1. A university within a business school 1 Integrating Resource Planning with Job Scheduling for Service Optimization Gang Li Bentley University Waltham, MA Joint work with Anant Balakrishnan University of Texas Austin, TX Brian Roth BNSF Railway Fort Worth, TX

2. Service Optimization Outline 1.Motivation 2.Modeling the problem 3.Solving the problem effectively 4.Application 5.Conclusion 2 Introduction | Motivation | Modeling | Solving | Application | Conclusion

3. 3 Motivation: Design Efficient and Effective Railway Track Maintenance Process Introduction | Motivation | Modeling | Solving | Application | Conclusion

4. 4 Motivation: Track Maintenance Rail transportation in USA 140,810 route miles (Compare to: Interstate Highway System, 47,000 miles) 7 Class I railroads $52.2 billion in revenue $6.8 billion (13% of revenue) on maintenance of railway Importance of track maintenance: increase productivity while ensuring safe railroad operations Major US railroads (e.g., BNSF, CSX, UP) each spent over $1 billion per year on maintenance Introduction | Motivation | Modeling | Solving | Application | Conclusion

5. 5 Track Maintenance Jobs Different Job Types RP: Rail Placement TP: Tie Placement UC (Under-Cutting): Ballast repl. Introduction | Motivation | Modeling | Solving | Application | Conclusion Thousands of Jobs Location Duration Time Window Service Requirements: Timing Coordinated Jobs Concurrence: Performance multi-jobs simultaneously. E.g., replace rail and ties at the same time Precedence: Perform one job before another. E.g., replace ties before replacing ballast Non-concurrence: Perform only one job at one time. E.g., perform jobs on the same corridor at different times

6. 6 Track Maintenance Resources Resources: Maintenance crews and equipment. (A typical Class I railway company hires about 5,000 maintenance workers) Different Types System vs. Local crews Cost o Selection cost. E.g., Overhead costs, bonuses of crews and costs of maintenance equipment. o Assignment cost: E.g., Payments to crew members to travel home on the weekends. o Routing cost: E.g., Costs for repositioning the equipment from one job site to the next job site. Introduction | Motivation | Modeling | Solving | Application | Conclusion

7. 7 Track Maintenance Planning Problem Decisions Selection: How many crews of each type (e.g., system vs. local crews) to employ? Assignment: Which crew to assign to which job? Scheduling/Routing:  When to start each job?  How to route each crew among assigned jobs? Constraints Perform each job within its time window Satisfy all inter-job timing coordination requirements Objective Minimize total selection, assignment, and routing costs Introduction | Motivation | Modeling | Solving | Application | Conclusion

8. Related Problems Vehicle Routing Problem with Time Windows (VRPTW) Vehicle Routing Problem with Time Windows (VRPTW) Desrosiers et al. 1995 Cordeau et al. 2001 Braysy and Gendreau 2005 Parallel Machine Scheduling with Time Windows (PMSTW) Parallel Machine Scheduling with Time Windows (PMSTW) Cheng and Sin 1990 Rojanasoonthon and Bard 2005 Resource-constrained Project Scheduling with Time Windows (RPSTW) Resource-constrained Project Scheduling with Time Windows (RPSTW) Dorndorf 2002 Neumann et al. 2002 Herroelen 2005 8 Introduction | Motivation | Modeling | Solving | Application | Conclusion

9. 9 Comparison with Classical Optimization Problems Features Vehicle Routing Machine Sched. Project Sched. Our Problem ObjectiveMin. routing cost Min. assign. cost Min. assign. Cost Min. selection, assignment, + routing cost Resource SelectionGiven Decision Variable Multiple Resource Types? No Yes Resource Routing?YesNo Yes Job Duration?NoYes Timing Coordination? No PrecedencePrecedence / Concurrence / Non-concurrence Introduction | Motivation | Modeling | Solving | Application | Conclusion

10. Modeling Method: Sequential vs. Integrated Loss of Feasibility: Decisions in previous stages may be infeasible for following stages. Loss of Optimality: Only consider a single objective each stage. 10 Introduction | Motivation | Modeling | Solving | Application | Conclusion Resource Selection based on aggregated demand Resource-Job Assignment Job Scheduling / Resource Routing Sequential Decisions Resource Selection Resource-Job Assignment Job Scheduling / Resource Routing Integrated Decisions Difficult to model Difficult to solve Strategic Tactic Operational

