Principal Investigators: Erhan Kutanoglu, Ph.D., U of Arkansas

1. Efficient Timing of Pickup and Delivery Assignment Decisions through Simulation and Optimization MBTC 2013 Principal Investigators: Erhan Kutanoglu, Ph.D., U of Arkansas G. Don Taylor, Ph.D., P.E., U of Louisville Research Assistants:Darsono Tjokroamidjojo, U of Arkansas Catherine McDowell, U of Louisville Industry Support: J.B. Hunt Transport

2. Background • Transportation Planning • Traditional tools • Focusing more on the assignment of drivers/trucks to loads as the loads are becoming available. • Proposed tools • Considering the timing aspect of when the the load assignment decision should be made.

3. Goals Of the Project • Allow dynamic planning • Determine the optimal timing for transportation planning (load assignment decisions) – how far ahead of a load pick up or delivery appointment should a planner make the load assignment decision? • Quantifying the trade off between early planning – increase driver satisfaction and other benefits; versus late planning – take advantage of last minute opportunities to achieve global optimum.

4. Methodology • Combined Optimization and Simulation • Optimization by the U of Arkansas researchers • Use an Integer Programming model to capture the tradeoff using AMPL/CPLEX • Simulation by the U of Louisville researchers • Using SIMNET simulation language to solve the problem by University of Louisville researchers.

5. Integer Programming Model • Sets : • I = set of trucks, indexed by i = 1,..,I. • J = set of loads, indexed by j and k = 1,..,J. • Parameters • AT(i,j) = 1, if truck i can fulfill load j, otherwise 0 • TT(j,k) = 1, if load k can be fulfilled immediately after load j by the same truck, 0 otherwise. • dep(j): departure location of load j. • dest(j): destination location of load j. • travel(j): travel time (or miles) of load j, from its departure location to its destination. • traveltime(l,m): travel time (or miles) between location/city l and location/city m.

6. Integer Programming Model • Parameters (cont’d) • truckloc(i): initial location/city of truck i at the beginning of planning horizon. • sch(k): if load k is already assigned to a truck and that decision is “frozen” • LKW: Load Knowledge Window – how far ahead you know the load • DTW: Decision Time Window– how far ahead you make the load assignment decision • Decision Variables • Zijk= 1 if truck i is assigned to load j then load k given AT[i,j] and TT[j,k] equal to 1; 0 otherwise. • Sj= 1 if load j is subcontracted to another company; 0 otherwise.

7. Integer Programming Model • Objective Function • Empty miles are due to assigning loads to own trucks and assigning loads by subcontracting

8. Integer Programming Model • Constraints: • For any loads not previously scheduled, it will be assigned to own trucks or by subcontracting • For any loads previously scheduled, it will be assigned to own trucks

9. Integer Programming Model • Constraints: • For all trucks, it has a first load or none at all • For any truck serving load j then load k, load j has to be either the first load or has to be served after some load q

10. Average objective function (total cost) values for dynamic models with denoted LKW, DTW values

11. Average percentage deviations of the total cost value from the best value

12. Simulation Model • Comprehensive load timing model built in the SIMNET language • Separate model built to generate data with specific experimental characteristics • Both models validated by J.B. Hunt Transport, Inc. • Multi-factor experiments currently being performed

13. Primary Experimental Design Full Factorial Design • Length of ‘visible’ time window for new loads (how far in advance of pickup do we learn of loads?) • Are intermodal and truck fleets operated together or separately? • Load distribution (urban & concentrated versus rural & dispersed) • Size of service area

14. Secondary Experimental Design 2k Design • Various cost parameters • Load interarrival time (load density) • Load truncation time (when loads turn into high priority loads) • Driver truncation time (when making a driver assignment becomes a high priority) • Probability of a bad estimated time of arrival

15. Conclusions • The IP results find that knowing loads in advance and making load assignment until the last minute is the most desirable scenario • With the same LKW, the smaller the DTW, the better the result: • an example: Obj[5,1] < Obj[5,3] < Obj[5,5] • With the same DTW, the larger the LKW, the better the result: • an example: Obj[5,1] < Obj[3,1] < Obj[1,1] • Simulation results to be examined pending final runs