Load Planning for Less-than-truckload Carriers. Martin Savelsbergh

Transcription

1 Load Planning for Less-than-truckload Carriers Martin Savelsbergh Centre for Optimal Planning and Operations School of Mathematical and Physical Sciences University of Newcastle Optimisation in Industry, June 7, 2013

2 Joint work with Alan Erera Michael Hewitt Mike Zhang 2/58

3 Outline Less-than-truck Load Transportation Static Load Planning Dynamic Load Planning 3/58

4 Less-than-truckload Transportation What does an LTL carrier do? Transports shipments from origins to destinations Shipments are small; do not fill a whole trailer ( less-than-truckload ) Shipments have a service standard (in terms of business days) Consolidates shipments to reduce costs Consolidation occurs at 2 terminal types End-of-Lines (EOL - "Spoke") Breakbulks (BB - "Hub") Cross-docking of shipments occurs at breakbulks Incurs handling cost Requires time from 30 minutes to a few hours Runs high-volume operations Each week, a large carrier: Moves shipments weighing hundreds of millions of pounds between tens of thousands of (o,d) pairs Hauls trailers millions of miles Spends millions of dollars on linehaul operations 4/58

5 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay 58 destination 5/58

6 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination 6/58

7 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination 7/58

8 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination 8/58

9 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination 9/58

10 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination 10/58

11 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination handling 11/58

12 Less-than-truckload Transportation origin Customer End-of-Line Breakbulk / Relay destination changing drivers 12/58

13 Load Planning: The Challenge A super-regional less-than-truckload carrier wants to reduce its linehaul costs to become more competitive and to increase profits. Therefore, they need to route freight through the linehaul network so as to minimise handling and transportation costs. 13/58

14 Part I: Improving Static Load Planning for Less-Than-Truckload Carriers 14/58

15 Less-than-truckload Transportation Load planning problem Given: Terminal locations & types Transportation & handling cost structure Origin, destination service standards Forecasted origin, destination freight volumes Determine: Origin, destination freight paths that meet the service standards and result in minimum linehaul operating cost 15/58

16 Less-than-truckload Transportation Load planning: Find consolidation opportunities #trailers (freight volume) 16/58

17 Less-than-truckload Transportation Load planning: Find consolidation opportunities Result: reduction in trailer miles 17/58

18 Less-than-truckload Transportation Freight moves on Paths of Directs Definitions Freight paths and directs A freight path is a sequence of direct trailer moves (directs) A direct specifies where handling (loading and unloading) occurs Each direct consists of one or more dispatches along physical networks arcs Direct: ATH-COL Physical path: ATH-ATL-CIN-COL 18/58

19 Load Planning Goal: Determine a nominal, pre-determined freight path for each shipment, minimizing system-wide linehaul costs Traditional Load Plan: Given: Current terminal of a shipment, say i Destination terminal of a shipment, say d Specify: Outbound direct (i,j) for shipment Thus, set of all freight paths to destination d form a directed intree Triples (i, d, j) for all i, d define load plan Observations: The load plan does not distinguish between days of the week The load plan does not specify how to reposition empty trailers 19/58

20 Improving Load Planning Requirements Optimisation models must produce loadplans that are practically useful Explicitly model freight path timing to accurately capture consolidation dynamics Integrate planning of loaded and empty trailers Optimisation models should be able to produce more flexible loadplans Traditional: (i, d, j) Day-differentiated: (i, d, wd, j) 20/58

21 Load Planning Requirements Why must we explicitly model freight path timing? Typical Service Levels 21/58

22 Load Planning Requirements Why must we integrate empty trailer repositioning? An Example Consider a current load plan that sends: 10 loaded trailers daily from Atlanta to Birmingham 3 loaded trailers daily from Birmingham to Atlanta When optimizing loaded movements only, sending a small amount of additional freight (say 0.2 trailers) from Birmingham to Atlanta seems like a bad idea But, actually this freight moves essentially for free by filling otherwise empty space And, we may get cost savings for moving other Atlanta-bound freight through Birmingham 22/58

23 Modeling Time-Space Network Node: Terminal and time Arc: Potential loaded dispatch or holding of loaded trailer, or potential empty dispatch or holding of empty trailer Commodity: Freight demand Origin, destination: (o, d) Ready time at origin, due time at destination Volume of freight Horizon: Single wrapped week 23/58

24 Modeling Time Discretization Tradeoff : The more time points, the more realistic the model of the execution of a load plan, but the harder the optimisation problem becomes Assumption: freight enters the system at 7 p.m. and exits at 8 a.m. At EOL: no freight transfers time points only for 7 p.m. and 8 a.m. At BB: freight typically handled at night time points for 1am, 3am, 5am, 8am, 2pm, 7pm, 9pm and 11pm 24/58

25 Modeling Timed Freight Paths For each commodity: A set of time-space paths connecting origin at ready time to destination at due time, where each path consists of a set of direct dispatches and optional holding 25/58

26 Modeling Time-space network with overnight time detail 26/58

27 Modeling Time-space network with overnight time detail 27/58

28 Optimisation Path-based integer program (IP) with side constraints Objective: Minimize sum of Transportation costs (linear in integer trailer variables) Handling costs (linear in integer path variables) Constraints: Select one path for each commodity Ensure that a single outbound direct is selected from each terminal i for freight destined to d [or one direct for each i, wd] Only allow selection of paths if all component directs are selected Count required trailers for each direct Ensure trailer count balance at all nodes (empty repositioning) 28/58

29 Optimisation Path Generation Trade-off: Solution Quality vs. Solution Time Two-Phase Approach: Phase I: Generate paths of direct moves (flat network) Existing path (current load plan) N shortest alternative paths Phase II: Generate timed variants of each path Focus on small set of timed variants that maximize consolidation opportunities 29/58

