Integrating Resource Planning with Job Scheduling for Service Optimization

Integrating Resource Planning with Job Scheduling for Service Optimization Gang Li Bentley University Waltham, MA Joint work with Brian Roth BNSF Railway Fort Worth, TX Anant Balakrishnan University of Texas Austin, TX

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

Track Maintenance Jobs • Different Job Types • RP: Rail Placement • TP: Tie Placement • UC (Under-Cutting): Ballast repl. • 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 Introduction | Motivation | Modeling | Solving | Application | Conclusion

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 • Selection cost. E.g., Overhead costs, bonuses of crews and costs of maintenance equipment. • Assignment cost: E.g., Payments to crew members to travel home on the weekends. • Routing cost: E.g., Costs for repositioning the equipment from one job site to the next job site. Introduction | Motivation | Modeling | Solving | Application | Conclusion

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

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

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

Modeling Sets JSet of jobs RSet of resource types LSet of locations: job terminals or transshipment points TSet of time periods (Assumption: discrete time) Decision Variables: Integer or Binary Yrlt Selection variable: Resource renters the network at location l in period t Xrjt Assignment variable: Resource rstarts job j in period t Wrll’tRouting variable: Resource rroutes from location l to l' in period t(Assumption: zero repositioning time) Zrlt Termination variable: Resource rleaves the network from location l in period t Introduction | Motivation | Modeling | Solving | Application | Conclusion

Selection cost Routing cost Assignment cost 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 Introduction | Motivation | Modeling | Solving | Application | Conclusion

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

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. Introduction | Motivation | Modeling | Solving | Application | Conclusion

Difficulty in Solving the Problem 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%;afterone 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

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

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 Introduction | Motivation | Modeling | Solving | Application | Conclusion

Speeding up the Solution Process • Preprocessing stage: Reduce size of the model • 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 • 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 • Customized branch-and-bound rule • Tuned computational parameters of CPLEX Introduction | Motivation | Modeling | Solving | Application | Conclusion

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

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

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

Example of Optimized New Maintenance Plan • 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 Introduction | Motivation | Modeling | Solving | Application | Conclusion

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

Performance Improvement in Track Maintenance • 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) • Lower maintenance costs:saves in average $5million 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 Introduction | Motivation | Modeling | Solving | Application | Conclusion

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 appliedthe proposed model and methods to annual railway track maintenance planning in a major railway company. Introduction | Motivation | Modeling | Solving | Application | Conclusion

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Integrating Resource Planning with Job Scheduling for Service Optimization