Arc-based formulations for coordinated drayage problems Christopher Neuman Karen Smilowitz Athanasios Ziliaskopoulos INFORMS San Jose November 18, 2002

Outline Drayage and the problems in Chicago Previous academic work A new formulation Results Future directions

What is drayage? OED definition: originally a handcart; drayage – process of draying. Now, the transportation of rail freight by truck, usually occurring at the beginning or end of the journey While a small (~5%) proportion of the distance of an average container, is usually a large (~40%) proportion of the cost (Reebie Associates)

The Chicago story A hub for rail freight transportation, and a major origin and terminus for freight (large manufacturing industry) 26 rail yards in/around Chicago; many are landlocked (no brown/greenfield alternatives) so no expansion Estimated 25,000 lifts (transfers on/off a train) per day

Problems with drayage No coordination of cars based on area origin/destination Lack of uniform equipment Fee structure penalizes agents Train schedules/takedown times vary City concerns: pollution, congestion, road damage, safety

Trip type – Drop and Pick Depot RY 1RY 2 ShipperConsignee

Trip type – Stay With Depot RY 1RY 2 ShipperConsignee CY 1 CY 2

Previous work in drayage Morlok and Spasovic (1990), Hallowell (1989): drayage problems might be improved using OR tools Arc-based IP formulation Multi-day model Movement of tractors and containers separately GAMS implementation Optimality through two-phase method

A new formulation for the drayage problem Aggregating customers limits usefulness to drayage companies Time windows for each customer, deadline and release times for containers Variables represent truck movement; container movement inherent in network structure One-day model, discretized time

Network: few nodes … S C S C RY CY

… many (feasible) arcs S RY Time window: 6-18 Deadline: 15 Arcs have four indices {i,j,r,s}: (i,j) origin and destination r: time truck leaves i s: time truck can leave j TT: 3 units, dwell: 1 unit {S,RY,6,10} … {S,RY,6,15} {S,RY,7,11} … {S,RY,7,15} {S,RY,11,15} This shows loaded arc set only; depending on (i,j) combination, may have empty and bobtail arc sets, defined if time windows are feasible

Formulation Objective: Minimize total distance traveled Distance (and travel time) can be adjusted for time- variant congestion, construction Constraints: All loaded movements must be served, and empties provided; Flow-balance constraints on each node Time-slice constraints

Results CPLEX 8, Multiprocessor Machine with 1GB RAM - computation time from 10 sec - 1 min #RY =  #Cust/3  ; #CY=  #Cust/5  ; TW ~ N(8,2) hours

Future Directions Increase problem size (# customers, RY, CY) Use real data, generate more realistic data Arc formulation as input to path-based formulation Incorporate more realistic trip types (DP empties) Allow penalized time window violations

Future Directions DSS for existing dispatchers 60% of a day’s trips known 3 days prior 90% known 1 day prior Dispatchers add non-model intelligence Dynamic replaces static New trip in existing sequence Variable or random dwell and travel times