30 Optimisation 7pm 7pm 8am BB BB BB BB cut time cut time cut time Consolidate freight with same destination Consolidate freight with different destination 30/58

31 Optimisation Linehaul network characteristics (of industry partner): 60 transfer terminals (break-bulk terminals and smaller transfer points) 100 end-of-line terminals 60,000 origin-destination freight pairs Resulting time-space network: 5,000 nodes 550,000 arcs Resulting integer program: 1,000,000 integer variables 2,000,000 constraints TROUBLE!!! Cannot even be loaded into commercial integer programming solvers 31/58

32 Optimisation Integer Programming Based Local Search While search time has not exceeded limit do Select a destination Optimise freight flow into the selected destination 32/58

33 Optimisation Inbound IP smaller version of full IP Paths are fixed for the majority of commodities Path decision variables for all commodities with specific destination Choosing a destination Loop through destinations in non-decreasing order of inbound freight volume Solving an inbound IP Not necessarily to optimality Short time limit (1 2 minutes) Accelerate via a priori addition of valid inequalities 33/58

34 Computational Results Traditional Load Plans Origin-destination freight volume for selected weeks Carrier's current load plan is used as an initial solution Solution time limited to 4 hours Results 1% represents about $50,000 per week 34/58

35 Computational Results Comparison 35/58

36 Computational Results Day-Differentiated Load Plans Origin-destination freight volume for selected weeks Carrier's current load plan is used as an initial solution Solution time limited to 4 hours Results 1% represents about $50,000 per week 36/58

37 Computational Results Analysis 37/58

38 Computational Results Integrating Empty Repositioning Matters Integrated Approach Sequential Approach Phase I: Don t enforce trailer balance Phase II: Restore trailer balance Results 38/58

39 Part II: Introducing Dynamic Load Planning for Less-Than-Truckload Carriers 39/58

40 Dynamic Load Planning Vision: Each day at a time when nearly all freight has been picked up by a pickup & delivery tour, adjust the load plan for the next 24 hours so as to reduce linehaul handling and transportation costs Goal: Adjust load plan in a few minutes Enabling technology: Hand-held scanners at pick up points of shipments allow accurate forecasts of freight picked up during the day Global positioning and mobile two-way communication devices allow tracking of in-transit freight Cross-dock automation allows instantaneous (re-)directing of arriving shipments 40/58

41 Dynamic Load Planning Each day at a time when nearly all freight has been picked up by a pickup & delivery tour adjust the load plan for the next 24 hours Dynamic Load Planning Optimisation Given: Nominal load plan In-transit freight and open trailers Freight volume projections for today, tomorrow Determine: Freight paths from origins to destination to be used for the next 24 hours 41/58

42 Dynamic Load Planning Planning horizon: Incorporate decisions for all overnight and 2-day freight Represents 83% of the total freight Plan for 38 hours, until the time 2-day freight is due at destination 42/58

43 Dynamic Load Planning Modeling freight paths: Avoid minimizing today s cost by jeopardizing tomorrows costs Freight must exit planning horizon at the same location it would have if following original load plan path load plan path potential path planning horizon 43/58

44 Dynamic Load Planning Path Generation: Consider a limited number of new path options, all of which adjust the nominal load plan Path options Skip direct Drop direct Alternate outbound loading at freight origin at origin breakbulk Milk run Outbound Inbound 44/58

45 Dynamic Load Planning Skip direct D B C A original load plan path potential path 45/58

46 Dynamic Load Planning Add direct D B C A original load plan path potential path 46/58

47 Dynamic Load Planning Alternate outbound at freight origin B C A F D E original load plan path potential path 47/58

48 Dynamic Load Planning Alternate outbound at origin breakbulk C A B E D original load plan path potential path 48/58

49 Dynamic Load Planning Milk run - outbound A O B original load plan path potential path 49/58

50 Dynamic Load Planning Milk run - inbound A O B original load plan path potential path 50/58

51 Dynamic Load Planning Integrating Empty Repositioning Recall: Carriers have backhaul lanes, i.e., lanes where empty trailers are likely to flow due to demand imbalances regardless of the load plan Ignoring backhaul lanes when routing freight may produce unrealistic plans Adjustment: Reject any path options that shift freight away from a backhaul lane 51/58

52 Dynamic Load Planning Time Zone Challenges: Pacific Mountain Central Eastern originating freight information may not be available decision time 52/58

53 Dynamic Load Planning Time Zone Implications: Run DLP several times every night, e.g., 6pm EST & 6pm MT, with then-current projection of originating freight in later time zones 53/58

54 Dynamic Load Planning Computation time IP-based Local Search 54/58

55 Solution Approach Greedy construction heuristic: Sequentially select paths for commodities: Process commodities in non-decreasing order of slack time Select minimum marginal cost path for a commodity Marginal cost of commodity c on arc a: Randomized greedy construction heuristic: Select k th commodity (in terms of slack time) with probability λ(1- λ) k-1 55/58

56 Solution Approach Greedy improvement heuristic: Sequentially replace paths for commodities: Process commodities in non-decreasing order of slack time Select minimum marginal cost path for a commodity Marginal cost of commodity c on arc a: Randomized greedy improvement heuristic: Select k th commodity (in terms of slack time) with probability λ(1- λ) k-1 56/58

57 Computational Results Computational Results (1 week) 57/58

58 Business Value Benefits: Increased insight into the characteristics/properties of costeffective loadplans. The ability to easily construct loadplans for different situations (first week of the month, last week of the month, two weeks before Christmas, etc.) An understanding of the potential benefits of daydifferentiated loadplans An understanding of the potential benefits of daily-adjusted loadplans Reduced linehaul operating costs 58/58