Vehicle Routing: Transforming the Problem. Richard Eglese Lancaster University Management School Lancaster, U.K.

Transcription

1 Vehicle Routing: Transforming the Problem Richard Eglese Lancaster University Management School Lancaster, U.K.

2 Transforming the Problem 1. Modelling the problem 2. Formulating the problem 3. Changing the problem 2

3 From Interfaces 1980 While all the academic investigation of this problem class has increased knowledge and scope of understanding of the problem, is it of any direct use? Based on my knowledge gained from theoretical study, detailed analysis of actual practice and attempted applications in a consulting environment, the answer is no! 3

4 A recent My company recently purchased a vehicle routing system the routes it planned made no logical sense to me whatsoever. This software was trialled for three days last month we got a record amount of failed deliveries. the software seemed to be routing my vehicles in a spirograph Do you believe routing software is a viable option for the industry? 4

5 Modelling the problem (1) Finding solutions to real-world problems involves understanding and taking account of issues that may be ignored in solving benchmark academic problems. Most real-world VRPs have additional constraints or considerations that are often not present in academic benchmark problems. 5

6 Modelling the problem (2) Temptation is to ignore inconvenient issues, but that can make results useless or even illegal. Routing installations tend to require a large degree of customization, as reflected in software prices, which often runs in the tens of thousands of dollars. OR/MS Today Survey February

7 Examples of modelling issues Vehicle issues Product issues Time issues Contract issues 7

8 Problem of axle weight Unfortunately on more than one occasion our vehicles have been stopped either by the police or the vehicle inspector and found to be overweight either in total or on the front axle. We have asked our supplier of our vehicle routing and scheduling system whether they could modify their software to highlight a potential error. They have looked into this and been unable to offer a satisfactory solution. Operations Director, Timber Merchants 8

9 Vehicle leaving depot 1.5 TONNES (X2) 1.5 TONNES (X2) 1.5 TONNES (X2) 1.5 TONNES (X2) PAYLOAD 3.5 TONNES 15 TONNES (TOTAL 17.5 TONNES) ACTUAL 2.8 TONNES 9.2 TONNES (TOTAL 12 TONNES)

10 Vehicle after first delivery 1.5 TONNES (X2) 1.5 TONNES (X2) LOAD TAKEN OFF ON ROUTE FROM REAR OF VEHICLE PAYLOAD 3.5 TONNES 15 TONNES (TOTAL 17.5 TONNES) ACTUAL 4 TONNES 2 TONNES (TOTAL 6 TONNES)

11 Problem of volume Our routing and scheduling system occasionally generates a trip with more product than our vehicles could carry we need to manually check each trip for this error Transport Manager, White goods wholesaler UK 11

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13 Product restrictions on loading Types of supermarket products: Frozen Produce and Perishable Grocery 13

14 Loading restrictions FROZEN PRODUCE & PERISHABLE GROCERY

15 Time Window Constraints Hard or soft? Supermarket example Electrical wholesaler example Connection with solution method 15

16 Payment contract Some contracts with third party logistics providers only involve payment while vehicle is loaded No need for the vehicle to return to the depot Modelled using an Open VRP 16

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18 2. Formulating the problem Having decided what to model, how will the problem be formulated? Different formulations or representations of a problem can lead to different solution methods. How general should your method be? To what extent will you take advantage of problem specific features? 18

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21 OVRP for larger problems Needs a heuristic Tabu search with a modified neighbourhood structure Tail swap Added soft time windows Solving with soft time windows led to new best solutions for some benchmark problems with hard time windows 21

22 Disruption management How to replan after the original plan cannot be completed? Could be caused by traffic accident, order delay, service delay etc. Look at the case of a vehicle breakdown

23 Disruption Management in VRP Single vehicle breakdown

24 Breakdown management Type of VRP: CVRP Type of commodity: Single commodity Allow cancellation or delay? No Objective: Minimize total distance Assumptions 1 extra vehicle is available in the depot A vehicle cannot be diverted until it has visited its current destination. 24

25 Disruption Management in VRP Method 1 Insertion based on the original plan Tabu Search

26 Disruption Management in VRP Method 2 Insertion from scratch Tabu search

27 Formulation issue The Disruption Management problem with a broken down vehicle has the same structure as an Open VRP with fixed end points. This led to an alternative heuristic using a method based on the Open VRP. 27

28 Arc Routing Formulation issue: Should you work with the original network or transform it to a node routing problem? Advantage: Can use node routing methods Disadvantage: May have a larger problem and/or have to deal with additional constraints 28