11. 11 Modeling Sets J Set of jobs R Set of resource types L Set of locations: job terminals or transshipment points T Set of time periods (Assumption: discrete time) Decision Variables: Integer or Binary Y rlt Selection variable: Resource r enters the network at location l in period t X rjt Assignment variable: Resource r starts job j in period t W rll’t Routing variable: Resource r routes from location l to l' in period t (Assumption: zero repositioning time) Z rlt Termination variable: Resource r leaves the network from location l in period t Introduction | Motivation | Modeling | Solving | Application | Conclusion

12. 12 Formulation Objective: subject to: Flow Conservation : Incoming flow = outgoing flow at each node of time- space network. Job Assignment : Each job must be performed once. Timing Coordination (next slide) Non-negativity, integrality  r  R, l  L, t  T  j  J j  J Selection costRouting costAssignment cost Introduction | Motivation | Modeling | Solving | Application | Conclusion

13. 13 Modeling Timing Coordination Requirements for all  JCC, t  T Concurrence T j j' j must start before j' starts and finish after j' finishes t for all  JNC, t  T Non-Concurrence T j j' Working times of job pair ( j, j ') must not overlap t for all  JPC, t  T Precedence T j j' t j must start before j' starts and finish before j' finishes (d j’ < d j ) (d j’ > d j ) Introduction | Motivation | Modeling | Solving | Application | Conclusion

14. Introduction: Solving Integer Programming Model A general solution procedure (for minimization prob.) Upper Bound: Apply a heuristic method to find a feasible solution, which provides a upper bound to the decision problem. Lower Bound: If relaxing integer requirements, the relaxed Linear Programming (LP) model can be efficiently solved, whose solution provides a lower bound to the decision problem. Gap: Keep improving both the lower bound and the upper bounds until the percentage difference between the two bounds, (defined as the gap), reaches to zero. We then ensure the optimal solution. This framework has been implemented in many commercial optimization software, such as CPLEX. 14 Introduction | Motivation | Modeling | Solving | Application | Conclusion

15. Difficulty in Solving the Problem 15 A medium-size instance 3 projects,200 jobs; 9 job locations 20 resource types; 50 time periods; 200 timing coordination requirements After 24 hours, the best CPLEX solution has a gap of 25%; after one week, the best solution has a gap of 10%. Questions:  Why is the LP bound weak?  Why is the solution process slow? Introduction | Motivation | Modeling | Solving | Application | Conclusion

16. Why is the LP Bound Weak? Objective: Cost-driven  Selection cost Selection cost  Assignment cost Assignment cost  Routing cost Routing cost 16 Constraint: Timing coordination constraint  Precedence Precedence  Concurrence Concurrence  Non-concurrence Non-concurrence Reasons that contribute to a weak LP solution Methods to strengthen LP Reformulate the timing coordination constraints Develop strong inequalities to prevent fractional solutions Introduction | Motivation | Modeling | Solving | Application | Conclusion

17. Model Enhancement: Improve the LP Bound Enhanced timing coordination constraints Enhanced precedence inequality Enhanced concurrence inequality Enhanced non-concurrence inequality Minimum resource inequality Ensure minimum number of resources at minimum workload Residual capacity inequality Ensure minimum number of resources at maximum workload Incompatible flow inequality Prevent incompatible flows coexistent in a solution 17 Introduction | Motivation | Modeling | Solving | Application | Conclusion

18. 18 Speeding up the Solution Process Preprocessing stage: Reduce size of the model Preprocessing stage Combine (aggregate) jobs Reduce size of repositioning network Reduce job time windows, eliminate variables and constraints Progressive solution strategy: Solve a series of simpler problems Progressive solution strategy Each problem is an extension of previous problem Optimal solution of previous problem provides a feasible initial solution and strong lower bound for the succeeding problem Cutting plane method: Dynamically add strong inequalities to the model Cutting plane method Customized branch-and-bound rule Tuned computational parameters of CPLEX Introduction | Motivation | Modeling | Solving | Application | Conclusion

