution of the script.

dataset.xlsx contains two spreadsheets. The sheet Demand has the demand data of the customers and Preferred has the preferred 17 locations for the DC. The file all_locations.csv contains the all 2,041 locations for the DC.

1. Demand Data: Please prepare the demand data as below

• df_demand: This is a dataframe for the demand of the customers. It should have Columns in the order ['Customer ID', 'Latitude', 'Longitude', 'Demand'].
  • Customer ID: Defines the identifcation of each of the customer e.g. C0001. Customer ID is a string data type.
  • Latitude/Longitude: Geographical coordinates for locations of customers. Geographical coordinates shall be in degrees and must have float data type.
  • Demand: Demand of the FG for each of the customer. Demand must be of positive int data type

2. Distribution Centres Data: A DC is a facility that is usually smaller than a firm's main warehouse and is used for receipt, temporary storage, and redistribution of goods according to the customer orders as they are received. The DC has a capacity upto which it can receive the maximum number of units. This is also a decision variable as what shall be the capacity of a DC. Further, to operate the DC, company incurs some cost recognised as the operating cost. Operating costs usually consist of a fixed cost and variable cost. The fixed cost is applicable upto a certain capacity called as initial capacity. For any capacity exceeding the initial capacity, marginal operating costs are applied. Below I describe how to prepare the data file for DCs.

Read more about distribution center here: https://en.wikipedia.org/wiki/Distribution_center

• df_DC: Preferred locations for opening the DC containing ['DC ID', 'Latitude', 'Longitude', 'Assemb', 'Fixed', 'q0', 'c0', 'q1_old', 'c1', 'q2_old', 'c2'] where:

  • DC ID, Latitude, Longitude: Represent the ID and geographical coordinates for each of the DC locations.
  • Assemb: Unit Assembly Cost of a FG at each DC.
  • Fixed: Represents the fixed cost of operating the DC having initial capacity q0
  • c0, c1, c2: Unit Cost of exceeding the capacities q0, $q1\text{_old}^$, $q2\text{_old}^$ respectively where:
    • $q1\text{_old}^* = q0 + q1\text{_old}$
    • $q2\text{_old}^* = q1\text{_old}^* + q2\text{_old}$

• df_all: Similar to df_DC, we have 2,041 locations where we can locate the DC. For the second model, this data has to be used in place of df_DC.