**What is Last Mile Delivery Problem?**

Last mile delivery is a significant issue for organizations, particularly those requiring delivery from distribution centers to clients, for example, internet business. The issue is essential in that it manages efficiencies in the delivery co-ordinations itself, whereby they are not done in mass and in clumps for evident reasons. The issue has been said, "The Last Mile Problem". There is a need to optimize the last mile delivery of goods, as most of the time the delivery is made during daytime, when most of the people are at work. This increases the cost and maintenance of the transportation.

According to a study, 53% of the total cost comes from the last mile delivery. It is an aspect to look into in order to reduce the cost of the last mile delivery.

Retailers are looking for ways to deliver goods faster to consumers' doorsteps to stave off Amazon's threat and meet customer expectations. To accomplish that, retailers and delivery providers are zeroing in on the "last mile" of fulfillment, the most expensive and time-consuming part of the delivery process, which is when a package reaches the customer's address. Startups like Postmates, Instacart, and others are looking to disrupt the last mile delivery space by leveraging the "Uber model," and connecting businesses to non-professional couriers who can deliver goods instantly.

**Objective:**

The business that is trying to solve the problem by introducing independent delivery model like Uber by utilizing electric vehicle in the logistics. The study of finance on this model will give a clear picture on whether the model will be beneficial in reducing the cost of the last mile delivery.

The comparison is made between Mahindra e2o and Piaggio Ape XTRA, as the business intends to use this vehicle for providing the delivery service to the region of Pune, Maharashtra, India. The Mahindra e2o will be modified for the purpose of making room for the package as the desired capacity is approximately 100 packages per trip. The comparison will be done with respect to the outright buying cost till the period of 15 years of usage. The study will help determine the total annual cost of operating electric vehicle and a diesel-powered vehicle, also the total CO_{2 }emission in tons.

The problem that this study intends to solve is a supply chain design using facility location for warehouse and has dedicated 12 parking lots, which will house an electric vehicle per lots. There are 12 clusters in the problem that needs to be served by the vehicles. Clusters are region in the city of Pune that are under the jurisdiction of Pune region. Each cluster has a parking lot and a dedicated electric vehicle for delivery purpose. The system optimization is done by travelling salesmen problem and for the study it is considered that the vehicle travels like a flying crow. The location of the warehouse is concluded by forming a heuristic algorithm for minimizing the distance travelled between cluster and the possible location point. After the location is determined for the warehouse, the supply chain problem is solved for optimizing the distance travelled by each vehicle in the particular cluster, by using branch and bound algorithm. The capacity of each vehicle is assumed to be 100 packages.

**Facility Location**

** **Facility location of the warehouse is crucial in the step of finding the minimum distance between the clusters and parking lots, that will ensure the minimum distance travel by the vehicle. The less the distance the vehicle has to travel less will be the CO_{2} emissions and will result in less consumption of energy. The parking lots play an important role in figuring out as the mixed integer programming is to be used to formulate the problem in order to find the minimization solution. The electric vehicle capacity is assumed to be 100 on all the 12 vehicles associated with the problem to measure the number of trips required per cluster. The number of trips also depends on the demand from the cluster. As the region is widespread and to keep the study in a flow, the demand is assumed for each cluster according to the population of each cluster. As per study in India only 28% of population is involved in e-commerce transactions. That is the basis for assuming the demand.

**Formulation**

The formulation is successfully formed by mathematical formulation using heuristic and solved for the longitudes and latitude of 12 parking lots to locate the optimal location.

N_{i }= Number of trips from parking lot to clusters per day

D_{i} = Distance to be calculated in terms of longitude and latitude

X_{i} = The x coordinate of the parking lot location

Y_{i} = The y coordinate of the parking lot location

x_{w} = The x coordinate of the warehouse location

y_{w }= The y coordinate of the warehouse location

**Data for coordinates of the parking lot**

**Table 1. data for coordinates of the parking lot**

**Travelling Salesman Problem**

The type of travelling salesman problem that we have used for optimizing the supply chain in each cluster is branch and bound. TSP is given a set of cities and distance between every pair of cities; the problem is to find the shortest possible tour that visits every city exactly once and returns to the starting point. in Branch and Bound method, for current node in tree, we compute a bound on best possible solution that we can get if we down this node. If the bound on best possible solution itself is worse than current best (best computed so far), then we ignore the subtree rooted with the node. In cases of a **minimization problem**, a lower bound tells us the minimum possible solution if we follow the given node.

