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Problem Statement: We are given an optimisation problem; with production centres, source airport, destination airports, transfer points and finally delivered to the customers. This is better explained in the following picture. Problem Statement

Objective function 1: Minimise costs = inventory costs + transportation costs + penalty costs + loading/unloading costs

  1. Inventory costs = inventory cost at source airport + inventory costs at distribution centres

  2. Transportation costs = cost of transporting cargo from production centre to source airport (via trucks) + cost of transporting cargo through itineraries (via flight) + cost of transporting cargo from distribution centre to transfer points (via trucks) + cost of transporting cargo from transfer point to customers (via drones)

  3. Penalty costs = cost of operating flight routes and delay penalty costs

  4. Loading/unloading costs = cost of loading cargo on trucks at production centres + cost of unloading cargo from trucks at the transfer point

Mathematical Solution (Using IBM CPLEX solver / Docplex): The complete python code (.ipynb file) with the formulation is present in this Google Drive Link. This gives an optimal solution.

Query: Is there any non-mathematical, non-formulation based method to solve this problem statement? Something on the lines of Reinforcement Learning? If any implementation is also provided, it will be icing on the cake.

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1 Answer 1

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To frame that problem to be solved with reinforcement learning (RL), first define an agent. The agent will try different policies in the environment. Policies that result will higher rewards will be used more often.

That problem is relative straightforward (for a RL problem) because the environment can be modeled as a directed acyclic graph (DAG) with a fixed set of discrete nodes. Brute force policy search could possible work.

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