19. Performance of the Solution Strategy 19 Using CPLEX’s default solution strategy 24 hours result Using our solution strategy (Optimization Stopping Criterion of: 1% gap) 5 hours result Introduction | Motivation | Modeling | Solving | Application | Conclusion

20. 20 Effective Solution Strategy Effectiveness of model enhancements (strong inequalities) Increase in LP bound (at the root node):  Enhanced Timing Coordination Inequalities: 0.5%  Minimum Resource Inequalities: + 5%  Residual Capacity Inequalities: + 2.5%  Incompatible Flow Inequalities: + 1% Progressive solution strategy Solved 4 sub-problems for each instance Found good feasible solutions, with gaps lower than 5%, within 5 hours for each instance Introduction | Motivation | Modeling | Solving | Application | Conclusion

21. 21 Application: Track Maintenance Planning Application to BNSF Railway  Largest railway network in North America  Owns and operates track in 27 U.S. states and 2 Canadian provinces  Route Miles: 50,000+  Number of Employees: 40,000  Average Freight Cars on System: 220,000 Track maintenance planning  5 job types  3,000 maintenance jobs  5,000 timing coordination constraints  10,000 physical stations  20,000 routing arcs  80 crew types  1 year planning horizon Introduction | Motivation | Modeling | Solving | Application | Conclusion

22. 22 Application: Track Maintenance Planning Application to BNSF Railway  Largest railway network in North America  Owns and operates track in 27 U.S. states and 2 Canadian provinces  Route Miles: 50,000+  Number of Employees: 40,000  Average Freight Cars on System: 220,000 Track maintenance planning  5 job types  3,000 maintenance jobs  5,000 timing coordination constraints  10,000 physical stations  20,000 routing arcs  80 crew types  1 year planning horizon Introduction | Motivation | Modeling | Solving | Application | Conclusion

23. 23 Assign the right people to the right place at the right time: BNSF’s Track Maintenance Problem Each year, the company needs to execute more than 3000 maintenance jobs to ensure its service quality. The company needs to hire about 5000 workers to form hundreds project teams to complete these jobs Introduction | Motivation | Modeling | Solving | Application | Conclusion

24. 24 Example of Optimized New Maintenance Plan Introduction | Motivation | Modeling | Solving | Application | Conclusion The New Maintenance Plan chooses dozens of best-fitted teams from hundreds of candidate teams assigns selected teams to jobs according to teams’ skills and costs determines a detailed work plan that satisfies all service requirements

25. 25  Manual Planning Process (Before 2005): Cumbersome and time- intensive o Find a feasible plan that satisfies all timing coordination requirements and time window requirements. Results: Lots of timing-coordination violations o Balance the three major cost components. Results: Only able to focus on a single cost component, e.g., the routing cost.  Large size of the model: 200,000 variables & 30,000 constraints  Resistance to change Solution: A slow but step-by-step implementation process o S1: Based on the manually selected no. of resources and job- resource assignment, determine the optimal job scheduling and resource routing. o S2: Based on the manually selected no. of resources, determine the optimal resource assignment, job scheduling and resource routing. o S3: Provide an integrated solution, which minimizes the total resource selection, assignment and routing cost. Change from Manual Planning to Model-based Planning Introduction | Motivation | Modeling | Solving | Application | Conclusion

26. 26 Performance Improvement in Track Maintenance Lower maintenance costs: saves in average $ 5 million per year Better maintenance quality: reduces 50 timing- coordination violations in manual solution to 0 violation Faster scheduling: permits solving (or re-solving) the problem quickly for iterative planning Safer and more efficient Railway Operations Improved structure of the workforce (by rewarding more skillful crews) Improved safety status (through reduced accident rates) Improved transportation efficiency (through increased train velocity) Improved service quality (through increased in-time delivery rates) Introduction | Motivation | Modeling | Solving | Application | Conclusion

27. 27 Conclusion: Main Contributions Addressed a complex resource planning and job scheduling problem that is a combined capacity planning, resource assignment, and job scheduling problem. Modeled the problem on a general framework and developed strong inequalities and effective solution strategies to improve the computational performance. Successfully applied the proposed model and methods to annual railway track maintenance planning in a major railway company. Introduction | Motivation | Modeling | Solving | Application | Conclusion

28. 28 Comment or Suggestion? Thanks!