Optimization of Vehicle Routing in a Supply Chain

Abstract

Supply chain is a sequence of organizations- their facilities, functions and activities that are involved in producing and delivering a product or service. The sequence begins with basic suppliers of' raw materials and extends all the way to the final customers. So product delivery to the final customer is the ultimate physical activity of a supply chain management. Human civilization has a long outstanding history for the efforts to optimize traveling routes or delivery routes. The first ever systematic initiative, so far known, is The travelling Salesman Problem. Fixed route transit schedule, Vehicle Routing Problem (VRP), Vehicle Routing Problem with Time Windows (VRPTW). Pickup and Delivery Problem with Time Windows (Pl)PTW), Single Vehicle Routing Problem with Deliveries and Selective Pickups (SVRI'DSP). etc are the initiative for optimizing vehicle routing. The aims are to design a vehicle route of minimum net cost, visiting each customer, performing all deliveries, etc. 1-Icre, A study was accomplished in a systematic manner on the delivery system of a renowned Multinational organization, targeting to optimize their delivery system. They have twenty sales centers around the country. All of their products are sold through these sales centers. From these sales centers, they sold the goods to their dealers and some special customers. They provide transport for the delivery of goods. One of their sales centers was studied which involved one pickup for their delivery purpose to serve about forty eight regular customers. Vs/hen we studied their order pattern, we found that the vehicle is sometimes overloaded and some other times under loaded. We further drilled down the issue and found that they have no specific schedule for their deliveries. Our intention was to develop a model for optimizing such delivery schedule. First of all, we examined the order quantity and order interval of each delivered customer as the model must be capable to handle the demands of the sales center and individual customer also. Then we identify feasible routes based on geographical location. Then we try to attach customers with the route. Route wise demand forecasting was done to rationalize the model. Cumulative order frequency of each route was identified. The organization, we studied, was intended to maintain high standard of safety of the driver and the vehicle. They are also keen to maintain all the rules and regulations of the government. So, they have their own embargo on the daily duty hours of the drivers, their speed limit, rest period, rated vehicle capacity, etc. Considering all the factors, for generic approach, let there are in numbers of routes and n numbers of time periods (days). A single vehicle was considered to perform the whole distribution system ensuring all the embargo of safety and demand. An integer transportation model was considered to solve the problem. Time periods were plotted in the rows and Routes were plotted across the columns of the model. Two objective functions were formulated to solve the problem. First one was considering to minimize numbers of total trip of a time period. The constraint equations were formulated to represent total driving time of a day, total demand