Ajoneuvojen reititysoptimointi tutkimusaiheena ja käytännössä

1. Ajoneuvojen reititysoptimointi tutkimusaiheena ja käytännössä Olli Bräysy Faculty of Applied Economics Prinsstraat 13, B-2000 Antwerp

2. Transportation of goods in Finland (EU) • We use on the average 80 minutes for traveling every day • 16% of consumption expenditures of households are due to traffic costs • The logistics expenditures 14-15% wrt GDP and 10% wrt turnover • Transportation costs 44% of the total logistics costs • The largest amount of transportation per capita in Europe • 89% of all goods is transported by trucks • In EU 1/2 mill. companies, 13 million trucks and annual turnover € 150 billion • The road transportation will increase by 30% by 2020 • Many SMEs • A lot of empty driving O. Bräysy, 13/11/2003

3. The Vehicle Routing Problem Known demand, travel times Capacity restriction on vehicles O. Bräysy, 13/11/2003

4. The vehicle routing problem • Hence the vehicle routing problem can be defined as the problem of designing routes for delivery vehicles (of known capacities) which are to operate from a single depot to supply a set of customers with known locations and known demands for a certain commodity. Routes for the vehicles are designed to minimise some objective such as the total distance travelled. • This problem is one that has a long history of systematic study, the problem first being considered in an academic paper by Dantzig and Ramser published in the late 1950's. • The problem has attracted a lot of attention in the academic literature for two basic reasons: • the problem appears in a large number of practical situations; and • the problem is theoretically interesting and not at all easy to solve. O. Bräysy, 13/11/2003

5. How hard is the VRP? • NP-hard problem • Largest VRP instance solved has 135 customers • Smallest VRP instance unsolved has 50 customers • Largest TSP instance solved has 13 509 customers • VRP is the intersection of two difficult problems: • Traveling Salesman Problem (routing) • Bin Packing Problem (packing) • We don’t have an effective polynomially sized relaxation • We know very little about the packing aspect O. Bräysy, 13/11/2003

6. Practical problem • The vehicle routing problem as encountered in practice involves many restrictions on the routes that delivery vehicles can follow (e.g. a limit on the number of hours that a driver can work) and we consider some of the more common restrictions below. We can classify these restrictions to a certain extent as relating either to the vehicles or to the customers. Note here that in any particular case not all of these restrictions may apply, however in thinking generically about the problem it is useful to list all restrictions that potentially can apply. O. Bräysy, 13/11/2003

7. Vehicle related restrictions • Each vehicle has a limit (capacity - usually weight and/or volume) on the goods carried, e.g. tankers delivering to petrol (gasoline) stations are volume limited, buses have a limit on the number of people legally allowed on board, etc. • Each vehicle has a total working time from departure to arrival back at the depot, typically to comply with legal restrictions on driver working hours. • Each vehicle has a time period within which it must leave the depot, typically to ensure that space is available for incoming vehicles to resupply the depot. • Each vehicle has a number of time periods during which it does nothing (driver rest periods). • Each vehicle has a cost associated with its use for deliveries. O. Bräysy, 13/11/2003

8. Customer related restrictions • Each customer has a certain quantity which has to be delivered (and/or collected), There are also operations involving a mix of collections and deliveries. Sometimes this quantity is known exactly (the deterministic case) and sometimes known with a degree of uncertainty (the stochastic case). • Each customer has a number of time periods during which delivery can occur (time windows). For example a customer might be prepared only to accept delivery between 10.30-11.30 or between 14.00 and 16.15. • Each customer has a set of vehicles which cannot be used for delivery (access restrictions). • Each customer has a priority for delivery (if the vehicles cannot deliver to all the customers). Typically this might happen due to driver/vehicle unavailability or due to poor weather conditions dramatically reducing vehicle speeds O. Bräysy, 13/11/2003

9. Other factors • Multiple trips by the same vehicle on a single day, where the vehicle returns to the depot and then goes out again (e.g. post office vans) • Trips by the same vehicle longer than one day (i.e. with overnight stops). • Compartmentalised vehicles with many different types of product to deliver. Petrol (gasoline) tankers are often compartmentalised (for leaded/unleaded and diesel), as are food delivery vehicles (frozen/non-frozen). • More than one depot, where vehicles can start/visit/end at different depots. O. Bräysy, 13/11/2003

10. Industrial use of VRP Tools Swedish report* 1999 (commercial road transport) • Large end users, food & beverage • Generation of static routes • Vendors claim operational and dynamic tools • Very high potential for savings * A. Henriksson, P. Liljevik: ”Dynamisk ruttplanlegging i verkligheten” Minirapport MR 123, TFK - Institutet för transportforskning, Stockholm October 1999 Size of market for routing software? • 1986: 13 packages • 1997: 113 packages • # implementations grown • Cost savings increased O. Bräysy, 13/11/2003

11. Existing tools - keywords • Large variety: simple SPP, TSP, sophisticated VRP solvers • Focus: road transportation of goods, local distribution • Used for generation of static routes, built for operative planning • Packages, targeted at specific application areas • Primitive integration, but good import facilities • Inflexible and simple or heavy on consultancy • Windows-platform • Good user interfaces, map visualization, manual changes • Priced at USD 10.000 and above • Picture is changing, but • modern VRP algorithms? • real-time planning? • multiple users? • continuous optimization? O. Bräysy, 13/11/2003

12. Trends and Developments • GIS - electronic road and address data • Positioning and Communication Technology • GPS, Galileo, Mobile Internet, GPRS • Integration technologies • Software Components • Better VRP Methods • Faster Computers • More robustness, user confidence, less interaction • home shopping, e-logistics • .com death, slow IT market • Focus on ROI O. Bräysy, 13/11/2003

13. VRP Solver - Algorithms • Construction • Savings • Sweep • Nearest Insertion • Improvement, move operators • 2-opt, Or-opt • Relocate • Exchange • Cross • Metaheuristics • Tabu search • Evolutionary algorithms • SA, VNS, TA, MSLS, ILS, GRASP, GLS, GTS (SD, AGES, RVNS)… O. Bräysy, 13/11/2003

14. Insertion heuristic Insertion criteria e.g. additional distance, time, waiting time... O. Bräysy, 13/11/2003

15. Cross-opt O. Bräysy, 13/11/2003

16. Issues in VRP research • Rich models • type of service • type of network • uncertainty • dynamics • multiple criteria • Reactive and proactive planning • disruption • slack • policies • Large problem instances • Over-constrained problems • Plan quality vs. response time performance • Human and organizational issues O. Bräysy, 13/11/2003

17. Research Agenda: VRP • Cooperating VRP solvers, hybrid methods • Mapping problem type - algorithm • Decomposition • Control Architectures • Combining exact and heuristic methods • Multi-criteria problems O. Bräysy, 13/11/2003

18. Conclusions • VRP increasingly important • Gap between VRP research / technology / implementation • Design of routing software is hard • VRP methods only one aspect O. Bräysy, 13/11/2003