29 29 3. Changing the problem

30 New issues and objectives New technology Vehicle telematics & dynamic VRP New data Information on road networks Information on flows and speeds at different times New objectives Green agenda Collecting waste for recycling Vehicle routing to avoid congestion 30

31 Using fuel more efficiently Those elements that influence fuel consumption are: Travel related factors such as speed and acceleration rates Road conditions such as congestion, inclines, bends, roundabouts and traffic lights Vehicle characteristics such as engine size, fuel type, payload and age 31

32 32 For example

33 Current Journey Time Calculations Problems: our (routing and scheduling) system cannot be relied upon to provide accurate results so significant manual adjustments need to be undertaken before we finalise our routes for the next day Time windows are missed Legal driving constraints stretched Using resources inefficiently 33

34 Data Sources UK s leading provider of traffic information and vehicle security services Largest commercial application of FVD TM Real road speeds time matched and day matched 96 (15 minute) time bins 8 days worth information 34

35 Rationale for a Road Timetable On one section of motorway in the North of England the same commercial vehicle speeds varied in one week from 5 mph (at on the Monday) to 55 mph (at on the Wednesday). When the recorded speeds were compared over a ten week period the variation in speed recorded for the same time of day and day of the week was less than 5%. 35

36 The LANTIME scheduler Given a set of customers and associated demands, central depot, vehicle fleet Objective: Min total time Constraints: Vehicle capacity (weight and space) Delivery time windows Driving time for each route Using time-dependent data requires significant changes to the vehicle routing algorithms 36

37 Tabu search algorithm 37 Uses best solution in selected neighbourhood Standard tabu list, aspiration criterion Long term memory based on penalising customers who have often been included in moves Accepts time-infeasible solutions, but penalises them to attain full feasibility in final solution

38 Case Study Electrical Wholesale Distribution in the South West of England Type of vehicle - all 3.5 tonne GVW box vans. No restrictions on any roads. Weight/Cube - No restrictions Time Windows - none Time constraint one shift per day 38

39 39 SOUTH WEST PROPOSED DELIVERY AREAS

40 ITIS Data information Data based on information aggregated into 15-minute time bins for a 3-month period covering February to April An average speed per time bin is used to construct the relevant Road Timetables. 40

41 Sample Comparisons For ten-hour shifts including legal breaks for drive time and work time. Depot based at Avonmouth Up to 7 vehicle routes required No. customers varies between 40 and 67 per day over 13 days. 41

42 Vehicle Routes on one day 42 Uncongested routes LANTIME routes

43 Sample solution for one day Total Vehicle time A A using uncongested speeds 43

44 Sample solution for one day Total Vehicle time A B A using uncongested speeds B using routes from A with actual speeds 44

45 Sample solution for one day Total Vehicle time A B C A using uncongested speeds B using routes from A with actual speeds C using LANTIME with actual speeds 45

46 Vehicle Routes for that day 46 Uncongested routes LANTIME routes

47 Future Work Modifying for least polluting rather than least time Harder with time-varying speeds because on each link we may need to travel faster or slower than the optimal speed to avoid being caught in congestion later. 47

48 Conclusion My hope is that current research will lead to transforming problems into solutions that can make a difference in practice now and in the future. 48

49 49 Questions?

50 References (1) C L Doll (1980) Quick and Dirty Vehicle Routing Procedure. Interfaces. 10, No. 1, R Hall and J Partyka (2008) Vehicle Routing Software Survey: On the Road to Mobility. OR/MS Today February Alan Slater (2005) Monograph on Vehicle Routing and Scheduling, Added Value Logistics Consulting. RW Eglese, A Mercer, and B Sohrabi (2005) The grocery superstore vehicle scheduling problem. J Opl Res. Soc. 56, AN Letchford, J Lysgaard and RW Eglese (2007) A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem. Journal of the Operational Research Society, 58(12), pp Z Fu, R Eglese and LYO Li (2005) A new tabu search heuristic for the open vehicle routing problem. J. Opl Res. Soc. 56(3), pp Corrigendum (2006) J. Opl Res. Soc. 57, p

51 References (2) Z Fu, LYO Li and R Eglese (2008) An improved tabu search heuristic for the open vehicle routing problem with soft time windows. Working Paper. Q Mu, Z Fu and R Eglese (2008) Disruption management of the vehicle routing problem with vehicle breakdown. Working Paper. RW Eglese, W Maden and A Slater (2006) A Road Timetable TM to aid vehicle routing and scheduling. Computers & OR., 33, pp W Maden, R Eglese and D Black (2008) Vehicle routing and scheduling with time varying data. Working Paper. 51