The project source code is referred from the tspvis.com for better visualization results. In the visualization as you apply different algorithms, the current best path is saved and used as input to whatever you run next. (e.g. shortest path first - branch and bound) The order in which you apply different algorithms to the problem is sometimes referred to the meta-heuristic strategy. This project uses shortest path method and then running it through branch and bound for getting a shorter branch and finding the minimum distance.

**Financial Evaluation**

The financial evaluation of this report is converted into US dollars from the data that was sourced from Indian marketplace. The amount and numbers for the evaluation will be considered as the vehicles are purchased outright and not on a lease or loan. The befrugal.com calculator is used to evaluate the CO_{2} emissions of both the electric vehicle viz. Mahindra e2o and diesel powered Piaggio Ape XTRA as it is a load carrying vehicle with specs suitable for Indian environment and conditions. The calculations for the CO_{2} emissions are as per the usage of each vehicle we optimized using travelling salesman problem branch and bound method. The distance that we discovered for each cluster will be used to evaluate the financial break-even of each vehicle with compared to the diesel-powered engine. The cost of the Mahindra e2o is $8571 with a subsidy of $2314 to buy outright. Similarly, the Piaggio Ape XTRA cost is $2857. The maintenance cost for both the vehicles per year is $748 and $857 respectively. The cost of diesel is considered to be $3.74 per gallon. Similarly, the price of electricity is taken from Indian source, that is 18.5 cents per KW load.

** Facility Location**

The location of the warehouse is located using the mathematical formulation discussed above in chapter two. The calculation led the location to 18.5046936 73.8502203, which is the minimum distance from all 12 clusters.

**Travelling Salesman Problem**

The problem for finding the distance travelled by 12 cars was calculated by a visualization tool called tspvis.com. The output from the tool is shown below.

The miles in the Table 2. varies as the total distance to travel is different for each cluster and it is an estimate of travelling per day. It also has the yearly approximate distance to travel per cluster for calculation of annual cost and maintenance.

**Table 2. Miles travelled per cluster**

**Financial Evaluation**

The financial evaluation is conducted for each vehicle that is 12 cars. One is a Mahindra e2o and other is a diesel powered Piaggio Ape XTRA. Table 2 is used for calculation of annual cost and maintenance. The prices of diesel and electricity are already mentioned above in the chapter two. The Table 3 and 4 shows the difference in the cost of both the vehicle when you are looking for the expenses that you are making on both type of vehicles. Clearly, the electric vehicles cost less that the diesel powered vehicle.

**Table 3. Annual cost and maintenance cost for Mahindra e2o**

**Table 4. Annual cost and maintenance cost for Piaggio Ape XTRA**

The annual environmental costs are calculated from befrugal.com for better accuracy keeping in mind the battery capacity and use of electricity for electric vehicle. Also, the emissions for the diesel-powered vehicle.

**Table 5. Mahindra e2o emissions**

**Table 6. Piaggio Ape XTRA emissions**

The comparison between the two types of vehicle shows that the CO_{2} emissions in the Piaggio is higher than the electric vehicle. In the electric vehicle there is only upstream emission and not the tailpipe emissions.

**Break Even Analysis **

Break even analysis is done to compare the point where all the revenue can be matched at a certain point by calculating the total cost from the acquisition date till 5 years of use of both the vehicles.

**Cost after 5 years for Mahindra e2o and Piaggio Ape XTRA**

The cost after 5 years is seen to be considerable higher than Mahindra e2o. The observation is based on the miles that vehicle travels in a year.

The Average breakeven chart for both vehicles is shown below with blue being the diesel vehicle and green being the electric vehicle. The average point is observed at 20 months.

**Average Break Even point for Mahindra e2o and Piaggio Ape XTRA**

**Conclusion**

The analysis is on Mahindra e2o, which is an electric vehicle and Piaggio Ape being a diesel-powered vehicle. The facility location that the study observed is at the minimum distance from the twelve clusters that the delivery is done. The Last Mile problem is rising and costs about 53 % of the supply chain cost. This is big number to be associated with the cost of supply chain and when the vehicle will travel less miles the cost will go down. Introducing electric vehicle to the supply chain will significantly go down as the results suggested. Traditionally, the delivery is done by diesel vehicles and increases cost for fuel. The electricity is cheaper and maintenance cost is lower than the diesel vehicle. The electric vehicle must be added to the last mile delivery fleet to reduce the cost in the supply chain. Table 14 gives a clear picture on the difference between the cost of diesel vehicle and electric vehicle. The cost of using a diesel vehicle is almost more than 50 % compared to the electric vehicle.